Proxyeconomics, the inevitable corruption of proxy-based competition
PProxyeconomics, the inevitable corruption of proxy-basedcompetition
Oliver Braganza , Institute for Experimental Epileptology and Cognition Research, University of Bonn,Germany* [email protected]
Abstract
When society maintains a competitive system to promote an abstract goal, competitionby necessity relies on imperfect proxy measures. For instance profit is used to measurevalue to consumers, patient volumes to measure hospital performance, or the JournalImpact Factor to measure scientific value. Here we note that any proxy measure in acompetitive societal system becomes a target for the competitors, promoting corruptionof the measure . This suggests a general applicability of what is best known asCampbell’s or Goodhart’s Law. Indeed, prominent voices have argued that the scientificreproducibility crisis, the financial crisis of 2008, and inaction to the threat of globalwarming represent instances of such competition-induced corruption. Moreover,competing individuals often report that competitive pressures limit their ability to actaccording to the societal goal. This suggests some kind of lock-in , i.e. a powerfulmechanism locking the system into a certain subset of possible outcomes. However,despite the profound implications, we lack a coherent theory of such a process,potentially due to problems posed by traditional disciplinary boundaries. Here wepropose such a theory, formalized as an agent-based model, integrating insights fromcomplex systems theory, contest theory, behavioral economics and cultural evolutiontheory. The model reproduces empirically observed patterns and makes predictions atmultiple levels. It further suggests that any system is likely to converge towards anOctober 3, 2019 1/51 a r X i v : . [ phy s i c s . s o c - ph ] O c t quilibrium level of corruption determined by i) the information captured in the proxyand ii) the strength of an intrinsic incentive towards the societal goal. Overall, thetheory offers mechanistic insight to subjects as diverse as the scientific reproducibilitycrisis and the lack of an appropriate response to global warming. In complex societal systems, any competition to promote an abstract goal must bynecessity rely on proxy measures to rank agents with respect to their performance. Thissuggests the applicability of Campbell’s or Goodhart’s Law to any proxy-basedcompetition [1–3]:
Any proxy measure in a competitive societal system becomes a targetfor the competing individuals (or groups), promoting corruption of the measure . In otherwords, societal competition should be generally expected to create an informationaldifference between proxy measures and the societal goals they were designed to promote.Importantly, this should happen both by active behaviors (gaming) but also by a rangeof purely statistical mechanisms [4, 5].The societal system performs the dual task of collecting the information to createthe proxy measure(s) and creating the institutions that implement competition. Whilemodern societies increasingly rely on competitive systems and the proxy measures theyrequire, there are prominent arguments and compelling evidence suggesting corruptionof the measures (Table 1 [5–16]). Indeed, it is conceivable that a highly proxy-orientedsystem leads to substantial effort- and resource misallocation with detrimental effects onthe actual societal goal. Importantly, this would remain hidden as long as the proxypersisted as the central evaluative tool of system performance. We suggest the termproxy-economy for a highly proxy-oriented, or in Campbell’s terms “corrupted”, system.In such a system a large portion of activities and resources would be devoted toward theproxy measures without furthering the actual societal goal. For instance in academia, asubstantial fraction of non-reproducible research across scientific disciplines, as well assubjective researcher assesments, suggest an excessive proxy orientation [11]. Similarly,a strong case can be made that rich economies as a whole have become mostlyproxy-oriented [13, 14, 17–19]. Consider for instance, that subjective as well as objectivemeasures of well-being are logarithmically related to income (GDP) [20, 21]. In otherOctober 3, 2019 2/51ords, the relevant returns (societal goal) to economic growth (proxy) are exponentiallydiminishing. Indeed, among rich nations the beneficial effect of economic growth isdwarfed by other sources of variability, and quite challenging to even detectstatistically [18, 20]. At the same time, the material footprint of economic growth,including environmental externalities such as CO emissions, are linearly related toincome (GDP), implying that we are likely substantially underestimating negativewelfare consequences of economic growth.Beside such macro-level arguments, another rich source of supporting evidenceresults from critical examination of individual practices under competing accounts ofproxy- or goal-orientation provides [5, 10, 22, 23]. For instance, it has recently beenobserved, that scientific sample size choices can be readily explained by a competitiveeconomic (proxy-driven) account, but are difficult to reconcile with scientificdeliberations (goal-driven) [23]. Finally, it is important to point out that the mentionedexamples appear to display what might be called a lock-in effect, i.e. persistentcorruption despite widespread acknowledgement of the arising problems, combined withaccounts of limited agency. Understanding the nature and mechanism of such lock-in islikely to prove crucial to addressing phenomena ranging from the scientificreproducibility crisis to combating anthropogenic climate change. Table 1. Illustratory examples of goals, proxies, and corruption claims in proxy-based competititivesystems. Science Medicine Education Politics MarketsSocietalGoal true and rele-vant research patienthealth knowledge,skills voter repre-sentation subjectiveand objectivewell-being
ProxyMeasure publicationcount, im-pact factor patient num-bers, profit standardizedtest scores publicity,votes income,profit, GDP
CorruptionClaims reproducibilitycrisis[5, 8, 9, 12, 16] bad pa-tient care,overtreat-ment [15, 24] teaching tothe test [6, 7] populism,lobby-cracy [25, 26] financialcrises,global warm-ing [10,13,14]Any competitive societal system to achieve and abstract goal must rely on proxy measures. However, and proxy measurebecomes a target for the competing individuals (or groups). Campbell’s and Goodhart’s Laws state that this will promotecorruption of the measures. [1–3] Despite the similarity in the arguments in these diverse competitive systems, theextensive evidence, and the profound implications for societal welfare, we lack acoherent theory of the underlying processes. We believe this has two main reasons, oneOctober 3, 2019 3/51mpirical, one theoretical. A general empirical problem is posed by an inherentcomplexity/ambiguity gradient between proxy and goal. Specifically, the aspects of thesocietal goal which are most easily quantified are most likely to be captured in theproxy, biasing corruption toward whatever is difficult to quantify. Accordingly, much ofthe evidence suggesting a corruption of practices tends to be qualitative, voiced ininterviews, editorials and surveys [8, 11, 12, 27]. Additional goal aspects may be costly toassess or only become apparent in the long term. Such aspects can be quantified asalternative proxies and will remain unaffected by corruptive pressures as long as theyplay a minor role in competition. For instance scientific reproducibility, long term costsof excessive financial risk taking and environmental degradation play a minor role incompetition and thus provide a quantitative measure of corruption [10, 28]. Additionalpotential quantitative measures are specific readouts of corruption, such as retractioncounts [29] or small sample sizes [5]. The current revolution in data-science promises toprovide ample testing ground for the present theory [9]. However, due to the complexityof societal systems any individual study providing evidence in any of these domainsremains difficult to interpret in isolation.The second, theoretical, challenge to a cohesive theory of proxy-based competition isits necessarily trans-disciplinary nature. We identify three fundamental questions such atheory must address. These are traditionally treated in separate disciplines.Importantly, all three questions arise directly from the core problem of proxy-basedcompetition in societal systems (Table 1):1. What is the informational relation between proxy measures and the societal goalin the space of all possible practices/actions? (complex systems and controltheory; information economics)2. How do individual agents make decisions, given potentially conflicting informationand value dimensions? (multitasking theory; contest theory; behavioral/neuro-economics; behavioral ethics)3. How do inter-individual mechanisms such as selection/ cultural evolution affectthe system? (sociology; cultural evolution theory)We separate these questions for narrative convenience and conceptual clarity, thoughthey are complexly interrelated. While the first and third questions address primarilyOctober 3, 2019 4/51he system level the second question concerns psychological decision mechanisms. In thefollowing, we describe a simple agent-based computational model, constructed tointegrate and formalize confluent insights across these disciplines and feedback loopsbetween levels. The overall goal is to determine the principal components necessary tocapture the processes described above and explore possible formal specifications. In theprocess, we outline the tenets of a unified theory of what we will call
Proxyeconomics ,which applies to any proxy-based competitive system maintained by society to serve anabstract goal. Briefly, our model results suggest that any such system approaches arelatively stable equilibrium level of corruption determined by the information capturedin the proxy and the strength of a putative intrinsic incentive ’to do your job well’.Moreover, the dynamics of corruption, or corruptive pressure, is governed by theintensity of competition and potentially the complexity of practices. Additionally, at themeso-scale, we find a range of incompletely understood but consistently observed effortchoice patterns, described in the experimental contest literature [30]. For instance,effort-incentivization appears to be hill shaped with respect to competition, i.e. effort ishighest for intermediate, rather than very mild or very intense, competition. In thefollowing, we will first sequentially introduce and motivate the model components. Wewill then present detailed results on model behavior and robustness. Next, we willdiscuss these results including the model’s limits, wider implications and possibleextension. Finally, we will briefly discuss a number of additional implications of thetheory of proxy-based competition including several psychological, economic, politicaland moral aspects.
We developed the model in order to capture the following general notions, eachrepresenting convergent insights by the respective disciplines, in the most parsimoniousyet plausible way.1. The proxy can be viewed as the ‘objective function’ of an optimization problem ina complex adaptive system [4, 31, 32]. Therefore there will always be someinformational difference between proxy measures and societal goal (likelyproportional to the complexity of the societal system).October 3, 2019 5/51. Individuals are motivated not only by egoistic interests but also by an intrinsicmoral motivation. [10, 33–36]. Furthermore, in competition, a powerful desire to(professionally) survive suggests some form of (proxy-based) reference dependence,well captured by a sigmoidal utility function [37–41].3. Variability in culturally/professionally transmitted practices and selection throughcompetition introduces cultural evolution at the system level [5].Importantly, there will be interactions including feedback loops within and betweenindividual and system level. The information affecting individual decisions will dependon the information at the system level. The competition experienced by individualsrelates to the competitive selection at the system level. Finally, and most importantly,proxy performances affect outcomes primarily as a relative measure, i.e. by theirrelation to other agents’ proxy performances. This implies feedback loops for i)psychologically driven proxy performance, ii) selection driven proxy performance and iii)between the two processes. An agent-based modeling approach is ideally suited tocapture these notions including the feedback loops within and between levels.The model draws from information/control theory and economic principal-agenttheory by viewing a societal system as an information processing device or principal,respectively (see detailed model description and discussion [4, 42]). A neuroeconomicallyplausible (utility and reference based) effort incentivization mechanism [43] is modeledusing concepts from prospect theory and multitasking theory [10, 37, 38, 42].Simultaneously, the processes described by Campbell’s Law are modeled as a form ofcultural evolution, on a slower but overlapping timescale [5, 44]. The combination ofthese approaches allows us to investigate the tension between positive and negativeeffects of competition. Specifically two positive effects, namely effort incentivization andsignaling/screening of talent, cooccur with negative effects, namely incentives to gamethe system and selection of corrupt practices. The model furthermore provides a way toprobe the power of ‘intrinsic motivations’ to bound a long term evolution towardscorrupt practices, as recently suggested by Smaldino and McElreath [5].Briefly, we model a societal system, in which utility maximizing agents repeatedlycompete with each other based on individual proxy-performances. Individualperformances result from both the individual’s effort and the orientation of theirOctober 3, 2019 6/51ractice toward the proxy. The system is characterized by the following: The amount ofcorruptible proxy information, parametrized as the goal angle ( ga , competition ( c ),parametrized as the fraction of losers; cultural evolution, parametrized through apractice mutation amplitude ( m ) and selection pressure ( sp ). Intuitively, ga and m reflect the complexity of the societal system while c and sp respectively reflect thepsychologically experienced and realized intensity of competition. Individualutility-maximizing agents are characterized by talent ( t ) and a parameter determiningthe relative power of an intrinsic moral incentive toward the societal goal over theextrinsic competitive incentive ( gs ). Finally, the individual agent’s properties of effort( e ) and practice orientation ( θ ) represent the main outcomes of interest, informing on i)the emergent corruption and ii) the systems overall efficacy. In the following we willsequentially introduce our model specifications and parameters in the three buildingblocks mentioned above, beginning with a short section on competition and model timecourse. Competition is a central variable, which is likely to impact individual decisions as wellas system-level selection. For a given population, we define competition simply as thefraction of ‘losing’ agents c ∈ [0 , c = 0 .
