Fairness at Equilibrium in the Labor Market
aa r X i v : . [ c s . G T ] J u l Fairness at Equilibrium in the Labor Market
Lily Hu
SEASHarvard UniversityCambridge, [email protected]
Yiling Chen
SEASHarvard UniversityCambridge, [email protected]
ABSTRACT
Recent literature on computational notions of fairness has beenbroadly divided into two distinct camps, supporting interventionsthat address either individual-based or group-based fairness. Ratherthan privilege a single definition, we seek to resolve both withinthe particular domain of employment discrimination. To this end,we construct a dual labor market model composed of a Tempo-rary Labor Market, in which firm strategies are constrained to en-sure group-level fairness, and a Permanent Labor Market, in whichindividual worker fairness is guaranteed. We show that such re-strictions on hiring practices induces an equilibrium that Pareto-dominates those arising from strategies that employ statistical dis-crimination or a “group-blind” criterion. Individual worker repu-tations produce externalities for collective reputation, generatinga feedback loop termed a “self-fulfilling prophecy.” Our model pro-duces its own feedback loop, raising the collective reputation ofan initially disadvantaged group via a fairness intervention thatneed not be permanent. Moreover, we show that, contrary to pop-ular assumption, the asymmetric equilibria resulting from hiringpractices that disregard group-fairness may be immovable withouttargeted intervention. The enduring nature of such equilibria thatare both inequitable and Pareto inefficient suggest that fairness in-terventions are of critical importance in moving the labor marketto be more socially just and efficient.
ACM Reference format:
Lily Hu and Yiling Chen. 2017. Fairness at Equilibrium in the Labor Mar-ket. In
Proceedings of Fairness, Accountability, and Transparency in MachineLearning, Halifax, Nova Scotia, Canada, August 14–17 (FAT/ML ’17),
Work in the growing field of algorithmic fairness proposes inter-ventions of discretion on algorithmic decision-makers when issuesof bias and discrimination are potentially at stake. The literatureis varied but may be broadly categorized as either proposing so-lutions that defend fairness at the individual level (similar indi-viduals are treated similarly) [1] or at the group level (groups areawarded proportional representation) [2, 3]. This paper constructs
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FAT/ML ’17, Halifax, Nova Scotia, Canada © 2017x ACM. 978-x-xxxx-xxxx-x/YY/MM...$15.00DOI: 10.1145/nnnnnnn.nnnnnnn a model of discrimination in the labor market along with fairnessconstraints that address both notions of fairness.As we focus on the particular domain of labor market dynam-ics, our paper draws upon an extensive literature in economics.The theory of statistical discrimination, originally set forth in twoseminar papers by Phelps [4] and Arrow [5], explains group-unfairoutcomes as the result of rational agent behaviors that lock a sys-tem into an unfavorable equilibrium. In the basic model, workerscompete for a skilled job with wage w . Skill acquisition requiresworkers to expend an investment cost of c , which is distributedaccording to a function F . Thus, a worker’s investment decision isan assessment of her expected wage gain compared with her costof investment. Firms seek information about a worker’s hidden ability level but can only base their hiring decisions on observableattributes: her noisy investment signal and group membership. Thefirm’s response to this informational asymmetry is to update its be-liefs about a worker’s qualifications by drawing on its prior for hergroup’s ability levels. Therefore, if a firm holds different priors fordifferent groups, it will also set different hiring thresholds. Further,since these distinct thresholds are observed and internalized byworkers, they adjust their own investment strategies accordingly—individuals within the unfavored group will lower their investmentlevels, and individuals in the favored group will continue to investat a high level. Notably, even when the distribution of costs F isthe same for each group , an asymmetric equilibrium can arisein which groups invest at different levels, further informing firms’distinct priors. In other words, rational workers and firms best-respond in ways that exactly confirm the others’ beliefs and strate-gies, and thus, the discriminatory outcome is “justified.”This equilibria perspective challenges our mission in designingconstraints to ensure fairness. For one, given that statistical dis-crimination and machine learning in general rely on data that har-bor historical inequalities, isolated algorithmic interventions thatdo not consider the dynamics of the particular system in whichthey are embedded will often fall short of addressing the self-perpetuatingnature of biases. We cannot look forward toward a future of fair-ness without first looking backwards at the conditions that havecaused such inequalities. Thus if the observed outcomes them-selves are trapped in a feedback loop, fairness constraints shouldaim to first jolt the system out of its current steady-state, and sec-ond, launch it on a path towards a preferable equilibrium. As such,a successful approach must consider fairness in situ. This paperpresents a dynamic model that is domain-specific and a fairnessintervention that is system-wide .In our model, workers invest in human capital, enter first a Tem-porary Labor Market (TLM), and then transition into a Permanent This has been the standard assumption in the statistical discrimination and laboreconomics literature since Arrow [5].
