Authoritarianism vs. democracy: Simulating responses to disease outbreaks
AAuthoritarianism vs. democracy:Simulating responses to disease outbreaks
A.E. Biondo ∗ , G. Brosio † , A. Pluchino ‡ , R. Zanola § Abstract
Disease outbreaks force the governments to rapid decisions to deal with.However, the rapid stream of decision-making could be costly in terms ofthe democratic representativeness. The aim of the paper is to investigatethe trade-off between pluralism of preferences and the time required to ap-proach a decision. To this aim we develop and test a modified version of theHegselmann and Krause (2002) model to capture these two characteristicsof the decisional process in different institutional contexts. Using a twofoldgeometrical institutional setting, we simulate the impact of disease outbreaksto check whether countries exhibits idiosyncratic effects, depending on theirinstitutional frameworks. Main findings show that the degree of pluralismin political decisions is not necessarily associated with worse performances inmanaging emergencies, provided that the political debate is mature enough.
JEL
Classification: C53, C63, H11, H12.
Keywords : political regimes; democracy; agent-based modeling; covid -19; pandemic.
The World Health Organization ( who ) has declared the 2020 pandemic of coron-avirus named covid -19 a global public health emergency. In less than seven monthsthe virus has spread from a limited number of epicentres in Asia (mainly China and ∗ Dept. of Economics and Business, University of Catania, corresponding : [email protected] † Dept. of Economics and Statistics “Cognetti De Martiis”, University of Turin ‡ Dept. of Physics and Astronomy, University of Catania and INFN - Section of Catania § Dept. of Law and Political, Economic, and Social Sciences, University of Eastern Piedmont. a r X i v : . [ phy s i c s . s o c - ph ] S e p orea) to practically every country. Uncertainty about the future of pandemic isgrowing (immunity, intensity of contagion, future vaccines, etc.) and it nourishesspeculation on national responses and feeds a worldwide debate on the best form ofgovernment to contrast it.In the early months of the pandemic China locked down millions of people wholived in an area with major outbreaks, with invasive surveillance and coercion. InHungary, Prime Minister was allowed by the parliament to rule without any controland time limit. Analogously, the autocratic regime of Venezuela faced with limitedcontagion, but with a health sector in total disarray adopted immediately strictlockdown measures. The opposition interpreted them as a political strategy tocut the manifestation of growing dissent against the regime. Belarus, the mostautocratic regime in Europe, delayed a response. As of April 23 restaurants, coffeeshops and movie theatres remain open. Professional soccer was in full swing. In thecapital, Minsk, the subways was crowded. Most businesses required workers to showup. As of April 27, there were 10,463 cases and 72 deaths. A state of emergencywas introduced in Kyrgyzstan, a Central Asia authoritarian regime, although thecountry had been spared from the pandemic. As of April, 695 cases were recordedand only 8 deaths. Other states in the region, such as Turkmenistan, one of the mostisolated states in the world, held a series of mass sporting events despite. Accordingto official sources, it had no case of coronavirus infection as of April 27.By contrast, since time and information to solve an issue involving the diversity ofconstituents in collaborative co-deciding is costly, democratically elected leaders inItaly, Spain, UK, United States were criticized for delaying adopting stringent mea-sures to coherently contain the pandemic. An exception being India, the world’slargest democracy, which applied heavy-handed measures in defeating the coron-avirus. Germany claimed and was credited with taking early response, althoughwithout strict containment measures. This did not contain the spread of the virusand it confronted with high fatality rates.A key issue the debate is going through is whether authoritarian countries per-form better than democratic ones to contrast pandemics (Alon et al. 2020). Forinstance, although the mix of strategies (and effects) to respond to the coronavirus,Kleinfeld (2020) sustains the superiority of the democratic model. Berengaut (2020)affirms that public health depends on public trust as it is the case of Western nations,irrespective of influential admirers of the Chinese decisive intervention. Schmemann(2020) questions the cures for covid -19, while Bieber (2020) highlights the risk ofabuse for both dictatorships and democracies. The uncertainty about which gov-ernment is better to answer to coronavirus is discussed in Khavanag (2020), who2uggests that Chinese autocratic rules seem to prove to be successful, but, at thesame time, he also suggests that open media which guarantee democratic politics aretime-consuming more than inadequacy. This present debate on pandemic responsehas plenty of antecedents in political literature. The theory of the political survivalof government affirms that democratic governments are prone to take quick