9) an agent has to be in the top 10% ofproxy-performers to be a ‘winner’. This then affects both the psychological decisionmechanism and system-level selection as described below.The model proceeds in time steps, each of which is subdivided into a decision phaseand an evolution phase. In the decision phase all agents are drawn in random order toadjust their efforts to maximize utility given their individual properties ( θ, t . see below)and the currently observed competitive rank (of proxy performance). In the evolutionphase, losing proxy performers are subject to stochastic death, and are instantaneouslyOctober 3, 2019 7/51eplaced by offspring from winning proxy-performers, such that the population sizestays constant. Together, this models a competitive system in which agents make theirdecisions based on the observed proxy-performances of all other agents, but are unsureabout the exact time frame of competition, i.e. to which degree other agents might stillchange their proxy performance before a selection event might occur. The continuousrepeated comparisons, occurring in consecutive time steps resemble what has beencalled ‘multi-contest tournament’ [45].
We conceptualize the informational relation between proxy and goal with respect to thevalue-creation associated with specific cultural practices. A cultural practice is definedas a specific pattern of actions, that can be associated with potentially differing relativecontributions to the societal goal and the proxy (similar to e.g. [5, 10, 26] in the fields ofscience, politics and economics, respectively). In the main model the cultural practice ispredominantly learned and transmitted within a given cultural entity (laboratory,company, ...), but we later also explore outcomes if practices are subject to individualagency. Four fundamental groups of practices can be intuitively differentiated based onthe degree to which they are beneficial or detrimental to the proxy and goal value(Fig 1A). For instance, in any specific societal context, we may consider if practices existthat exclusively contribute to either the proxy measure or the societal goal. Theexistence of such practices motivates the dimensional reduction of the practice space totwo dimensions representing the proxy and the goal (as in economicmultitasking [10, 42]). The degree to which the proxy captures true and incorruptibleinformation ( i ) about the societal goal can then be represented as the angle between themain axes (goal angle; ga ∈ [0 ◦ , 180 ◦ ]), where information i ∈ [ − ,
1] is given by Eq. 1. i = cos ( ga ) (1)Intuitively, information measures the effect on the societal goal when practices areexclusively oriented towards the proxy. A good proxy (0 < i <
1) captures sufficientinformation about the societal goal, such that even fully corrupted practices producepositive outcomes for the actual societal goal (Fig 1B). In contrast, when full proxyOctober 3, 2019 8/51 roxy measure A s o c i e t a l g o a l proxy measure s o c i e t a l g o a l practices beneficial to goal beneficial to the proxypractices beneficial to the goaldetrimental to the proxypractices detrimental to the goaldetrimental to the proxy practices detrimental to the goalbeneficial to the proxy i = 0, ga = 90° g o a l ( o c ) ga ga i > 0, ga < 90° fully proxy oriented (=corrupted) practices still contribute to the actual societal goal BC g o a l ( o c ) ga proxy measure s o c i e t a l g o a l i < 0, ga > 90° full proxy oriented (=corrupted) practices adversly affect the actual societal goalfully proxy oriented (= corrupted) practices do not affect the actual societal goal Fig 1. The practice space,
Individual practices may contribute to different degreesto the proxy measure and the societal goal, motivating the mapping of all practices to atwo-dimensional practice space. Sections of the practice space which are beneficial/detrimental to the proxy/goal are color coded (see colored labels in A ). The degree towhich the proxy captures true and incorruptible information about the societal goal canthen be represented as the angle between the main axes, denoted goal angle ( ga ) withinformation ( i = cos ( ga )). Exclusively proxy oriented practices are located on thehorizontal axis (proxy measure). Accordingly, when such (corrupted) practices areneither beneficial nor detrimental to the societal goal, then ga = 90 ◦ and i = 0 (A) .Presumably, in most cases the proxy captures sufficient incorruptible information aboutthe goal such that even even fully proxy oriented practices contribute to the societalgoal (0 ◦ < ga < ◦ ; 1 > i > (B) . However, full proxy orientation may also lead tonegative outcomes for the actual societal goal (90 ◦ < ga < ◦ ; 0 > i > − (C) . When ga (cid:54) = 90 ◦ the goal component orthogonal to the proxy is labeled ‘goal (oc)’.orientation produces negative externalities which outweigh the beneficial effects for thesocietal goal, this is captured by − < i < ◦ < ga < ◦ (Fig 1C).Externalities beyond the dimensions described above, i.e. that are independent of bothproxy and goal (e.g. leisure time), are not considered in the current model. We reasonthat i and ga relate directly to the complexity of the system with i tending toward 0 and ga toward 90 ◦ as complexity and, with it, the number of failure modes increases [46]. We can most easily think of the proxy as a simple scalar metric, such as the journalimpact factor or quarterly profits. More generally, the proxy should be thought of as anarbitrarily complex regulatory model [47], embodied in the societal mechanismsdesigned to collect information and transform it into competitive rankings. ArbitrarilyOctober 3, 2019 9/51omplex, here, explicitly includes mechanisms relying on expert judgement [3], as longas the outcome is a competitive ranking. In analogy to the economic revealed preferenceapproach, we can think of the proxy as the set of attributes that factually determineselection within the competitive system (the revealed preference of thesystem/mechanism). In analogy to the machine learning and artificial intelligenceliterature, it is helpful to think of the proxy as an objective function [4]. In all theseanalogies, the societal system is conceptualized as an information processing device,collecting complex input information and converting it to an actionable output metric(competitive rankings). The boundary case of a perfect regulatory model maps to a goalangle of ga = 0 ◦ . The societal goal is the arbitrary consensus set of properties society wants toachieve/regulate (see examples in Table 1). Though this is difficult to precisely define inany specific context, it is important to bear in mind that such a consensus set is impliedby the fact that society maintains an artificial competitive system in the first place.Practical and information-theoretic considerations further help to predict the ways agoal is likely to differ from the proxy [4, 31, 47]. This can allow a relational or negativedefinition (e.g. a preponderance of irreproducible publications may not further thesocietal goal). Note that, in the present model, we define the societal goal as only thosegoal-aspects, which are privately known to individual agents. This definition of thesocietal goal may be most productive, since aspects of the goal unknown at theindividual and the institutional level may be particularly difficult to address. In thepresent model, individuals are assumed to have superior knowledge as to the preciseprofiles of their actions and their implications. Indeed, there are numerous reports ofindividuals in competitive systems who state that competition is impeding their abilityto act according to the societal goal. This directly implies private knowledge ofimplications for the goal which are not captured by the proxy (for instance see [10, 48]for examples from science and banking, respectively). Similarly, a substantial portion ofthe general population personally feels that their whole job (which is the result ofcompetitive market mechanisms) does not contribute to societal welfare in any way [49].October 3, 2019 10/51 .3 Individual choice - multitasking
The system-level definition of the practice space now allows us to intuitively capture thenotion of proxy-orientation of a given agent’s practices by their ‘practice angle’ ( θ ;Fig 2A-C). The agents effort level is assumed to be the length of a vector along thispractice angle and the true contributions to proxy and goal value are the projectionsonto the main axes. This captures a positive effort to output relation, where only thetype of output depends on practice orientation. To allow both, an intrinsic (goal) and acompetitive (proxy) incentive to elicit effort, we adapt an economic principal-agentmultitasking model (Fig 2A). Note that in contrast to traditional multitasking models,we here allow practice angles to be established either through individual choice, orthrough a process of cultural evolution (i.e at the system level). The practice angle ofan agent reflects the average outcome of all the different actions and choices she makesin an individual time step, i.e. it may include strategies such as cheating or sabotaginga fraction of the time, which would translate to a lower average θ .Accordingly, the effort of the i th agent e i ∈ R ≥ is modeled as the length of thevector with orientation θ i and the resulting proxy and goal values are the projectionsonto the main axes capturing the practice dependent trade-off (Eq 2,3). V gi ( θ i , e i ) = cos ( ga − θ i ) · e i (2) V pi ( θ i , e i ) = cos ( θ i ) · e i (3)The utility derived from the goal performance is simply the goal value multiplied bya constant ( gs ), determining the relative psychological strength of an intrinsic, moralincentive toward the societal goal (Eq 4). Given that goal in our settings refers toaspects known to agents, gs can be seen as a product of i) goal valuation and ii)individually available goal information. U gi ( V gi ) = gs · V gi (4)October 3, 2019 11/51 proxy measure g o a l ( o c ) e ff o r t θ s o c i e t a l g o a l a g e n t s p r o s p e c t survival thresholdrisk preference reversal a g e n t s p r o s p e c t survival thresholdrisk preference reversal proxy measure g o a l ( o c ) proxy value( V ip )goal value( V ig ) s o c i e t a l g o a l ga = 135°ga = 45°c = 0.5 c = 0.9 e ff o r t θ A proxy measure e ff o r t ( e i ) θ i s o c i e t a l g o a l ga = 90° BCE
Fig 2. Agent decision model,
Agents derive utility both from contributing to thesocietal goal and performing well according to the proxy measure (blue, redrespectively). An individual agent (index i) produces goal value ( V gi ) and proxy value( V pi ) as determined by the practice angle ( θ i ) and effort ( e i ), simply as the projection ofthe effort vector onto the main axes (eqs. 2 and 3; A-C ), where the goal angle ( ga ) isthe angle between the main axes (see Fig 2). The utility derived in the proxy dimension(denoted prospect) depends not on the absolute proxy value but on the relative rankingof proxy values and the survival threshold according to eqs. 5 and 6. Panels D, E showillustrative prospect functions (dark red) for competition c = 0 . c = 0 . c ) denotes thefraction of losers. Accordingly, for c = 0 . c = 0 .