AT/ML ’17, August 14–17, Halifax, Nova Scotia, Canada Lily Hu and Yiling Chen
Labor Market (PLM) . We use this partition to impose a constrainton firms’ hiring practices in the TLM that enforces group-fairness.However, the restriction need not apply in the PLM, and firms nat-urally select best-response hiring strategies that guarantee individ-ual worker fairness. Our model of the labor market is reputational —a worker carries an individual reputation, which is a history of herpast job performances, and belongs to one of two groups that hasa collective reputation, summarized by the proportion of workersin the group producing “good” outcomes.Working within this model, we show that by imposing an outcomes-based fairness constraint on firms’ hiring strategies in the TLM, theresulting steady-state equilibrium in the PLM is group-symmetricand Pareto-dominates the PLM asymmetric equilibria that arisedue to either group-blind optimal hiring or statistical discrimina-tory hiring. Within this model, our fairness intervention is con-structed to exploit the complementary nature of individual andcollective reputations such that the system produces a feedbackloop that incrementally addresses initial inequalities in group so-cial standing. As such, our TLM fairness intervention is not permanent—the guarantee of group-level fairness gradually morphs into a guar-antee of individual-level fairness as group equality is restored.This paper’s application of notions of group-based and individ-ual fairness to a reputational model of statistical discriminationin the labor market melds the perspectives and techniques of la-bor economics with the motivations and framework of algorith-mic fairness. Our proposed fairness constraints address individualand group fairness in separate treatments in the labor market thatare nonetheless linked via a complementarity feedback loop. Thus,these constraints are aimed at creating system-wide conditions offairness that are self-sustaining. As algorithms are increasingly de-ployed to make employment-related decisions, we hope our worksheds a light on the equilibrium nature of discriminatory outcomesand may inform the design and implementation of fairness con-straints.In Section 2, we present our model of labor market dynamicsand the imposed fairness constraint. Section 3 contains an overviewof the equilibria results of the model under the fairness require-ment along with a comparison against equilibria arising from tworational hiring strategies free from such a constraint. The paperends with a reflection on the general equilibrium tendencies of dis-crimination and their implications on the design of fairness con-straints. We also offer some comments on the dynamic feedbackeffects that are inherent features of persistent inequalities and thechallenges they issue upon future work in algorithmic fairness. Within the algorithmic fairness literature, Zemel et al. [7] addressboth group and individual notions of fairness by constructing amap of agent data to an intermediate layer of clusters that eachpreserve statistical parity (ensuring group fairness) while obfuscat-ing protected attributes. A second mapping to classification basedon cluster assignments then allows “similar” agents to be treatedsimilarly. This dual-map approach corresponds to our TLM and This type of worker movement in a segmented market is common in the labor eco-nomics literature. Of these, our work shares a structure and purpose most similar toKim & Loury [6]. However, notably their model is one of statistical discrimination,while ours explicitly requires group-fairness.
PLM fairness constraints. Related work has sought distance met-rics to guide the initial mapping [1], but since criteria for similarityvary by domain, such general approaches often face obstacles ofapplication. We hope that our paper’s concentrated treatment ofdynamics in the labor market addresses this concern. We answera call by Friedler et al. [8] to specify a particular world view offairness within a domain and classification task. Our model startswith the important stance of inherent equality between groups. Assuch, any indications of difference in group ability distribution be-cause of observable investment decisions or outcomes is due tounequal societal standing, producing myriad secondary effects ofinequality, rather than fundamental differences in the nature of theindividuals. Following the vocabulary used in Friedler et al., ourmodel of group differences in the labor market subscribes to theaxiomatic assumption of “We’re all equal.”
We disentangle the concerns of group-based and individual fair-ness by constructing a dual labor market that addresses each no-tion of fairness independently. A firm’s hiring process in the Tem-porary Labor Market (TLM) will guarantee group-based fairness;the mechanisms of the Permanent Labor Market (PLM) will ensureindividual fairness. While the labor market is divided as a whole,their dynamics are not separable—workers flow from the TLM tothe PLM, wages are labor-market-wide, and individual worker rep-utations in the PLM produce externalities for the collective groupreputations that play a key role in individual’s pre-TLM investmentdecisions.