actionsto help victims of disasters to maximize their time in office (Bueno de Mesquitaet al., 2003; Morrow et al., 2008). Moving the logic of political survival to the2009 H1N1 pandemic, Baekkeskov and Rubin (2014) show that mature democraciesadopted massive vaccination as a precautionary strategy the cost of which is muchlower than the cost of failing subsequent election. Moreover, the response to pan-demic could be strictly correlated with the country electoral cycle, calling for moreintensive actions the shorter the period to the next election. Finally, the responseintensity depends upon the degree and intensity of political participation which isexpected to vary across democracies. In summary, according to Baekkeskov and Ru-bin, it is not democracy per se which can suggest the response to the pandemic, buthow democracy operates de facto. A clear distinction between democratic vs. auto-cratic response to pandemics emerges in Schwartz (2012) who compares China’s andTaiwan’s response to the SARS outbreak in 2002/3. Why, the author wonders, didauthoritarian China succeed while democratic Taiwan failed to respond to SARS?To explore the issue Schwartz makes a useful distinction between routine crises andnovel crises. In the first case, politicians defer to operational commanders moder-ate responses, usually experienced in similar crises. By contrast, novel crises, beingpandemic an example of, are much more insidious, due to the delay in recognizingthe true nature of them and, consequently, to set adequate responses. This delay toidentify priorities and actions is strengthened in democratic countries, where novelemergencies imply multiple jurisdictions and different levels of representative gov-ernment to coordinate to deal with difficulties. They recognize two different delaysin contrasting actions. Firstly, the lack of disease surveillance to detect outbreaks.Secondly, the delay to recognize the international concern of the outbreaks, a casein which political mobilization plays a fundamental role. The distinction betweendemocratic and autocratic regimes is here irrelevant to explain different mobiliza-tion. Rather, disease severity, globalization, disease spread to the whole populationrather than smaller groups, its perception by the public, are key factors to explaincountries’ response. This is not the position expressed in Burkle (2020). Autocraticregimes are incapable of understanding the health consequences on populations ofpandemics causing sensible delay to manage crises, placing the rest of the world atincreasing risk. 3n summary, analysing the present debate on governments? responses to pan-demic, it seems to emerge a trade-off between the democratic representativeness ofopinions and the necessity to be quick to deal with outbreaks. Dictatorships are,in principle, faster than democracy by neglecting the time-demanding coordinationeffort, but at the cost of ignoring the consensus of the entire population. The aimof the paper is to investigate the trade-off between time and representativeness ofpreferences, simulating the performance of different political systems facing an emer-gency, being pandemic a clear example of an emergency problem involving an entirecommunity.Models of opinion dynamics are particularly helpful in providing the minimalset of analytical tools describing the consensus formation . They have received awide interest, from different contexts, e.g., from mathematics, physics, and eco-nomics. Early examples of such contributions are Harary (1959), French (1956),Abelson (1967) and DeGroot (1974), among others. More recent models are Lehrerand Wagner (1991) and Friedkin and Johnsen (1999) and, with regards to non lin-ear models in Krause (1997 and 2000), Hegselmann and Flache (1998), Deffuant et al. (2000), and Sznajd-Weron and Sznajd (2000). Acemoglu and Ozdaglar andLorenz (2007) interestingly survey relevant parts of the topic. Many opinion dy-namics models can be considered, indeed, as a class of agent-based models (ABMs).Such frameworks, in which the interaction among different individual entities isable to generate emerging aggregate outcomes, are particularly useful when dealingwith complex evolving socio-economic systems, for their ability in characterizingmicro motives within macro dynamics (Tesfatsion, 2006a, 2006b). By means of thebottom-up design of such a class of models, the analysis of complexity and emer-gent phenomena is in fact possible (Delli Gatti et al. , 2008, 2011, and Fagiolo andRoventini, 2008). The early origin of ABMs can be traced back to the von Neumannself-reproducing cellular automata in the first half of last century (von Neumann andBurks, 1966), but their full expansion has started in the 90s, thanks to the suddenincrease of computational power (Epstein and Axtell, 1996, Bonabeau, 2002). Par-ticularly interesting have been the further developments of ABMs in the context ofsociophysics (as in Galam, 2002) and econophysics, where they have been appliedto the analysis of financial markets (Mantegna and Stanley 1999, Chakraborti et al. hk -Politics, hk-p henceforth. Two different characteristics areconsidered, namely, the democratic representativeness