9, the survival threshold is the 50 th or the the 90 th percentile of the population distribution of proxy values respectively(grey histograms in D, E respectively).October 3, 2019 12/51 .4 Individual choice - competition as incentive The utility derived from the proxy value, denoted ‘prospect’ ( U pi ), is determinedthrough competition (Fig 2D, E). It depends on the relation of the own proxy value V pi and the proxy value required for professional survival (the survival threshold, ST ). Thesurvival threshold is the proxy value which separates winners and losers for a given levelof competition. For instance c = 0 . th percentile of the distribution of all proxy values, i.e. an agent has tobe in the top 10% proxy performers to be a winner. The survival threshold is assumedto be the salient reference point with respect to which agents evaluate the utility oftheir own proxy value. Accordingly, they will derive negative/positive utility if they arebelow/above the survival threshold. In the first version of this manuscript/model wehave considered a prospect function based on a Gaussian uncertainty distributionaround the survival threshold (based on [38, 40, 50]). Though the main results weresimilar (see manuscript history on arXiv), this function was not scale invariant withrespect to proxy value. Therefore we here choose a similarly sigmoid, but scale invariantprospect function, namely that of cumulative prospect theory (Eq 5 [51]). U pi ( V pi , ST, (cid:15) ) = ( V pi − ST ) . (5)Additionally, we assume agents are loss averse, i.e negative prospects are multipliedby 2.25 (Eq 6, [51]). U pi (cid:55)→ U pi , if U pi ≥ U pi · . , otherwise (6)In a subset of models, we additionally probed a simple step function as prospectfunction [-1,1]. Each agent A i , when she is drawn, chooses her effort level to maximizeher individual utility U i given the observed current proxy performances of all otheragents (Eq 7), U i ( U gi , U pi , cost ) = U gi + U pi − cost ( e i , t i ) (7)where effort cost is given by:October 3, 2019 13/51 ost ( e i , t i ) = e i /t i (8)Here t i is the talent of the agent, i.e. a constant determining the relative cost ofeffort independent of θ . Agents are given variable talent according to N (10 , tsd ) suchthat the effort to proxy-performance relation depends on both individual practiceorientation and talent. This allows us to capture beneficial effects of the proxy assignaling/screening device for talent, as well as detrimental effects (Campbell’s Law).Note, that the the latter could similarly be described as signaling/screening of corruptpractices, and our model allows beneficial and detrimental mechanisms to actsimultaneously. In order for individual agents to compute the complex maximizationproblem described above, we assume they consider a limited range of effort adjustments,namely [-10, -5, -1, -0.5, -0.1, 0, 0.1, 0.5, 1, 5, 10]. The rationale behind this is that theagent intuitively judges what might happen if she changes her effort just a little or a lotbut lacks the computational capacity for perfect maximization. Nevertheless, if thesystem is stable enough, she will iteratively approach the optimal effort. Note, thatalternative effort choice lists (e.g. -10 to 10 in 0.1 increments) did not change modeloutcomes but dramatically increased the computational burden of agents (and model).Furthermore, the specific range (-10 to 10) simply covers the magnitude of plausibleeffort changes in the system arising from the arbitrary mean talent choice of 10, andchoosing a larger range did not change outcomes. In a subset of models, practice agencywas introduced by letting agents maximize utility over the effort test-list for each of arange of practice-adjustments in an angle-list of [-5 ° , -1 ° , 0 ° , 1 ° , 5 ° ], following the samerationale. When all agents have been randomly drawn to adjust their efforts (and potentiallypractice), the ranking of proxy-performances is reassessed. Each potential loser( V pi < ST ) is then subject to professional death with probability = selection pressure( sp ∈ [0 , sp determines the approximate number of steps one can affordto be a loser before being actually removed, relating experienced to realized competition.Upon each death a position opens up, which allows a randomly chosen ‘winning’October 3, 2019 14/51roxy-performer ( V pi > ST ) to professionally reproduce, passing her practice angle onto her offspring.During practice inheritance, θ mutates stochastically, such that θ offspring = θ parent + N (0 , m ). We reason that the magnitude of the mutation rate m isproportional to the complexity of the societal system. Large mutation rates reflectpotentially large and frequent effects of minor practice changes on proxy and goal valuesdriven by i) an increasing number of nonlinear interactions in more complex systemsand ii) the combinatorial explosion of possible action to outcome mappings withincreasing complexity [46]. In this context it is important to remember that the practicespace represents a dimensional reduction to the orthogonal components of proxy andgoal. Accordingly, mutations can be thought of as comprising arbitrary changes inadditional independent dimensions, for instance animal welfare in meat production(assuming animal welfare is not considered a societal goal of the industry). The model was implemented in the agent-based modeling framework ‘Mesa0.8’ inPython3.6 and run on a standard Windows7, 64bit operating system. The full code torun the model and generate figures is attached as supplemental material.Table 2 shows an overview of the explored parameter space with the parametersshown here highlighted in boldface (also see Fig 5). A number of additional parameterswere varied to probe robustness, but lead to no change, and will be reported atappropriate locations throughout the manuscript. The model was initialized withpopulation size N (typically 100), where every agent received a practice angle θ drawnrandomly from a uniform distribution between proxy and goal axes U (0 , ga ) and initialeffort 0. Model runs were typically repeated 10 times for each level of competition toobtain measures of the mean and spread of system behavior. In each model run, allagents in a population compete against each other via their proxy performances asdescribed above.October 3, 2019 15/51 able 2. Parameter spaceParameter BaseValue(s),Range Description Main effect (if parameter is increased)equilibrium determining parameters goal angle( ga ) 45 ,
90, 135 ,0 -180 angle ( ◦ ) defining the amount ofcorruptible proxy information hill shaped effect on equilibrium corrup-tion, the optimal level of competitiondecreases goal scale( gs ) 1 , 2, 0-10 scaling factor of psychologicalgoal valuation (relative to experi-enced prospect value) increased effort, decreased equilibriumcorruptiondynamics determining parameters competition( c ) , ,0.1-0.9 competitive pressure, i.e. thefraction of potential losers perround complex effects on effort, evolution andutility (see main text), increased speedof convergence to equilibria selectionpressure( sp ) , ,0.001-1 probability of death for each los-ing agent in each round increased speed of convergence to equi-libriaparameters affecting variability talent stan-dard devia-tion ( t sd ) 1 , 0-6 standard deviation of talentwithin the population increased effort spread populationsize ( N ) 100 , 10-500 number of agents in the system decreased variability over models practicemutationrate ( m ) 2 , 0-30 standard deviation ( ◦ ) of prac-tice angle mutations during in-heritance increased practice variability and, if theequilibrium practice is outside the ini-tialization range, speed of convergenceto equilibriaOverview of the parameter space. During sensitivity analysis individual parameters were varied in the specified ranges holdingall other parameters at the base values. Presented base values are in boldface (Fig 5, 6). The remaining base values wereadditionally probed. We will first introduce the model using an exemplary parameter set and short timescale,emphasizing the emergent patterns of effort and practices, in order to demonstrate thesurprising scope of overlap with empirical observation from the experimental contestliterature. We will then demonstrate the main result of competition-induced equilibriumcorruption at a longer timescale. Finally we will present the results of a detailedsensitivity analyses demonstrating the robustness of equilibrium corruption andrevealing the parameters governing it.To introduce the model we consider a system in which the proxy contains someincorruptible and some corruptible information about the societal goal( ga = 45 ◦ ; i = 0 . gs ) is set to one implying comparable weighting of proxyOctober 3, 2019 16/51nd goal incentive. Selection and mutation are mild ( sp = 0 . , m = 2 ◦ ), implying a 10%probability of death for losers at each time step and small changes of practiceorientation during inheritance. At initialization each agent receives a random practiceangle between full corruption and full goal orientation θ = U (0 , ga ) and normallydistributed talent t = N (10 , We begin by describing the emergent behavior resulting from iterative effort choice. Inbrief, at each time step, agents in random order adjust their effort given the noisyobservations of proxy performances of competing agents and their personal parameters(prospect function, practice angle and talent). This simple contest specificationproduced a range of behaviors observed in experimental economics including i) optimaleffort incentivization at intermediate levels of competition, ii) a discouragement effectand iii) effort bifurcation [30]. Importantly, we did not consider or anticipate any ofthese effects during model design, but rather strove to create the simplest effort choicealgorithm applicable in a step wise agent-based model with plausible preferences,information acquisition and computation of individual agents. The algorithm produceda range of interesting individual effort trajectories, highly dependent on competition(Fig 3A, four exemplary model runs ranging from very low to very intense competition).Note that individual agent properties (practice orientation θ and talent t ) are identicallydistributed between competition levels. However, in higher competition, individualagents are forced to increase effort to cross a higher survival threshold (the competitivecutoff between winners and losers). This in turn affects the population distribution ofproxy values leading to a positive feedback loop and higher effort levels in highercompetition. When marginal effort cost begins to outweigh the expected utility gain,individual agents may stop increasing or begin to decrease effort. Indeed, due to theflattening of the prospect function when the observed survival threshold (given otheragents performances) is far beyond the own proxy performance, agents may become‘discouraged’, i.e. decrease effort (Fig 3A, e.g. black arrows). In such cases the prospectof winning becomes unrealistic with acceptable effort expenditure, such that agents optOctober 3, 2019 17/51o save effort cost. Discouragement becomes more frequent in more competitive systems,leading to an eventual reversal of the competition to effort relation for some agents, asobserved empirically [52–54]. Increasing prevalence of discouragement with highercompetition also entails an increase in variance of effort at the population level. At theindividual level, agents similarly show more variable effort over time in highercompetition. This competition to effort-variance relation is highly robust, notably evenwithout agent heterogeneity (not shown), a testable prediction contrasting our modelwith previous contest models [30]. Notice, how some agents progressively increase effortin order to compete, but eventually become discouraged (Fig 3A, black arrows). Theresulting decrease in the survival threshold may in turn provide other agents with aprospect of winning, such that they can gain utility by increasing effort (Fig. 3A, greyarrow). To the best of our knowledge, this is the first neuroeconomically plausibleiterative effort choice algorithm which provides a mechanistic account of howequilibrium effort is approached in contest settings (see also [55]). Notably, itreproduces a remarkable range of empirically observed but incompletely understoodphenomena concerning both static effort distributions and effort trajectories and isamenable to experimental verification.Additional to these psychologically driven effects, competition determines selectionby defining the proportion of losers. Agents with insufficient proxy-performance (losers)are subject to stochastic professional death with probability = sp , where death meanspermanent elimination from the competitive system (indicated by white rectangles;Fig 3A, e.g. white arrow). Upon a death, the free slot is immediately filled up by theoffspring of a random winning agent. Given, that competition determines the proportionof losers and losers have uniform probability of death, selection events increaseproportionally with competition. Note that this specification keeps the population sizeconstant, modeling a societal system with fixed size and resource consumption whereincreased competition is realized through an increased throughput of new agents.October 3, 2019 18/51 s t e p e ff o r t g o a l ( o c ) t a l e n t v a l u e proxygoal 0 50 100step 0 50 100step 0 50 100step0 50 100step01020 m e a n p r a c t i c e ( ° ) m e a n v a l u e proxygoal 0.25 0.50 0.75competition−15−10−5 m e a n u t i l i t y g o a l ( o c ) m e a n p r a c t i c e ( ° ) c o m p e t i t i o n competition = 0.1 competition = 0.3 competition = 0.6 competition = 0.9 ABCDE
Fig 3. Short term dynamics
October 3, 2019 19/51 ig 3. Short term dynamics (100 time steps), with N = 100 , ga = 45 ◦ , θ initialization = U (0 ◦ , ga ) , gs = 1 , t = N (10 , , sp = 0 . , m = 2 ◦ .Data are collected from 10 model runs per competition level ( c ). A-D show four levels ofcompetition (major columns) while D shows c = [0 . , . , ..., . A) Agent Dynamics,
Each subpanel shows effort over time for each of the100 agents (random run for given c ). Columns within subpanels represent individualagents or positions. White squares indicate death/birth events (two example highlightedwith white arrows). Black arrows indicate examples of agents becoming discouraged bycompetition. Grey arrows indicate examples of agents increasing effort to gain theprospect of winning. B) Agent Values,
Realized proxy and goal values of each agentat the 50th time step. Values are the result of the current chosen effort given theindividual agents practice angle (compare Fig 3B). Each data point represents an agent(agents accumulated from 10 runs per panel). Talent is color coded. The black and greyarrows indicate highly proxy or goal oriented agents, respectively. Note that the agentsindicated by the grey arrow are outperforming those indicated by the black arrowconcerning their goal performance, but not proxy performance.