Consider a society of n workers who pass through the labor mar-ket sequentially at times t = , , ... . The labor markets maintaina constant relative size: m proportion of the workers reside in theTLM, and 1 − m reside in the PLM. Movement is governed by Pois-son processes—workers immediately replace departing ones in theTLM, transition from the TLM to the PLM according to the param-eter κ , and leave the PLM at rate λ .Each worker belongs to one of two groups µ ∈ { B , W } withinwhich the distribution of individual abilities is identical, describedby the CDF F ( θ ) . Firms hire and pay workers based on expectedperformance, awarding wage w ( д t ) for a “good” worker, where д t gives the proportion of “good” workers in the PLM at time t . This isformalized by assigning workers to either skilled or unskilled taskswith distinct wages. Thus for simplicity, “bad” workers are alsohired but are assigned to the unskilled task and paid a wage normal-ized to 0. The wage premium w ( д t ) is decreasing in д t , since as therelative supply of “good” workers increases, imperfect worker sub-stitutability lowers their marginal productivity, thus decreasingwage. We impose a minimum wage ¯ w such that lim д t →∞ w ( д t ) = ¯ w and a maximum wage ¯ w such that lim д t → w ( д t ) = ¯ w . First, a worker i at time t chooses to invest in human capital η i > w ( д t ) and her personal Workers are boundedly rational and unable to anticipate future wage dynamics. eedback to Fairness FAT/ML ’17, August 14–17, Halifax, Nova Scotia, Canada cost function for investment, c π µt ′ ( θ i , η i ) , which is a function ofher individual ability θ i , group µ “reputation,” π µt ′ where t ′ repre-sents the time interval [ t − τ , t ] , and selected level of investment η i . The collective reputation gives the proportion of “good” work-ers of group µ in the interval t ′ = [ t − τ , t ] , where the parameter τ controls the time-lag effect of a group’s previous generations’reputation on a member’s investment cost in the present. c is de-creasing in θ , increasing in η , and ∀ π µt ′ ≤ π νt ′ , c π µt ′ ( θ i , η i ) is a posi-tive monotonic transformation of c π νt ′ ( θ i , η i ) . The incorporation ofgroup membership into an individual’s cost function is informedby the vast empirical literature that demonstrates the differentialexternalities produced by groups of differential social standing [9].Investment in human capital operates as an imperfect signal,and workers have a hidden true type, qualified or unqualified, ρ ∈{ Q , U } with proportion γ Q being qualified, and 1 − γ Q being unqual-ified. For investment level η , P ( Q | η i ) ≥ P ( Q | η j ) , ∀ η i > η j . Thus,a firm’s TLM hiring strategy is a mapping H T : R > { B , W } →{ , } such that the decision for agent i is based only her observedinvestment level η i and group membership µ . Definition 2.1 (Group Fairness).
A hiring strategy H is group-fair if and only if for all agents i , the event of i being hired is condition-ally independent of her group-membership, and thus P ( W ) = P ( W |H ( i )) and P ( B ) = P ( B |H ( i )) Group-fair hiring results in employee representation that satis-fies statistical parity. We impose this fairness constraint on hir-ing strategies in the TLM, requiring firms to move beyond “group-blind” practices.