and the time efficiency. Cor-respondingly, the sequential policy-making problem is described in two steps: firstly,the political debate showing the degree of free circulation of ideas and the possibilityof discussion among different points of view; secondly, the converging process lead-ing to the final policy decision. Using a two-fold geometrical institutional setting,referred to specific indicators, i.e. the press freedom and the democracy index, arepresentative sample of twenty countries is adopted to build an original index tocapture the distortion in the political representation of citizens’ preferences rela-tive to the efficiency of decisional time requirements. Information systems revealto be crucial in the diffusion of values and priorities in public planning problems(Hoos, 1971), where the strategic weight of decisions is rooted in the ability of thedecision-maker to manage the situation at hand, analogously to what happens inmanagerial decisions (Green and Kolesar, 2004). In our benchmark model, we simu-late the impact of disease outbreaks to check whether countries exhibit idiosyncraticeffects, depending on their institutional frameworks. Our main findings show thatthe degree of pluralism in political decisions is not necessarily associated with worseperformances in managing emergencies, provided that the political debate is matureenough. Thus, even in case of emergencies, the concentration of power does notnecessarily lead to desired improvements in the efficiency of policy actions.The remainder of the paper is organized as follows: section two presents themodel; section three illustrates the case study with simulation results; section fourcontains concluding remarks. In a model of opinion dynamics, agents are typically described by means of theiropinion profiles, consisting in vectors of length n ≥
1, according to the dimension ofthe preference space in which they are modeled. Thus, a society can be described asa community of N individuals with different opinions, influencing each other. Thedecisional process is represented by the route to convergence towards one or morenon-reducible states. Such states are steady states , for the dynamic forces drivingthe adaptation rest in that condition. 5s typical in bounded confidence opinion dynamics models, we will restrict ourattention to the case of a partial interaction of agents, deriving from the spatialproximity of their opinions. This appears quite realistic, since political mediation isreasonably possible even between far, but still not incompatible, positions. Proxim-ity is, then, proposed as a measure of compatibility: each agent will consider onlyopinions within a given neighbourhood of the opinion space around himself, i.e., acompatibility interval. The opinion space Ω = [0 , n is an hypercube with n dimen-sions and open boundary conditions, whose points define profiles of each individual i as n -dimensional vectors of the type x i = [ x i, , x i, , ..., x i,n ], for i = 1 , , ..., N ,collecting the opinions about each of the n political topics. Consistently with thenumber of dimensions, the compatibility interval is represented by an hyperspherewith radius of length ε i = ε , being ε ∈ [0 ,
1] the confidence bound. Thus, the com-patibility interval of each agent can be defined as B ( x i , ε ), ∀ i . The main dynamicfeature of the hk model consists in the update of each opinion vector x i ( t ) which,at time t + dt , becomes equal to the average of all and only opinion vectors includedwithin B ( x i , ε ).Such a dynamics produces different outcomes according to the value of the con-fidence bound. Below a critical threshold ε c , it asymptotically generates a non-reducible state with clusters of opinions, n χ ∈ [2 , N ], such that lim ε → n χ = N andlim ε → ε c n χ = 2. Above such a critical threshold, consensus is always achieved, i.e., n χ = 1, independently of the initial opinions distribution. In Fortunato (2005a), ithas been shown that the value of ε c strictly depends on the type of graphs whichmodels the community of the N interacting agents. For a complete graph, i.e. for afully interacting community, one finds that ε c = 0 . hk dynamics, defining a uniform opinion distribution function P ( x , t ) such that (cid:90) Ω P ( x , t ) d x = N ( t ) (1)is the count of the entire population at any t . Following some of the advancesproposed in Fortunato et al. (2005b), the rate equation of the model is describedby the following integro-differential equation: ∂∂t P ( x , t ) = (cid:90) Ω P ( x , t ) δ (cid:16) x − ¯ x B ( x ,ε ) (cid:17) d x − (cid:90) Ω P ( x , t ) δ (cid:16) x − x (cid:17) d x (2)6here ¯ x B ( x ,ε ) ≡ (cid:82) B ( x ,ε ) x P ( x , t ) d x (cid:82) B ( x ,ε ) P ( x , t ) d x is the average opinion profile calculated over the hypersphere B ( x , ε ) ⊂ Ω, centeredat x with diameter ε , and δ ( x ) = (cid:81) j δ ( x j ), with j = 1 , , ..., n , being δ ( · ) theDirac delta function. Eq.