C, D) ModelDynamics,
Model level dynamics of proxy and goal value (C) and the mean practiceangle (D).
E) Model Values,
Final (step 100) mean proxy and goal values (left) andutility and practice angle (middle) as a function of competition. Data on mean proxyand goal values can be projected back into the practice space (right) as in Fig 2A. Theshaded area around lines represents the standard deviation over model runs.
The relative ability of individual agents to compete depends on two parameters, namelytalent and practice orientation, both of which are not directly observable. Talent allowsgreater effort, independent of practice orientation. Accordingly, if practices are fixed, theproxy fulfills its intended role as signal of goal performance, allowing efficient screeningby the competition. At the same time, however, high proxy performance may resultfrom higher proxy orientation of the practice, implying wasteful or even detrimentalsignaling (Campbell’s Law). In our model, both processes act simultaneously and canbe assessed by visualizing realized practice-effort pairs of individual agents back into thepractice space with color-coded talent (Fig 3B). Here each data point represents theendpoint of the effort vector (as in Fig 3A-D) of an individual agent at time step 100.The resulting goal and proxy performances correspond to the projections onto the mainaxes, as shown in Fig 3B). Across all levels of competition, we observe a dominant effectof the competitive incentive on realized effort levels, as outcomes tend to organize invertical lines, i.e. they cluster around a specific proxy value. Further analysis showedthat the vertical line corresponded to proxy-values just above the emergent survivalOctober 3, 2019 20/51hreshold for a given level of competition. Agents just below this threshold had eitherincreased effort attempting to enter the win-domain or decreased effort further, to saveeffort cost. Accordingly, the sigmoidal prospect function, including loss aversion, driveseffort bifurcation, particularly when judging effort by proxy performance.Also across all levels of competition, but most prominently for high competition, weobserve a beneficial signaling/screening effect of the proxy as higher talent translates tohigher proxy performance. We furthermore Another interesting emergent phenomenonis a competition dependent reversal of relative effort expenditure by agents with highpractice angles. In low competition (Fig 3B, c = 0 .
1, leftmost panel) agents with highpractice angles are forced to put in extra effort, but are still able to compete, leading toparticularly high relative contributions to the societal goal. By contrast, whencompetition is intense (Fig 3B, c = 0 .
9, rightmost panel) agents with more goal orientedpractices can no longer compete on the proxy scale and are preferentially discouraged,even if they have high talent. Notice, that the emergent practice-effort realizations coverseveral qualitatively distinct domains across the practice space, where observable proxyperformance only partially predicts unobservable goal performance. Some agents arepeak proxy performers, while only moderately contributing to the actual societal goal(Fig 3B, black arrow). Simultaneously, some highly talented agents are ‘losing’ inproxy-competition, while actually outperforming many ‘winners’ regarding the actualsocietal goal (Fig 3B, grey arrow). More generally, the model predicts that for anyobserved proxy performance and at any time point, there is a mix of agents with highlyvarying degrees of proxy orientation. Thus our model intuitively captures thesimultaneous effects of beneficial and detrimental signaling, which we believe toinvariably arise in any proxy-based competition.
Preferential discouragement of goal oriented agents might translate to a divergencebetween proxy and goal performance at the system level. To visualize variability at thesystem level, the following data are displayed as mean and standard deviation overmodel runs where each run is represented by the population mean of its agents. Indeed,mean proxy and goal performance of populations of agents show distinct competitionOctober 3, 2019 21/51ependent dynamics (Fig 3C). Note an initial phase (within the first 10 steps), visibleas a steep rise in value as effort first adjusts to an initialization independent level(models initialized with effort levels of 0, 1, 10 or 20 all converged to the same valuesduring this initial phase). Subsequently, value may progressively increase (Fig 3C, c = 0 . .
6) or decrease (Fig 3C, c = 0 .
9) due to feedback loops between individualeffort and survival threshold. More intense competition also leads to an increasingdivergence between proxy and goal value (Fig 3C). One driver of this effect is thepreferential discouragement of agents with high goal orientation, implying an overalleffort redistribution toward the proxy (a psychological mechanism of Campbell’s Law).A second potential driver is a selective removal of goal oriented agents due to inferiorproxy performance (a cultural evolution mechanism of Campbell’s Law). The degree towhich this happens can be assessed by viewing the dynamics of the population meanpractice angle, which is independent of effort (Fig 3D). With a goal angle of 45 ◦ , theinitial uniform distribution of practices between proxy and goal leads to an initialpopulation mean practice of θ = ga/ . ◦ . However, as selection removes agentswith high practice angles, replacing them with offspring from agents with lower angles,the population mean evolves toward the proxy. As expected, the speed of evolutiontowards the proxy is proportional to the intensity of competition since the quantity ofselection events drives population change of practices. Thus, our model reproduces acentral finding by Smaldino and McElreath [5], namely the the powerful corruptive forceof proxy guided cultural evolution. To obtain a more complete view of proxy and goal performances we next plot the meanfinal values of this short period (step 100) as a function of competition (Fig. 3E, left;data points represent model runs). Note that for both proxy and goal value, there is anoptimal level of competition. No increases in goal performance are achieved bycompetition greater than c ≈ . c ≈ . So far, we have explored the model dynamics in the short term (100 time steps). Wereason this timescale is most relevant when assessing the dynamic effects of parameters,such as the competitive pressure. Notably, additional mechanisms, such as delayedOctober 3, 2019 23/51dentification and removal of corrupted practices, or a generally continuously changingsystem might render these short term pressures dominant in determining systembehavior. However, our model also provides the opportunity to examine the long termsystem behavior resulting only from effort choice dynamics and cultural evolution(Fig 4, 10000 time steps). In a previous similar study, practices were found to inevitableevolve to full corruption [5]. Our model allows to test if a moral incentive componenthas the power to bound this detrimental evolution. As observed above, the range ofexisting practices in our model evolves toward the proxy for all levels of competition(Fig 4A, D). However, even in the most intense competition, an equilibrium is reached,beyond which the average practice no longer becomes more corrupted (Fig 4D). Notably,this equilibrium level of corruption was similar for all levels of competition (Fig 4E,middle panel), differing only in the speed with which it was reached (Fig 4D). Given theequilibrium corruption level, effort dynamics nevertheless produced an optimal level ofcompetition ( c ≈ . lock-in state,i.e. a stable system orientation toward the proxy, while individual agents i) know theimpact of their actions toward and ii) value the societal goal. Next we tested the sensitivity of these results to parameter variations. Since a fullcombinatorial exploration of the parameter space is unfeasible, we followed a three-stagestrategy: We first systematically varied one parameter at a time holding the otherparameters constant (Fig 5; base value in boldface), monitoring the effect on corruption( θ ). We found that parameters fell into three main groups: i) equilibrium determiningparameters (Fig 5A; ga, gs ), ii) dynamics determining parameters (Fig 5C, D, c, sp, m )and iii) parameters affecting predominantly system variability (Fig 5B; t sd , N ) . Wethen attempted to find deviations from this initial classification by repeating one at atime analysis with a selected range of alternative anchor values, (Table 2, base values initalics). In over 100 targeted additional model runs, we failed to find such deviations,suggesting our mapping of the main parameter effects was robust. Finally, weOctober 3, 2019 24/51 BCDE e ff o r t g o a l ( o c ) t a l e n t v a l u e proxygoal 0 5000 10000step 0 5000 10000step 0 5000 10000step0 5000 10000step01020 m e a n p r a c t i c e ( ° ) m e a n v a l u e proxygoal 0.25 0.50 0.75competition−14−12−10−8 m e a n u t i l i t y g o a l ( o c ) m e a n p r a c t i c e ( ° ) c o m p e t i t i o n Fig 4. Long term dynamics, (10000 time steps), with N = 100 , ga = 45 ◦ , θ initialization = U (0 ◦ , ga ) , gs = 1 , t = N (10 , , sp = 0 . , m = 2 ◦ .For panel descriptions please refer to Fig 3. In (A) only a subset of agents and every10 th time step is depicted.October 3, 2019 25/51ndertook two major modification, namely we introduced a step-prospect-function orpractice agency, and again found the general relations to hold (with the exception of thesystem dynamics under practice agency, see below, Fig 6).Across all model specifications equilibrium corruption was determined predominantlyby the informational quality of the proxy ( ga ) and the psychological power of theintrinsic incentive towards the societal goal ( gs ; Fig 5A). In the main model, thedynamics of corruption was predominantly determined by the level of competition ( c )and the degree to which competition was realized in actual selection events ( sp ; Fig 5C,D). Practice mutation rate ( m ) had no notable effect on equilibrium or dynamics ofcorruption for these standard models (Fig 5D, F, top), but did contribute to thedynamics of corruption when the equilibrium practice was outside the initializationrange (Fig 5D, F, bottom). By contrast, the number of agents in competition ( N ) andtalent spread ( tsd ) affected mainly system variability (Fig 5B). Thus, our modelsuggests, that equilibrium corruption is determined primarily by proxy information ( ga )and the intrinsic moral drive toward the societal goal ( gs ). Additionally, the drivetoward this equilibrium corruption is governed by the intensity of competition ( c, sp )and potentially the complexity of the system ( m ).Finally, we tested the robustness of these main findings for two major modelmodifications, a step-prospect-function and practice agency. First we replaced theprospect function by a simple step function (prospect = -1 for losers, 1 for winners;Fig 6A-C). While overall effort and value creation was lower (given the lower maximalprospect differential), the respective effects of the parameters remained robust. This isimportant, given that the Kahnemann/Tversky type prospect considered primarily mayapply to individual agents, but may not hold when larger entities, such as labs orcompanies, are considered as agents. Second, we introduced agency over the practiceangle by letting agents choose not only effort but also practice to maximize utility atevery time step. Remarkably, the main determinants of equilibrium corruption, i.e. ga and gs , again followed the same pattern (Fig 6, D-E). However, introducing practiceagency led to a dramatically increased speed of convergence and decreased variability ofpractices within a population. Indeed, our specification of practice agency was topotent, that it effectively overrode the cultural evolution mechanism and relatedparameters. Interestingly, it also markedly increased the ability of gs to counteractOctober 3, 2019 26/51 m e a n v a l u e proxygoal −14−12 m e a n u t i l i t y m e a n p r a c t i c e ( θ )