Once hired, worker i exerts on-the-job effort e ∈ { H , L } , whichstochastically produces an observable outcome o ∈ { G , B } that im-pacts her individual reputation and thus future reward. e = L isfree, but exerting e = H is costly with c ( θ i , ρ ) as a function ofqualification status and ability level. Effort exertion cost functionshere are distinct from the previous investment cost functions—theformer are pertinent to the PLM and differ by qualification status,whereas the latter relate to the TLM and differ by group member-ship. Effort is more costly for unqualified individuals and c ( θ i , U ) ≥ c ( θ i , Q ) , ∀ θ , and high effort increases the probability of a good out-come G . Thus if p ρ , e gives the probability of achieving outcome G with qualifications ρ and effort level e , we have the followinginequalities p Q , H > p Q , L ; p U , H > p U , L ; p Q , L > p U , L Notably p Q , H = p U , H . Since the effect of qualifications on exert-ing high effort is already incorporated in its cost, we write bothquantities as p H .A worker keeps the same TLM job until the Poisson processwith parameter κ selects her to move into the PLM, where firms areable to observe her history of job outcomes, including her TLM per-formance. A worker i ’s time t history is h ti = ( o i , , o i , , ..., o i , t − ) ,a sequence of outcomes that corresponds to her past performances.Firms are boundedly rational and distill a worker’s past histories “Ability” should be broadly interpreted as encapsulating all personal attributes thatbear on success within traditional institutions of education and work. to her “individual reputation” Π ti , which gives the proportion ofoutcomes G ∈ h ti . A firm’s PLM hiring strategy is a mapping H P : [ , ] → { , } such that the decision regarding agent i issolely a function of Π ti . Similar to the H T , the optimal H P is alsobased on a threshold strategy such that for a chosen reputationthreshold ˆ Π t at time t, ∀ i such that Π ti ≥ ˆ Π t , H ( i ) =
1, and in-versely, ∀ i such that Π ti < ˆ Π t , H ( i ) = Due to feedbacks between individual and collective reputations,multiple equilibria exist. To focus on a particular equilibrium, wesuppose that firms in the PLM prefer to only hire workers who con-sistently exert high effort. We start by describing PLM strategiesand then analyze firms’ and workers’ best responses together.A worker in the PLM is both history-cognizant as well as future-anticipatory. Agent i ’s strategy is a selection of time, reputation,wage, and hiring threshold-dependent probabilities of effort exer-tion e ( Π ti ) . The discount factor δ incorporates workers’ present-bias as well as the possibility of exiting the market via the λ -ratePoisson process. Her exertion decisions are chosen according tothe expected marginal reward for a G outcome over a B outcomeat time t . R ( θ i , Π ti , ˆ Π t , д t ) = E h ∞ Õ j = t ( δ Φ j ) j w ( д t ) − ( e ( Π ji − e ( Π ji − j − )) c ( θ i , ρ ) i (1)where Φ j = ϕ (cid:16) e ( Π ji ) (cid:17) − ϕ (cid:16) e ( Π ji − j − ) (cid:17) with ϕ (cid:16) e ( Π ti ) (cid:17) = t + τ Õ k = (cid:6) ˆ Π t + τi ( t + τ )− Π ti t (cid:7) (cid:18) t + τk (cid:19) [ e ( Π ki ) p H + ( − e ( Π ki ) p ρ , L )] k (2) ∗ [ e ( Π ki )( − p H ) + ( − e ( Π ki )( − p ρ , L )] t + τ − k We simplify R ( θ i , Π ti , ˆ Π t , д t ) to R ∞ t . Φ j describes the dynamics ofagent i ’s individual reputation as a function of her effort exertionprobability at each possible previous level of reputation, e ( Π ji ) . Theexpectation is taken over wage paths w ( д t ) , and effort exertion isonly warranted if p H R ∞ t − c ( θ i , ρ ) ≥ p ρ , L R ∞ t . In the PLM, if firms wish to hire all and only workers who con-sistently exert high effort, their equilibrium strategy is to select areputation threshold ˆ Π t = p H ∗ t − ∆ ( δ ) where ∆ ( δ ) > δ . Under theparticular hiring strategy, there will be a steady-state wage ˜ w suchthat all workers with ability θ ρ > c − ρ ( ˜ w ) will exert effort H even iftheir history has “fallen behind” ˆ Π t . Although immediate rewardis not guaranteed, in the long-run, exertions of effort will be re-warded.However, in this setup in which employers observe reputations Π ti of outcomes up to t −
1, workers hold a first-mover advantage.
AT/ML ’17, August 14–17, Halifax, Nova Scotia, Canada Lily Hu and Yiling Chen
A worker i with reputation Π ti − t > ˆ Π t who has secured a job attime t may find it profitable to exert effort L given that she knowsthat she will be hired in the next round regardless of her round t outcome. Thus the optimal worker strategy entails exerting effortin a manner that maintains a reputation exactly oscillating aroundthe threshold ˆ Π t . In response, the firm will optimize its hiringthreshold ˆ h t = p H − ∆ ( δ ) by decreasing ∆ just enough to motivateconsistent high effort from these workers. As δ → ∆ →
0, andˆ Π t = p H such that workers always exert effort if they can afford todo so. All other workers exert low effort in each round. Thus at anytime t , given the firm’s reputation threshold ˆ Π t , its equilibriumPLM hiring strategy H P is a mapping such that if and only if aworker i has reputation Π ti > ˆ Π t , H P ( i ) =
1, else H P ( i ) = γ Q gives the proportion of candidates who are quali-fied, leaving 1 − γ Q who are unqualified. Then the proportion ofworkers in the PLM who produce good outcomes follows the re-cursive model b д t = p H [ − F ( c θ Q ) γ Q − F ( c θ U )( − γ Q )] + p Q , L F ( c θ Q ) γ Q (3) + p U , L F ( c θ U )( − γ Q ) where c θ ρ = c − ρ ( w ( д t − )( p H − p ρ , L )) (4)To determine wage dynamics, we consult TLM strategies beforeproceeding to the full equilibrium description.Since a TLM firm prefers high-ability candidates, optimal hiringfollows a threshold strategy: Given a hiring threshold ˆ η , ∀ i suchthat η i ≥ ˆ η , H T ( i ) =
1, and inversely, ∀ i such that η i < ˆ η , H T ( i ) =
0. However, since firms must abide by the group fairness hiringrule, if a firm aims to hire a fraction ℓ of all workers, investmentthresholds will be implicitly defined and group-specific. Proposition 1.