(2) captures the hk dynamics explained above: indeed,the variation of P ( x , t ) at each x , in the time interval dt , is the net sum of twocomponents: the first one, constituted by the positive contribution of all incomingopinion vectors x , when ¯ x B ( x ,ε ) = x ; the second one, constituted by the negativecontribution of the outgoing opinion vectors x , when x = x .In this study, dealing with a finite number of agents, N , we build our hk-p model by considering a discrete time version of the hk dynamics on a completegraph. We refer to a 2 D opinion space, whose dimensions can be interpreted as theset of policy tools ( x axis) and policy targets ( y axis). In this space, the placement ofopinions should not be intended as the traditional perspective of left- or right-partypositions. Instead, it stands for the variety of ideas in terms of specific objectivesand methodologies to adopt in order to obtain desired results. Each one of our N agents, or politicians, is endowed with an individual political profile, i.e. theopinion x i = [ x i, , x i, ], i = 1 , , ..., N , which will be defined as a point in the two-dimensional opinion space. Thus, we define the compatibility interval B ( x i , ε ) as acircle of radius equal to the confidence bound ε .At t = 0, the N political profiles are uniformly distributed in the allowed opinionspace. At each subsequent time step, agents adopt a parallel update process in orderto adapt their opinions in response to compatible ones, according to the followingupdate rule: x i ( t + 1) = (cid:80) j : (cid:107) x i ( t ) − x j ( t ) (cid:107) <ε a ij x j ( t ) (cid:80) j : (cid:107) x i ( t ) − x j ( t ) (cid:107) <ε a ij (3)where (cid:107) x i ( t ) − x j ( t ) (cid:107) is the metric distance between the opinion vectors i -th and j -th, and a ij is the adjacency matrix of the graph. Since we consider here a completegraph, it is a ij = 1 for i (cid:54) = j and a ij = 0 for i = j . According to equation (3), at time t + 1, x i ( t + 1) will become equal to the average of all the opinion vectors included,at time t , within the compatibility circle of agent i -th.In order to address the dynamics of a set of K countries, with different politicalsystems, in the hk-p model we will relate the size of the 2D opinion space andthe confidence bound ε with two main attributes of the political debate withina given country C k , namely, the press freedom and the democracy index. The7ormer, quantified by the parameter b pf , will be related to the initial setup of theopinion space, as it expresses the attitude of the policy-maker to restrict, by meansof subservient media, the official opinion space in order to control the focus of thepolitical debate. We will underline later that the sudden occurrence of an emergencysituation could be translated in a further reduction of the allowed space, proportionalto the level of alarm. The latter, quantified by the democracy index b d , will refer tothe attitude of individuals to discuss their opinions and approach a partial or a totalcommon consensus, taking into account the decentralized points of view allowed bythe level of democracy in the country. This process will be regulated by the valueof the confidence bound, tuned according to the democracy index, which should beable to distinguish in a natural way democratic systems from authoritarian ones.We provide below, in a dedicated section, the description of both used indexes andtheir wide adoption in literature.All in all, the model here proposed is aimed to describe the process of convergenceto a final decision, starting from initial different positions, given the institutionalfeatures of a country. Thus, each country k of the considered set will be characterizedby the couple C k = (cid:8) b k pf , b k d (cid:9) , k = 1 , ..., K , which defines its typical configurationfor the modelled dynamics, as explained in next sections. t = 0 ): Press freedom and emergencypressure The press freedom index b pf determines the boundaries of the opinion space of the hk-p model. The simulated opinion space is a square world of 300 ×
300 unitswhere, as above explained, the two dimensions represent, respectively, the varietyof targets and tools discussed in the policy debate. The width of the policy targets(the vertical axis) is influenced by the press freedom, in terms of reduction of theopinion space due to a specific direction operated by the media communication.For a given country C k with press freedom index b k pf the reduction, applied beforestarting any simulation, is modelled by restricting the opinion space as 300 × (300 · b k pf ), with 0 < b k pf ≤
1. Then, a country with complete press freedom ( b k pf = 1)will be characterized by the full opinion space, whereas, a country with reducedpress freedom will be depicted by a correspondingly reduced space. In Figure 1(a),an example of initial conditions in the opinion space of a country is shown. Thepress freedom is non complete, i.e., b k pf = 0 . N = 500 opinion profiles x i (0) , i =1 , ..., N , represented by red dots, are uniformly distributed at random over the wholespace. However, the subsequent dynamics - which will be addressed in the nextsection - will take into account only the reduced number of opinions/agents included8 igure 1: (a) An example of initial setup for the simulation of a generic country C k , with non complete press freedom, b k pf = 0 .