0° 90° 180°goal angle (ga)0 5 10goal scale (gs)2040 m e a n v a l u e proxygoal 0 5 10goal scale (gs)050100150200 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) m e a n v a l u e proxygoal 0 200 400num Agents (N)−14−13−12−11−10 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) m e a n v a l u e proxygoal −14−13 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) m e a n v a l u e proxygoal −15−10−5 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) practice mutation rate (m)0° 10°5° practice mutation rate (m)0° 10°5°0.0 0.1 0.2selection pressure (sp)910111213 m e a n v a l u e proxygoal 0.0 0.1 0.2selection pressure (sp)−14−12−10 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) Equilibrium effect Variability effect m e a n v a l u e proxygoal 0.25 0.50 0.75competition (c)−14−12−10−8 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) Dynamics effect
Conditional dynamics effect m e a n p r a c t i c e ( θ ) m e a n p r a c t i c e ( θ ) m e a n p r a c t i c e ( θ ) m=0° m=3° m=6° m=10° m e a n p r a c t i c e ( θ ) A BC DE F θ init. = U(0°,45°)θ init. = 45°θ init. = U(0°,45°)θ init. = 45° 0 2talent sd (tsd)101214 m e a n v a l u e proxygoal 0 2talent sd (tsd)−20−15−10 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) Fig 5. Sensitivity Analysis
October 3, 2019 27/51 ig 5. Sensitivity Analysis , parameter base values: N = 100 , ga = 45 ◦ , θ init. = U (0 ◦ , ga ) , gs = 1 , t = N (10 , , sp = 0 . , m = 2 ◦ . Oneparameter at a time was varied while leaving the other parameters at their base values.Overview plots (panels A-C, E) show mean model outcomes at equilibrium /theta (stepnumbers were increased until convergence to equilibrium was confirmed for eachparameter). Data points represent mean population outcomes of individual runs andlines represent mean ± sd. over runs A) Parameters controlling equilibrium corruption( θ , grey): goal angle ( ga ), top; goal scale ( gs ), bottom. B) Parameters controllingsystem variability: number of Agents ( N ), top; talent standard deviation ( tsd ), bottom. C, D)
Parameters controlling the speed of convergence: competition ( c ), top; selectionpressure ( sp ), bottom. ( sp = 1 produced the same equilibrium, but is not shownbecause the dynamics could no longer be resolved.) E, F)
Parameter controlling systemdynamics if equilibrium θ is outside the initialization range. For our standard practiceinitialization range ( θ init = U (0 ◦ , ◦ )) m had no notable effect (top). If all practiceswere initialized at θ init = 45 ◦ , m governed the dynamics of convergence, and in the caseof m = 0 ◦ precluded convergence (bottom).corruption, leading to approximately twofold higher equilibrium θ (compare Figs 5Aand 6D). Thus our main finding, that equilibrium corruption is determined by ga and gs was highly robust, while the dynamics determining effects of c , sp and m become lessrelevant when agents continuously choose their practice orientation to maximize utility.These results further suggest, that increased agency over practices may help counteractcorruption given sufficient gs . We have presented an agent-based computational model, sketching the centralcomponents of a socio-economic theory denoted
Proxyeconomics . The theory ismotivated by the central insight, that any societal competition to achieve an abstractgoal must rely on proxy measures. These invariably capture only partial information,and become targets for the competing individuals, resulting in a susceptibility tocorruption. In the following, we will first discuss the agent-based model (section 5.1)and then proceed to discuss additional implications of proxy-based competition, towardsa more general theory of proxyeconomics (section 5.2).
In this section we will discuss the more general background of our model, includingspecific limitations and potential extensions. We will begin by exploring the iterativeOctober 3, 2019 28/51
BC DF m e a n v a l u e proxygoal 0.25 0.50 0.75competition (c)−15.0−12.5−10.0−7.5−5.0 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) −5051015 m e a n v a l u e proxygoal −14−12−10−8−6 m e a n u t i l i t y m e a n p r a c t i c e ( θ )
0° 90° 180°goal angle (ga) 0° 90° 180°goal angle (ga)0 5 10goal scale (gs)204060 m e a n v a l u e proxygoal 0 5 10goal scale (gs)0100200 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) m e a n v a l u e proxygoal 0.25 0.50 0.75competition (c)1.01.52.02.5 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) −20246 m e a n v a l u e proxygoal −20 m e a n u t i l i t y m e a n p r a c t i c e ( θ )
0° 90° 180°goal angle (ga)0° 90° 180°goal angle (ga)0 5 10goal scale (gs)02040 m e a n v a l u e proxygoal 0 5 10goal scale (gs)0100200 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) m e a n v a l u e proxygoal 0.0 0.1 0.2selection pressure (sp)0.81.01.2 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) m e a n v a l u e proxygoal 0 2talent sd (tsd)0.60.81.01.21.4 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) m e a n v a l u e proxygoal 0 200 400num Agents (N)1.01.5 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) m e a n v a l u e proxygoal 0.0 0.1practice mutation rate (m)0.60.81.01.21.4 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) m e a n v a l u e proxygoal 0.0 0.1practice mutation rate (m)−13.5−13.0−12.5 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) m e a n v a l u e proxygoal 0 200 400num Agents (N)−12−10−8 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) m e a n v a l u e proxygoal 0 2talent sd (tsd)−17.5−15.0−12.5−10.0 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) m e a n v a l u e proxygoal 0.0 0.1 0.2selection pressure (sp)−13.5−13.0−12.5 m e a n u t i l i t y m e a n p r a c t i c e ( θ ) E Fig 6. Robustness , parameter base values: N = 100 , ga = 45 ◦ , θ init. = U (0 ◦ , ga ) , gs = 1 , t = N (10 , , sp = 0 . , m = 2 ◦ . Oneparameter at a time sensitivity analyses was repeated for two alternative models: Onecontaining a step-function prospect [-1,1] (A-C) and one containing agency over thepractice angle (D-F) October 3, 2019 29/51ffort choice algorithm (section 5.1.1), and the cultural evolution mechanism 5.1.2). Wewill then discuss a range of broader informational, psychological and sociologicalimplications (sections 5.1.3 - 5.1.5), embedding the model in a larger, trans-disciplinaryliterature.
The relation of our model to the economic contest literature deserves particular mention,since to the best of our knowledge we are the first to implement a neuroeconomicallyplausible iterative effort choice heuristic in an agent-based model of contests. Oursimple, neuroeconomically motivated, contest heuristic contains i) a neuralrepresentation of utility, ii) multiple sources of input to this utility and iii) referencedependence of this utility [43]. The sigmoidal prospect function represents a confluencebetween ecological, psychological and economic theory [38]. It requires plausible, noisyinput information and computational capacity from individual agents. Intriguingly, theemergent behavior reproduced many empirical findings, the origins of which are stillpoorly understood [30]. Firstly, effort incentivization is usually optimal at intermediatelevels of competition, consistent with experimental and field observations [52–54].Secondly, agents performing far below the survival threshold display a ‘discouragementeffect’ [30]. While traditionally discouragement is thought to result from agentheterogeneity, our model predicts it even in cases without agent heterogeneity, simplydue to chance and the emergent distribution of proxy performances. For the samereason, our model predicts a bifurcation of effort, particularly in the presence ofheterogeneity, but even without. Additionally, the model makes specific predictionsabout how competition affects the variance of effort over time and the population. Atthe same time, the model allowed to intuitively capture the signaling/screening effect ontalent but also proxy-orientation. This simultaneous screening for talent andproxy-orientation, is suggested to arise in any proxy-based competition under mostconditions. Accordingly, observed high performers are likely to generally represent a mixof true high performers (on the goal scale) and highly proxy-oriented agents. Aparticularly interesting set of studies in this context are investigations of contests withthe possibility of sabotage [52, 57]. A mixed strategy containing productive effort as wellas sabotage is analogous to a low practice angle in our model. Indeed, increasedOctober 3, 2019 30/51ompetition (a smaller fraction of winners or increased prize spread) led to aredistribution of effort towards sabotage, consistent with our results. Notably, studiesaddressing contest incentives in explicit multitask settings appear to be lacking and thusremain a crucial avenue for future research [58]. Finally, our iterative effort choicealgorithm makes predictions about the temporal evolution of effort expenditure,including its variability in time and the path of convergence to potential equilibria. Inthis, it resembles previous experimental contest models based on reinforcementlearning [55] or belief-updating [45]. A specific prediction is variability of individualeffort over time and over the population, which is proportional to the level ofcompetition (qualitatively matching data presented in [52, 59]). Accordingly, wespecified what is to our knowledge the first agent-based iterative effort choice algorithm.This generative agent-based algorithm reproduced a remarkable range of empiricallyobserved effort patterns observed in the experimental contest literature, which were notconsidered during model design [30, 58]. Embedding this algorithm within amultitasking framework further allowed us to intuitively model the complex screeningeffect of competition on observed (proxy) as well as unobserved (goal) performance.