Taken together, firms’ equilibrium hiring strate-gies for the TLM and PLM, H T and H P , both satisfy group fairness. Given the time t TLM investment threshold ˆ η , all workers i with c π µt ′ ( θ i , ˆ η ) ≤ w ( д t ) will invest at exactly the level η i = ˆ η and besuccessfully hired, while all other workers will invest at level η i = д t , the proportion of workers producinggood outcomes in the TLM, follows the structure of (3) and (4). Thisis because a single-shot game imposes the same type of pressureas does the stringent threshold history hiring strategy in the PLM.In both, every outcome “counts.”Having elaborated upon the dynamics of both the TLM andPLM, we incorporate worker movement and combine the results toobtain a recursive relationship that governs the equilibrium pathof workers’ performance results, sequence of { д t } ∞ , from an ini-tial wage w . Note that the multiplicity of possible firm hiringstrategies produces a multiplicity of equilibrium paths, but giventhat firms are willing to hire only and all workers who consistentlyexert high effort, firm and worker equilibrium strategies are as pre-viously described, and there exists a unique equilibrium path. Theorem 3.1.
Suppose firms and workers play the following equi-librium strategies: A firm in the TLM hires a proportion m of workersunder the fairness constraint. A firm’s PLM strategy follows a time-invariant threshold rule ˆ h = p H − ∆ ( δ ) . A worker i of type ρ exertseffort in the TLM or PLM if and only if c ( θ i , ρ ) ≤ w ( д t − )( p H − p ρ , L ) .Under the above conditions, the proportion of workers producinggood outcomes at time t follows the recursive relationship д t = p H [ − F ( θ Q ) γ Q − F ( θ U )( − γ Q )] + p Q , L F ( θ Q ) γ Q (5) where θ ρ = c − ρ ( w ( д t − )( p H − p ρ , L )) The proportion д t is equal for each group B and W , satisfying group-fairness throughout the labor market. Under the TLM fairness constraint, groups with unequal ini-tial social standing will gradually approach the same reputationlevel according to time-lag τ . If the TLM fairness intervention oc-curs at t = t , and initially π Bt < π Wt , the function π Bt ′ where t ′ = [ t − τ , t ] is strictly increasing for all t > t until some timeT when π BT = π WT . The “self-confirming” loop is now co-optedfor group B ’s reputation improvement—collective reputation pro-duces a positive externality, lowering individual group members’cost functions, thus improving investment conditions for futureworkers, further raising individual and group reputation.We next compare this equilibrium under the TLM group-levelfairness constraint with equilibria under other rational hiring strate-gies that are not bound by any notions of fairness and show that un-der weak conditions, the fairness equilibrium is Pareto-dominant. Consider a TLM hiring strategy that is individual-based, operatingunder a pure equal-treatment philosophy. A firm hires a propor-tion q of workers by setting an investment level η defined implicitlyas q = ( − σ B )( − F ( c − W ( η )) + σ B ( − F ( c − B ( η )) (6)where σ B and 1 − σ B give the proportion of individuals in groups B and W respectively and the function c µ ( θ ) gives the group µ investment level function. Writing c − µ ( η ) = f θ µ for µ ∈ { B , W } ,these TLM ability thresholds are ranked with respect to the abilitythreshold under the fairness constraint θ as g θ W < θ < f θ B .In the PLM, the steady-state wage ˜ w enforces thresholds c − j ( ˜ w ) = c θ ρ for ρ ∈ { Q , U } . If c θ Q ∈ [ θ , f θ B ] , then asymmetric equilibria inwhich group reputations π µ differ may arise. Firms’ TLM hiringstrategies inequitably bound the proportion of high-ability work-ers in group B who are eligible to compete for jobs in the PLM,thus maintaining the reputation gap and differences in group in-vestment costs, producing the “self-confirming” equilibrium effect.Further, since 1 − F д ( c θ ρ ) < − F f ( c θ ρ ) where F д and F f are theability CDFs under the “group-blind” and fair regime respectively,firms that demand more workers strictly prefer the equilibria un-der the fairness constraint. This is because the effective higher abil-ity threshold for group B under this “group-blind” TLM strategyis inefficient, leaving behind an untapped resource of skilled and c θ Q > θ is not a stringent requirement since it is expected that the PLM thresholdis higher than the TLM threshold, else