7, and absence of any emer-gency pressure, e = 0. At t = 0, the N = 500 individual opinions (or agents,represented by red dots) are uniformly distributed over the whole space. Thelimited press freedom in the country reduces the allowed space (coloured inwhite) for the subsequent opinion dynamics, thus censoring part of them.Opinions (agents) outside from the allowed space represents extreme (or sim-ply uncomfortable) positions that remain off from the official debate.(b) If in the considered country C k is a democratic system, i.e., b k d > b th d , afree political debate is permitted. Thus, the N k pf = 350 opinions involved inthe dynamics approach a situation in which political agreements are reached.In other words, the hk-p dynamics leads to a fragmented state with severalclusters (each labelled by its size).(c) After political clusters have been formed, such N k pf opinions are finallycollapsed over just a single point, representing the final decision. In an au-thoritarian country (i.e. a country with b k d < b th d ), the political debate (b)is not even experienced, since the dynamics drives directly towards the finaldecision (assumed by either the dictator or the regime). in the allowed space (coloured in white). For b k pf <
1, this number will be lower than N , let us call it N k pf . In general, for N (cid:29)
1, one has that N k pf tends to ¯ N k pf ∼ N · b k pf .The appearance of an emergency can worsen the press freedom situation byadding a second restriction to the allowed opinion space. In particular, an emergencyparameter e ≥
0, equal for all the countries, can be introduced in order to furtherreduce the press freedom parameter, according to the following rule: b k pfe = b k pf · (100 − e ) / N k pfe ∼ N · b k pfe opinions/agentsinvolved in the dynamics.Summarizing, we interpret the reduction of the opinion space as the censoringactivity operated either surreptitiously by the regime (controlling the press freedom)or spontaneously by the mass-media (with regards to the emergency situation). Ourmodel will present a possible measure for the negative effects of such a censoring ac-tivity and the consequent loss of democratic representativeness due to the exclusionof all opinions out from tolerated positions.9 .2 Dynamics ( t > ): Democracy index, debate and deci-sion The second main parameter of the hk-p model is the democracy index b d , whichregulates the dynamics for t >
0. We assume that 0 < b d <
1, being 1 the idealvalue for a perfect democracy and 0 the ideal value of a perfect dictatorship. Indemocratic systems, one expects to have a political debate before the convergencetowards the final consensus is reached. In other words, the free discussion leads toa dynamical fragmentation of opinions in several (more than one) clusters, repre-senting a plurality of different points of view about both policy objectives and toolsrequired to obtain them. On the other hand, for authoritarian systems, one canexpect that any decision will be taken without any intermediate debate, thus thedynamical process should directly produce a single cluster in the opinion space, rep-resenting the achievement of the final consensus. These two qualitatively differentbehaviours can be obtained by putting in a one-to-one correspondence the democ-racy index with the confidence bound ε , which will become a function ε = f ( b d ) asexplained below.Let us imagine to perform a ranking of the set of K countries, ordered ac-cording to decreasing values of their democracy indexes b k d , so that b k d > b k +1 d for k = 1 , ..., K −
1. Let b th d a threshold value separating democratic countries fromauthoritarian ones. Our goal is to rescale the democracy index in the interval [0 , ε c = 0 . b k d > b th d and above this threshold for authoritariancountries with b k d < b th d . This can be done by choosing a scale factor α according tothe equation: α = ε c − b th d (4)In such a way, for simulating the dynamics of a generic country C k = (cid:8) b k pf , b k d (cid:9) ,we will set ε k = (1 − b k d ) α (5)This will ensure that, for a democracy, the higher the value of b k d , the smaller ε k and the more numerous the separate clusters of different opinions produced duringthe debate process; contrariwise, for more authoritarian regimes, a low value of b k d will induce an high value of ε k and a collapse towards a single opinion cluster. Forsake of clarity, let us describe separately these two different cases.10 Case b k d > b th d : Democratic Countries . An example of the opinion cluster-ing due to political debate is shown in Figure 1(b) for the same country C k presented in panel (a), which has been chosen to be a democratic one. Eachcluster has been labelled by its size (i.e. the number of opinions includedin it). The configuration reported in this figure is a stationary state for the hk-p dynamics, since the surviving clusters are made of incompatible opin-ions, i.e. groups of agents