A central question we posed of our model, was if such a multitasking mechanism couldalter a simultaneously acting mechanism of cultural evolution. Indeed, a previousagent-based evolutionary model of cultural practices had reported a robust evolutiontoward the worst possible practices [5]. The central unifying element with the presentmodel is the existence of a practice variable ( θ in the present study), which alters therelation between true (goal) and selected (proxy) performance, formalizing theassumption that there exist practices which contribute differentially to proxy and goal.Furthermore, this variable can be imperfectly inherited, formalizing the assumption thatprofessional practices are complex and transmitted from senior to junior professionalsimperfectly. In our view these assumptions are nearly self evident, and the resultingdetrimental evolution becomes a powerful prediction. However, even the authors note,that this prediction seems overly pessimistic and invoke intrinsic incentives as acounteracting power [5]. Here we have modeled such an intrinsic incentive, and observethat it is able to bound the evolution to fully corrupted practices. Specifically, ourOctober 3, 2019 31/51odel led to an equilibrium corruption level, which was substantial, but still markedlydifferent from full proxy orientation. This result is intuitively appealing and, in fact,better matches the results of a meta-analysis of sample sizes within the same study [5].The mean proxy-orientation as equilibrium was determined primarily by theinformational quality of the proxy ( ga ) and the relative psychological strength of anintrinsic incentive toward the societal goal ( gs ). How both parameters may bedetermined, or altered, will be further discussed below (sections 5.1.3 - 5.1.5). Notably,our model suggests that increased agency over the practice orientation has the ability tofurther decrease the level of corruption. Such agency may result from training in goodresearch practices, allowing a conscious deviation from questionable norms within aresearch field. In the absence of practice agency, the dynamics of corruption in ourmodel were governed by competition ( c and sp ) and potentially complexity ( m ).Adding practice agency let the model converge to equilibrium nearly instantaneously,effectively occluding the dynamic effect of c, sp and m . However, in our implementation,practice agency is substantial (with the similar speed and range as effort agency). Inreal systems practices may be determined by a mix of social norms and individualchoice, suggesting outcomes may lie between our models with and without practiceagency. The interaction between the evolutionary process and an active practice choicecould be investigated in more detail by for instance probing models where practiceagency is allowed only stochastically. Indeed, exploratory analysis in such a modelsuggests, that in such cases the level of competition can mediate between the equilibriawith and without practice agency. Accordingly, our model shows a reliable convergenceto a corruption equilibrium. This provides a mechanistic explanation for what we havecalled lock-in . The model further suggests two general strategies to modify theequilibrium, namely i) improving proxy information and ii) promoting goal valuation(for instance through narratives [60], see below). Finally, it suggests competition andagency as central variables determining the dynamics of the system. The general approach of the current model was to view competitive societal systems asinformation processing devices, which collect information to create the proxy and canOctober 3, 2019 32/51ltimately be characterized by their realized competitive decisions. This approachembeds the theory into a larger framework of optimization in complex systems discussedin an extensive literature on complex systems, artificial intelligence and machinelearning [4, 31, 46, 47, 61]. The proxy measure is analogous to an objective function andthe competitive pressure corresponds to optimization pressure. We suggest that all theprincipal types of challenges that occur during machine learning optimization also applyin competitive societal systems, including reward hacking, negative side effects andscalable oversight [31]. For instance, the process of Campbell’s Law is closely related toreward hacking. Negative side effects include reduced value in dimensions which do notdirectly impact either proxy or goal. For instance, [12] suggest young scientistsprogressively constrict their valuation repertoire to competitivity, at the cost of‘sociability’. Scalable oversight describes the process of balancing the cost of creatingthe proxy with the benefits from better proxy information. One main reason why proxymeasures will imperfectly reflect the societal goal is because they need to be costefficient. For instance, the information contained in an impact factor could be arguablyarbitrarily increased by adding more reviewers or having experiments reproduced.Clearly, the cost of improving the proxy needs to be balanced with the potentialdetrimental effects of an imperfect proxy. Note that both the cost of improving theproxy and the potential detrimental effects of an imperfect proxy are likely to interactwith competition. More frequent competitive evaluations may be more costly toperform while simultaneously incurring a higher unobserved cost due to corruptionpressures [16]. Introducing stochastic and/or delayed assessment and correctionmechanisms for corrupted practices may lead to new dynamic equilibira (but see [5]).Importantly, considering which types of information are likely to be lost due to theidiosyncrasies of specific competitive societal systems offers a prime path to predictingcorruption. For instance if proxies are assessed in predefined short time intervals, thenany outcome with longer time frames is subject to corruptive pressure. Other importantconsiderations include reliance on representatives and sampling in space and time. Forinstance, market mechanisms collect information in a direct, decentralized andcontinuous manner while other systems rely on representatives and predefined samplingprocedures (e.g. peer reviewers/ political representatives). Finally, if multipleinterlocked competitive systems interact it is important to consider if they share orOctober 3, 2019 33/51eciprocally counteract informational deficits (see section 5.2.3).Accordingly, the analogy to machine learning suggests three central conclusions: 1.There is an optimal optimization-pressure which crucially depends on the informationcaptured in the proxy. 2. Problems are likely to arise through both continuous systemchange and the optimization pressure itself, necessitating a continuous higher levelassessment process. 3. Analysis of the information generating mechanism of the proxy islikely to provide detailed predictions on patterns of corruption. In other words, weshould continuously expect, attempt to measure, and mitigate corruption in anycompetitive societal system. Importantly, the term corruption must be understood asan inevitable system-level force arising through actions based on imperfect information,which may, but need not, involve intention.
Our model draws on a large experimental literature addressing the individual leveldecision mechanism, by including a moral component into decisions. While the adoptedeconomic multitask model provides an elegant way to formalize this, it must be statedclearly, that the actual mechanisms are far from understood. For instance, it is unknownwhat the relative motivational power of moral and competitive incentives is, particularlyfor real professionals. Compared to laboratory settings both the moral incentive (e.g.treating a patient well) and the competitive incentive (actual professional survival), maybe substantially more powerful. Nevertheless, experimental investigations [33, 34, 62]consistently demonstrate that both moral and egoistic incentives play a role, and provideessential insight about the potential psychological mechanisms during incentive conflicts.Recently, Chugh and Kern [35] have even suggested that the need to maintain an ethicalself-image is the dominant principle, and that self-interested actions are only permittedto the degree, that this self-image can be maintained. In light of this it is important tonote that implications of a decision for the societal goal are likely to be associated withhigher ambiguity, longer time frames and less personal relevance than implications forthe proxy [63]. This results directly from the concept of proxy-based competition, sinceproxy is almost by definition an attempt to make an abstract societal goal concrete,immediate and personally relevant. Of course this has unavoidable consequences fordecisions, given the well known phenomena of ambiguity discounting, temporalOctober 3, 2019 34/51iscounting and social discounting [64–66]. Another important question, addressed in aseparate literature, concerns the effect of competition on decisions [58]. While a largebody of experimental evidence demonstrates the power of competition as an incentive,the underlying mechanisms remain poorly understood, particularly in multitask settings.However, neuroeconomic research is beginning to reveal the important role ofloss-aversion in contests [39]. More generally, the fields of behavioral economics,psychology and neuroeconomics are beginning to converge towards set of actual,empirically validated, decision mechanisms. Specifically, they suggest a computationallybounded mechanism with multiple (moral/ egoistic), potentially reference dependent,valuation inputs converging into a single utility computation [43, 67]. While we haveattempted to capture these confluent insights into our simple decision model, futureresearch, and more complex empirically validated decision models will unquestionablyyield a superior basis for generative agent-based models.Finally, there is substantial empirical evidence for interindividual differences inmoral/egoistic drive. For instance, there is direct experimental evidence for an increasedpropensity to sabotage in males than females [68], which may partially explain observedproductivity differences concerning the proxy [69]. Variable incentive strengths could beeasily modeled as variations in goal scale (or prospect function variability).Incorporating such variability could inform on the outcomes of empirically observeddifferences between genders or in ‘machiavellanism’ scales [70, 71]. Accordingly, oursimple formalization of an agent-decision mechanism is i) neuroeconomically plausibleand ii) captures many important empirical findings. However, a large range ofadditional complexities could be integrated into the model, in order to investigate theirimplications. The most fruitful way to pursue this would, in our view, be through closeinteraction between modeling and experimental approaches.