all Q workers would be hired at equilibrium. eedback to Fairness FAT/ML ’17, August 14–17, Halifax, Nova Scotia, Canada qualified individuals who would have otherwise been hired in thePLM. Even the hired workers in group W who are not hired in thefair regime do not fare better, since all such workers have abilitylevel lower than the PLM reputation threshold and are not hired atequilibrium anyway.Firms may also select hiring strategies that use statistical dis-crimination, in which priors regarding a worker’s observable at-tributes (such as group membership) are used to infer a particularindividual’s hidden attributes. However, when groups face differ-ing underlying investment cost functions, firms that statisticallydiscriminate may push the system toward Pareto-dominated equi-libria similar in kind to the asymmetric equilibria in the “group-blind” case.In particular, if TLM firms hold priors ξ B and ξ W about the twogroups’ capabilities, upon observing an agent’s group membership µ and investment level v , they will update their beliefs accordingto: P ( S | µ , v ) = p S ( v ) ξ µ p S ( v ) ξ µ + ( − ξ µ ) p U ( v ) (7)where p S ( v ) and p U ( v ) gives the probability of a skilled and un-skilled worker having investment level v respectively.If ξ W > ξ B , then P ( S | W , v ) > P ( S | B , v ) , and the groups facedifferent incentive compatibility constraints. As Coate & Loury[11] show, self-confirming asymmetric equilibria also exist underthis regime, and lower investment levels within the group withlower social standing are justified by firms’ more stringent hiringstandards. These TLM choices have ramifications in the PLM thatmirror the Pareto-dominated results under “group-blind” hiring. Given the specific nature of demands in fairness, domain-specificapproaches lend themselves to better modeling of the impact anintervention can make on a particular ecosystem. Describing un-fair outcomes in employment as caused by rational agent best-response strategies suggests that the field of algorithmic fairnessshould consider the labor market’s inherent dynamic setting in itsapproach to potential interventions. Fairness constraints that areconceived as isolated procedural checks have a limited capacity toinstall system-wide fairness that may be self-sustained and long-lasting. The problem of fairness is fundamentally tied to historicity.Within all societal domains in which fairness is an issue, past andcurrent social relations differentially impact subjects, producingdistinct sets of resources, options, and opportunities that continueto mark agents’ choices and outcomes today. This fact presents achallenge for the standard learning theory formulation of the prob-lem in which agent attributes are treated as a priori givens ratherthan themselves the products of a lineage of previous social choicesand conditions. A dynamic model recognizes the powerful rippleeffect of the past and calls for a fairness intervention that carriesmomentum into the future. The labor market as a source of eco-nomic opportunity is ripe with positive externalities and is thusan ideal setting for a notion of fairness that is oriented toward afuture beyond the short timeline of firm hiring cycles. We arguethat fairness conceived in this way is a project that aims to achievegroup egalitarianism—an ambition that is not only a worthy goalin itself but one that we show is also socially optimal. Our model of individual reputations as a sequence of previousoutcomes in the PLM fits within the hiring process regime today, inwhich employers have increased access to worker data. Since algo-rithms will be largely responsible for making sense of this individ-ual historical data, future work should consider interventions thatare able to sift through a worker’s historical data and determinewhether a group-based fairness constraint, such as the one consid-ered in this paper in the TLM, should be imposed, or whether aPLM individual-based hiring decision will suffice. Beyond servingefficiency, such practices should protect fairness.The entry of algorithms into hiring must grapple with a longtradition of explicit and implicit human biases that have renderedthe labor market prone to discriminatory practices. We hope thatthis work can suggest ways that algorithmic fairness interventionscan shift hiring strategies towards a better, fairer future.
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