separately synchronized on disjoint opinion profiles,each outside others’ compatibility circle. Notice that only a reduced number N k pf = 350 of opinion/agents have been involved in the dynamical process,i.e. have moved from their initial positions in the opinion space - shown inpanel (a) - x i (0) , i = 1 , ..., N k pf , to the position of the clusters they belong. Wecan indicate their shifted opinion profiles as x i ( T kD ) , i = 1 , ..., N k pf , being T kD the debate time required to obtain such a partial consensus for country C k ,measured in terms of the needed parallel simulation steps. It is worth to no-tice that we consider such a process costless in terms of distortion of citizen’spreferences, since we assume that the political debate is a positive feature offree systems through which agents achieve agreements by mutual persuasion.Then, new positions in the opinion space, i.e., clusters, are representative ofdeliberated compromise.Once the political debate has been concluded, also in a democratic country thedetermination of the final decision is required. This requirement is modelledby considering that any institutional framework has its own constitutionalmechanisms, which are not being discussed here: we opportunely rescale theconfidence bound to the value ε k = 0 . hk-p dynamics start againfor all countries with b k d > b th d . Thus we do not create artificial differencesfor different institutional settings. Since N k pf clusters represented the non-reducible state of fragmented political agreements, all distances from theirpositions and the final decision point are considered as the distortion in termsof preferences representation, called ’opinion shift’. For the sake of symmetry,the decision point is approximately depicted as the center of the opinion space.Such a distortion can be evaluated as the length of the path x i ( t ) along whichthey have to travel from their temporary positions x i ( T kD ) to their ultimateposition x c ( T kF ) (independent of i ) within the final cluster, being T kF the numberof time steps needed to get the final decision. Let us define a partial opinionshift for the democratic country C k as the sum of all these contributions: O (cid:48) k = (cid:80) N k pf i =1 L [ x i ( T kD ) , x c ( T kF )], being L [ x , x ] the length of the (in general nonlinear) path travelled by a certain agent from x to x and expressed in terms11 igure 2: (a) An example of time evolution of the x i, ( t ) coordinates of the N k pf = 400 opinion profiles for a democratic country with b k pf = 0 . b k d = 0 .
7. A sequential (serial) update of opinions has been assumed fora better visualization. It is clearly visible the transition from the debatephase, with its opinion clustering, to the quick convergence towards the finaldecision at T kD . (b) The corresponding time evolution of the global opinionshift O k ( t ) shows a sudden increment starting at T kD , while the final decisionis approached. of the unit measure of our opinion space Ω .An analogous consideration is valid also for all N − N k pf censored agents,remained not included, from the beginning, in the allowed opinion spacedue to the press freedom restrictions (possibly even worsened in presenceof some kind of emergency pressure): since their initial positions x j (0) , j =1 , ..., N − N k pf , remain fixed during the whole dynamical process, we accountfor such a distortion of preferences by defining another partial opinion shift O (cid:48)(cid:48) k = (cid:80) N − N k pf j =1 β (cid:107) x j (0) − x c ( T kF ) (cid:107) , where each single distance (cid:107) x j (0) − x c ( T kF ) (cid:107) is multiplied by a constant factor β >
1, equal for all agents, representing thepenalty weight of censorship. Therefore, the final global opinion shift O k ( T kF )for the k -th democratic country can be written as the sum of the two contri-butions O (cid:48) k + O (cid:48)(cid:48) k : O k ( T kF ) = N k pf (cid:88) i =1 L [ x i ( T kD ) , x c ( T kF )] + β N − N k pf (cid:88) j =1 (cid:107) x j (0) − x c ( T kF ) (cid:107) (6)12ur results will be presented in terms of the per capita global opinion shift: o k = O k /N , which is the first output key variable of the model and will bealso called gos .The final, stationary, configuration is reported in Figure 1(c) for the samedemocratic country that we are considering in this example: it clearly appearsthat the N k pf = 350 opinion points have now collapsed in the central cluster.The total decision time T kF needed to reach such a final configuration for theconsidered country will be our second output key variable. It will be also called tdt . Differences in the total decision time, according to the situation in thecountry at hand, explain why the institutional setting of different countriescan manifest different efficiency in policy action.In Figure 2 an example of the whole dynamical process is depicted for a genericcountry with b k pf = 0 . b k d = 0 .