The sociological/ cultural perspective explicitly acknowledges the complexity of culturalpractices and the degree to which these are determined beyond the individual level. Wehave drawn from the model by [5], in order to capture the slow evolution of a large bodyof cultural information implicit in professional practices. Additional, factors which mayprove highly relevant to long and short term outcomes, are the network structureOctober 3, 2019 35/51etween agents and the precise formulation of information transmission between them.In our model, all agents observe the noisy proxy performances of all other agents,implying full network connectivity. Though this may seem unrealistic, the idea thatprofessionals are generally aware of their approximate competitive standing seemsjustified. To verify robustness against the full connectivity assumption, we probed ifrestricting the sampled proxy performances to 9 or 22 neighboring agents alteredoutcomes, but this had no effects other than increasing variability (not shown). Futuremodels could further explore system dynamics if practice angles are influenced by socialforces such as the formation of social norms [72]. While, social-norm transmission isimplied in the hereditary transmission of practices modeled here, they may also bedetermined more directly through neighboring agents (see e.g. [60]). This is likely tointroduce additional nonlinear effects in space and time, as locally normative practicesemerge or collapse. Notably, similar mechanisms could directly impact the knowledgeabout, and valuation of, the societal goal ( gs ). For instance, Benabou et. al., [60] haverecently modeled the spread of moral narratives through populations. Such mechanismscould be included to endogenize gs as a locally determined variable for each agent.Another partially sociological factor, that has here been simplified into a singleexogenous variable is the goal angle, i.e the informational relation between proxy andgoal. In real systems, the proxy will be determined by the institutions creating it. Fromthe complex adaptive systems perspective, such institutions are best viewed asautopoietic systems whose existence and stability is not necessarily related to any societal goal [61, 73]. A variation of this view is that competitive institutions areprimarily self-reinforcing power-structures, and that the societal goal may serve only astheir public justification. We would argue that the public justification of the systemshould be viewed as its societal goal. Moreover, the autopoiesis of institutions is likely anecessary requirement for their existence and hence also for any contribution toward thesocietal goal. Modeling societal institutions as autopoietic entities and probing how theymay be brought to additionally serve some abstract societal goal, could help tounderstand how the goal angle may actually arise. Accordingly, our simpleformalization of cultural evolution captures some important sociological mechanisms,but is dramatically simplified. Nevertheless, we believe that the progressive culturalevolution toward the proxy, described here, should be a central component of any theoryOctober 3, 2019 36/51f proxy-based societal competition.In sum, our agent-based model captures a range of crucial implications ofproxy-based societal competition. It provides a first attempt to integrate two of thecentral arising forces, and it’s central mechanisms are amenable to experimentalverification. Finally, it provides a versatile framework to explore additional complexities,ranging from agent-level decision biases to network effects or implications of agentheterogeneity. In this section we will discuss some broader implications of our theory. We will firstoutline some striking policy and moral implications of the central premise. Next, we willoutline how proxy-based competitions may interlock and act over different scales, e.g. inmarkets. A final brief section will suggest how we can systematically assess thecorruption of real systems, proposing that findings from behavioral economics can beleveraged into predictions of corrupt patterns.
Interestingly, a number of familiar policy arguments can be directly derived from thesetup of proxy-based competition. For instance, one party may focus on the divergencebetween proxy and societal goal, advocating costly improvement of proxies or regulationof specific proxy-oriented practices. An opposing party may suggest that regulation orimproving proxies will not be cost effective, and that unilateral reorientation toward anambiguous societal goal will result in i) losing competition and ii) no change in proxyorientation at the system level. The present theory implies that both arguments resultfrom a deep intuitive understanding of the system and that a confrontation of bothviews is likely necessary for an optimal regulation of that system. Moreover, it suggests,that the optimal degree and design of regulation will depend on the specifics of asystem, where importantly the degree of corruption, the potential cost/benefit ofimproving the proxy, and the necessity for coordinated rather than unilateral action,can be assessed systematically and scientifically (see e.g. section 5.1.3). One specific,perhaps somewhat counter-intuitive policy prescription to mitigate corruptive pressures,October 3, 2019 37/51hile avoiding associated costs are partial lotteries. Intriguingly, these have beensuggested for several domains independently such as politics and science [26, 74]. Finally,it is important to again note that the institutions which create the proxy should at leastpartially be viewed as self-reinforcing power structures (section 5.1.5). This is simplybecause they are likely to be primarily designed by current proxy winners (professionalswhich have excelled within the current system). Accordingly, we might generally expectsome inertia in societal systems where current proxy winners would decrease theircompetitive advantage (or the valuation of their life legacy) by questioning the proxy.
Another simple yet profound implication of the central setup of proxy-basedcompetition concerns the moral structure of decision problems. So far we haveconsidered only an egoistic incentive, and an incentive toward an abstract societal goal.However, individual competitive success is often linked to others, e.g. one’s family, teamor employees. In such cases the ‘egoistic’ action may become a moral imperative. Forinstance, a lead investigator may have to weigh a questionable research practice againstthe social responsibility of securing funding for her employees. Note, that due to theinherent ambiguity and temporal gradients between proxy and goal, this will tend toimply weighing a relatively certain social harm against a relatively uncertain societalharm. This arguably has direct moral implications. Similarly, a CEO may have toweigh her responsibility toward her employees against ambiguous environmental orsocial damage. Indeed, in practice, securing jobs is frequently invoked as a justificationfor morally problematic practices, such as selling arms, damaging the environment, oreconomizing on worker safety and well-being. Such cases demonstrate that this is not atheoretical argument, but a central part of current public moral discourse. The presenttheory implies that this type of moral dilemma will tend to be automatically created byproxy-based competition.
So far we have referred to the institutions/mechanisms which create the proxy as singlecoherent entities. However, this was an operational choice. In practice theseinstitutions/mechanisms are often complex and may contain proxy-based competitionOctober 3, 2019 38/51hemselves. For instance, the allocation of publication space in high impact journals isdetermined through competition between authors but also between journals. Suchnested, or interlocked proxy-based competitions may counteract or amplify corruption,depending in part on the overlap between informational deficits of the respective proxies.Generally, increasing the scale and complexity of a system is likely to increase thenumber of failure modes and thereby the scope for corruption [46]. However, the marketmechanism arguably represents a system of interlocked competitions which powerfullyprevents many kinds of corruption. For instance, in firms, competition for consumerscounterbalances competition for capital leading to a product price which incorporatessubstantial information about consumer valuation as well as production cost.Furthermore, the distributed, continuous, and direct (incentive compatible) processes ofmarkets are likely to prevent many sources of information loss. For instance, marketscollect information directly and continuously from consumers rather than fromrepresentatives in preset intervals. Nevertheless, above we have suggested whole marketeconomies might become proxy-oriented, implying some degree of conservation oramplification of corruption. Among industrialized nations, this suggestion is supportedby macro-level similarities of the observed phenomena, namely the fact that exponentialeconomic growth leads to a statistically negligible changes in subjective as well asobjective measures of well-being (e.g. [13, 17, 18, 21, 75]). This is consistent with datashowing that within countries subjective well-being saturates (and sometimes reverses)with increasing income (e.g. [75, 76]). However, the self-referentiality of proxyperformance in competition suggests that economic growth (proxy-performance) will bepursued regardless. An evolutionary/neuroscientific understanding of human decisionmaking suggests how evolutionary mismatch, status seeking behaviors, and/orpreference learning dynamics could be exploited to maintain economic growth withoutcontributing to human well-being [77]. In the following, we will go through a concreteexample of how evolutionary mismatch and preference learning could be exploited. Theexample should furthermore demonstrate how the superior efficiency of marketmechanisms may amplify rather than counteract corruption across scales. Assumeconsumers display an excessive preference for high sugar products due to evolutionarymismatch. Excessive here means, that if they were to make a fully informed decision,including all aspects of health and long term well-being, they would choose a lower levelOctober 3, 2019 39/51f consumption. Producers may gain an advantage in competition for consumers byincreasing sugar content and obscuring information about negative long term healthconsequences. Investors may gain a competitive advantage by investing in producersperforming these two practices, and thus generating higher profits. If we accept thesocietal goal of the food-industry, including stakeholders at all levels, as maximizingconsumer welfare, then this implies that corruption at one level entails promotingcorruption at other levels. For instance companies at all levels have an incentive toobscure detrimental health consequences of high sugar products. This is an example ofsynergistic corruption paths for proxy-competitions at multiple scales. Similar perversescenarios are plausible for other addictive products (eg. opioids, gambling, etc). Wesuspect that obscuring or removing information about detrimental effects of proxyorientation of a shared proxy represents a frequent basis for amplifying corruptionbetween interacting proxy-competitions. For instance, a number of industries maintainan elaborate and costly network of institutions designed to obscure information aboutdetrimental long term health and environmental consequences of their products [78, 79].Indeed, it appears this network has been instrumental in preventing action againstglobal warming. In this context, we want to note that the theory presented here isclosely related to public goods dilemmas, where the socially optimal action (nodefection) corresponds to goal orientation and corruption corresponds to coordinationfailure [46, 80]. Indeed, the payoff matrix in a public goods (or prisoners) dilemma canbe disaggregated into a goal and a proxy component, showing how the typical payoffpatterns may naturally arise in proxy based competition. The implication is that anyproxy-based competition is likely to create a public goods dilemma to some degree(again depending on the information captured in the proxy).
Finally, we want to suggest how the present theory may guide diagnosis andintervention for real societal systems (applied proxyeconomics). A general strategywould be to systematically investigate informational idiosynchrasies of proxy-generationto predict patterns of corruption. Such predictions would allow to diagnose corruptionwithin societal systems, as well as to design mitigation strategies. For instance, we haverecently leveraged the scientific phenomenon of positve-publication bias to make a rangeOctober 3, 2019 40/51f otherwise baffling predictions concerning observed scientific sample sizes [23].Positive publication bias here is an informational idiosynchracy of the proxy (thepublication record of an author), in that it determines which information is capturedand which is lost. Including this idiosyncrasy into a simple model then allowed to makepredictions about patterns of sample size choices, which could then be compared tocompeting goal-orientation accounts as well as empirical data. It has further, recentlybeen used to explore mitigation strategies [81]. Similarly, we believe decision biasesidentified in behavioral economics can be systmatically leveraged to predict patterns ofcorruption within societal systems. For instance, excessive proxy-orientation would beexpected to prominently shape consumer choice architectures such that they capitalizeon known decision biases to increase profit [22, 82, 83]. Indeed, behavioral economistsemphasize that there is no neutral choice architecture, and suggest that we shouldconsciously and transparently structure choice architectures to systematicaly nudgecitizens into beneficial behavior [83]. Critics argue that this approach is paternalisticand should be avoided. The present theory suggests, that in the absence of consciousand transparent structuring of choice architectures, proxy-measures will be the principalforces. Accordingly, behavioral economics can be used to derive fine grained, falsifiablepredictions of actual corruption patterns. Prevalent marketing and advertising practicescould be readily analyzed with respect to their implications for proxy- and goalperformance, given known decision biases. For instance, advertisements have recentlybeen used to analyze behavioral market failure in the payday lending market [84].Behavioral economics can then be further used to design choice architectures, whichmitigate decision biases and therewith corruption.
We have outlined a transdisciplinary theory of proxyeconomics, which applies whenevera societal system employs proxy measures to mediate competition towards an abstractgoal. Our agent-based computational model synthesizes several major insights acrossdisciplines into a formal framework, suggesting a central role of competition on effortexpenditure, individual utility, selection and cultural evolution. Accordingly, there maybe an optimal level of competition, depending on the complexity of the system and theOctober 3, 2019 41/51references of the participating agents. Furthermore, we have demonstrated, that anindividual-level decision mechanism, which includes an intrinsic goal-oriented motivationcomponent, can bound the evolution to corrupt practices. More generally, the theoryprovides a conceptual and predictive framework to empirically assess the degree towhich actual societal systems may be wastefully or detrimentally oriented towards proxymeasures. Importantly, it includes a mechanistic account of how a system can remain locked in to a relatively proxy oriented state, even if all individual agents know of, andvalue, the actual societal goal. This may help to explain and address diverse phenomenasuch as the scientific reproducibility crisis or inaction to the threat of global warming.
Acknowledgements
I thank Heinz Beck for continuous support. I further thank Christina Selenz, EverardBraganza, Johnathan and Laura Ewell, Klaus G. Troitzsch and Gerben Ter Riet andthe participants of various conferences for many helpful comments. The project wasfunded through the VW-Foundation program
Originalitaetsverdacht . Supporting information
S1 Code Main model code , Python3 code, based on mesa framework.
S2 Code Batch run & figure generation code: Competition , Code to run afamily of models, analyze outputs and create figures, with competiton as the main inputparameter of interest.
S3 Code Batch run & figure generation code: Goal angle , Code to run afamily of models, analyze outputs and create figures, with goal angle as the main inputparameter of interest.
S4 Code Batch run & figure generation code: Goal scale , Code to run afamily of models, analyze outputs and create figures, with goal scale as the main inputparameter of interest.October 3, 2019 42/51 , Code to runa family of models, analyze outputs and create figures, with the number of agents in thepopulation as the main input parameter of interest.
S6 Code Batch run & figure generation code: practice mutationamplitude , Code to run a family of models, analyze outputs and create figures, withpractice mutation amplitude as the main input parameter of interest.
S7 Code Batch run & figure generation code: Selection pressure , Code torun a family of models, analyze outputs and create figures, with selection pressure asthe main input parameter of interest.
S8 Code Batch run & figure generation code: talent variability , Code torun a family of models, analyze outputs and create figures, with talent standarddeviation as the main input parameter of interest.
References
1. Campbell DT. Assessing the impact of planned social change. Evaluation andProgram Planning. 1979;2(1):67–90. doi:10.1016/0149-7189(79)90048-X.2. Goodhart CAE. Problems of Monetary Management: The UK Experience. In:Monetary Theory and Practice. London: Macmillan Education UK; 1984. p.91–121.3. Strathern M. ’Improving ratings’: audit in the British University system.European Review Marilyn Strathern European Review Eur Rev.1997;55(5):305–321. doi:10.1002/(SICI)1234-981X(199707)5:33.0.CO;2-4.4. Manheim D, Garrabrant S. Categorizing Variants of Goodhart’s Law; 2018.Available from: https://arxiv.org/abs/1803.04585v3 .5. Smaldino PE, McElreath R. The natural selection of bad science. Royal SocietyOpen Science. 2016;3(9):160384. doi:10.1098/rsos.160384.October 3, 2019 43/51. Nichols SL, Berliner D. The Inevitable Corruption of Indicators and EducatorsThrough High-Stakes Testing. East Lansing: The Great Lakes Center forEducation Research & Practice; 2005.7. Koretz DM. Measuring up : what educational testing really tells us. HarvardUniversity Press; 2008.8. Wilsdon J, Allen L, Belfiore E, Campbell P, Curry S, Hill S, et al. Metric Tide -Report of the Independent Review of the Role of Metrics in Research Assessmentand Management; 2015.9. Fire M, Guestrin C. Over-Optimization of Academic Publishing Metrics:Observing Goodhart’s Law in Action; 2018. Available from: http://arxiv.org/abs/1809.07841 .10. B´enabou R, Tirole J. Bonus Culture: Competitive Pay, Screening, andMultitasking. Journal of Political Economy. 2016;124(2):305–370.doi:10.3386/w18936.11. Baker M. 1,500 scientists lift the lid on reproducibility. Nature.2016;533(7604):452–454. doi:10.1038/533452a.12. Fochler M, Felt U, M¨uller R. Unsustainable Growth, Hyper-Competition, andWorth in Life Science Research: Narrowing Evaluative Repertoires in Doctoraland Postdoctoral Scientists’ Work and Lives; 2016.13. Stiglitz JE, Sen A, Fitoussi JP. Mismeasuring our lives : why GDP doesn’t addup : the report. New Press; 2010.14. Jackson T. Prosperity without Growth. Routledge; 2009.15. Gigerenzer G, Gray CM. Bessere ¨Arzte, bessere Patienten, bessere Medizin :Aufbruch in ein transparentes Gesundheitswesen. Medizinisch WissenschaftlicheVerlagsgesellschaft; 2013.16. Gross K, Bergstrom CT. Contest models highlight inherent inefficiencies ofscientific funding competitions. PLOS Biology. 2019;17(1):e3000065.doi:10.1371/journal.pbio.3000065.October 3, 2019 44/517. Kubiszewski I, Costanza R, Franco C, Lawn P, Talberth J, Jackson T, et al.Beyond GDP: Measuring and achieving global genuine progress. EcologicalEconomics. 2013;93:57–68. doi:10.1016/J.ECOLECON.2013.04.019.18. Wilkinson RG, Pickett K. The Spirit Level: Why More Equal Societies AlmostAlways Do Better. Allen Lane. 2009; p. 330.19. J M van den Bergh JC. A third option for climate policy within potential limitsto growth. Nature Climate Change. 2017;7. doi:10.1038/NCLIMATE3113.20. Stevenson B, Wolfers J. Economic Growth and Subjective Well-Being:Reassessing the Easterlin Paradox. Brookings Pap Econ Act. 2008;39:1–102.doi:10.3386/w14282.21. Kahneman D, Deaton A. High income improves evaluation of life but notemotional well-being. Proceedings of the National Academy of Sciences of theUnited States of America. 2010;107(38):16489–93. doi:10.1073/pnas.1011492107.22. Gabaix X, Laibson D. Shrouded Attributes, Consumer Myopia, and InformationSuppression in Competitive Markets. Cambridge, MA: National Bureau ofEconomic Research; 2005.23. Braganza O. Economically rational sample-size choice and irreproducibility; 2019.Available from: http://arxiv.org/abs/1908.08702 .24. Poku M. Campbell’s Law: implications for health care. Journal of health servicesresearch & policy. 2016;21(2):137–9. doi:10.1177/1355819615593772.25. Gowdy J, Mazzucato M, van den Bergh JCJM, van der Leeuw SE, Wilson DS.Shaping the Evolution of Complex Societies. In: Wilson DS, Kirman A, editors.Complexity and Evolution. Cambridge, MA: The MIT Press; 2016. p. 327 – 351.26. Pluchino A, Garofalo C, Rapisarda A, Spagano S, Caserta M. Accidentalpoliticians: How randomly selected legislators can improve parliament efficiency.Physica A: Statistical Mechanics and its Applications. 2011;390(21-22):3944–3954.doi:10.1016/J.PHYSA.2011.06.028.October 3, 2019 45/517. Hicks D, Wouters P, Waltman L, de Rijcke S, Rafols I. Bibliometrics: The LeidenManifesto for research metrics. Nature. 2015;520(7548):429–431.doi:10.1038/520429a.28. Open Science Collaboration. Estimating the reproducibility of psychologicalscience. Science. 2015;349(6251):aac4716–aac4716. doi:10.1126/science.aac4716.29. Brembs B, Button K, Munaf`o M. Deep impact: unintended consequences ofjournal rank. Frontiers in Human Neuroscience. 2013;7.doi:10.3389/fnhum.2013.00291.30. Dechenaux E, Kovenock D, Sheremeta RM. A survey of experimental research oncontests, all-pay auctions and tournaments. Experimental Economics.2014;18(4):609–669. doi:10.1007/s10683-014-9421-0.31. Amodei D, Olah C, Steinhardt J, Christiano P, Schulman J, Man´e D. ConcreteProblems in AI Safety; 2016. Available from: http://arxiv.org/abs/1606.06565 .32. Flake GW. The computational beauty of nature : computer explorations offractals, chaos, complex systems, and adaptation. MIT Press; 1998.33. Hochman G, Gl¨ockner A, Fiedler S, Ayal S. “I can see it in your eyes”: BiasedProcessing and Increased Arousal in Dishonest Responses. Journal of BehavioralDecision Making. 2016;29(2-3):322–335. doi:10.1002/bdm.1932.34. Pittarello A, Leib M, Gordon-Hecker T, Shalvi S. Justifications shape ethicalblind spots. Psychological science. 2015;26(6):794–804.doi:10.1177/0956797615571018.35. Chugh D, Kern MC. A dynamic and cyclical model of bounded ethicality.Research in Organizational Behavior. 2016;36:85–100.doi:10.1016/J.RIOB.2016.07.002.36. Holmstrom B. Agency costs and innovation. Journal of Economic Behavior &Organization. 1989;12(3):305–327. doi:10.1016/0167-2681(89)90025-5.October 3, 2019 46/517. Kahneman D, Tversky A. Prospect Theory: An Analysis of Decision under Risk.Econometrica. 1979;47(2):263. doi:10.2307/1914185.38. Mishra S. Decision-Making Under Risk. Personality and Social PsychologyReview. 2014;18(3):280–307. doi:10.1177/1088868314530517.39. Delgado MR, Schotter A, Ozbay EY, Phelps EA. Understanding overbidding:using the neural circuitry of reward to design economic auctions. Science (NewYork, NY). 2008;321(5897):1849–52. doi:10.1126/science.1158860.40. Nieken P, Sliwka D. Risk-Taking Tournaments: Theory and ExperimentalEvidence. IZA Working Paper. 2008;No. 3400.doi:10.1111/J.0042-7092.2007.00700.X.41. Gonzales J, Mishra S, Camp RD. For the Win: Risk-Sensitive Decision-Makingin Teams. Journal of Behavioral Decision Making. 2017;30(2):462–472.doi:10.1002/bdm.1965.42. Holmstrom B, Milgrom P. Multitask Principal-Agent Analyses : IncentiveContracts , Asset Ownership , and Job Design. Journal of Law , Economics , &Organization. 1991;7(January 1991):24–52.43. Glimcher PW. Proximate Mechanisms of Individual Decision-Making Behavior.In: Wilson DS, Kirman A, editors. Complexity and Evolution: Toward a NewSynthesis for Economics. vol. 1. The MIT Press; 2016.44. McElreath R, Boyd R. Mathematical Models of Social Evolution. University ofChicago Press; 2007.45. Fu Q, Ke C, Tan F. “Success breeds success” or “Pride goes before a fall”?:Teams and individuals in multi-contest tournaments. Games and EconomicBehavior. 2015;94:57–79. doi:10.1016/J.GEB.2015.09.002.46. Manheim D. Overoptimization Failures and Specification Gaming in Multi-agentSystems; 2018. Available from: https://arxiv.org/abs/1810.10862v2https://arxiv.org/abs/1810.10862v2