7. In panel (a), the time evolution ofthe x i, ( t ) coordinates of the opinion profiles, i = 1 , ..., N k pf , shows the initialformation of the clusters due to the political debate which, after t = T kD simulation steps, start to converge towards the final decision taken at t = T kF .Correspondently, as shown in panel (b), the global opinion shift O k ( t ), startingfrom the reference value O (cid:48)(cid:48) k ( T kF ), increases for t > T kD due to the furtherdistortion of preferences represented by the term O (cid:48) k ( t ). • Case b k d < b th d : Authoritarian Countries . For these countries the hk-p dynam-ics is simplified by the fact that, as previously said, they do not allow a debateprocess inside themselves. This is automatically obtained by the requirement b k d < b th d which implies, for a given authoritarian country C k = (cid:8) b k pf , b k d (cid:9) ,a confidence bound ε k above the consensus threshold (see Eq.5). Therefore,starting from the usual initial conditions at t = 0 x i (0) , i = 1 , ..., N k pf , for t > x c ( T k ) representing the final decision. T k is here the totaldecision time, tdt , needed for the dynamics to reach such a stationary state,which essentially is analogous to that one shown in Figure 1(c) for the demo-cratic country. The corresponding behavior of the x i, ( t ) in the opinion spacewill also be similar to that shown in Figure 2(a) for t > T kD .Also in this case, like in the democratic one, is it possible to define theglobal opinion shift as the sum of two terms: O k = (cid:80) N k pf i L [ x i (0) , x c ( T kF )] + β (cid:80) N − N k pf j (cid:107) x j (0) − x c ( T kF ) (cid:107) , concerning the contribution of both the N k pf agentsinvolved in the dynamical process and the N − N k pf agents censored by the po-13itical regime, which of course are expected to be here more numerous thanfor the democratic countries. The penalty factor β hase the same value thanin the previous case. Again, o k = O k /N will be the corresponding per capita global opinion shift, gos , which will be adopted for presenting the simulationresults. In the previous section we introduced the hk-p model, describing in detail its dy-namical aspects with reference to a generic set of ideal countries C k = (cid:8) b k pf , b k d (cid:9) .Let us now present a sample of K real countries, considered as a case-study. Foreach country we identify two real indexes able to give back a classification of thecountries in terms of their two main parameters, the press freedom index b k pf andthe democracy index b k d . Our scope will be to statistically evaluate, with the help ofextended numerical simulations, the performance of each country in terms of both gos and tdt , and to highlight how the emergency pressure may asymmetricallyaffect the efficiency of the decision process in different contexts. Political regime is the key characteristic to set institutional framework. Althoughthere is not a universally accepted criteria, there seems to be a general agreement ona clear distinction between democracy and dictatorship as polar types of systems.Based on such a distinction, Cheibub et al. (2010) identify a six-fold classifica-tion of political regimes: parliamentary democracy; semi-presidential democracy;presidential democracy; monarchic dictatorship; civil dictatorship; and military dic-tatorship. According with this classification, we select a sample of K = 20 countries C k ( k = 1 , ..., K ) to work with, each of them defined by the following two realindexes.The first index, which is assumed as press freedom parameter b k pf , is the WorldPress Freedom Index as published yearly since 2002 by Journalists Sans Frontiers.It ranks 180 countries and regions according to the level of freedom available tojournalists and it is based on an evaluation of pluralism, independence of the media,quality of legislative framework and safety of journalists in each country and region.The second index, assumed as democracy parameter b k D , is the Democracy Indexcalculated by Economist Intelligence Unit, a UK-based company. It is a compositeindex that integrates four distinct components. The first one aims at representing14 egime EC country b k pf b k d ¯ N k pf Parliamentary democracy FUD germany ,
878 0 ,
868 439FLD india ,
547 0 ,
690 273FLD japan ,
711 0 ,
799 356FLD italy ,
763 0 ,
752 382FUD sweden ,
908 0 ,
939 454FUD uk ,
771 0 ,
852 385Semi-presidential democracy FUD canada ,
847 0 ,
922 424FUD finland ,
921 0 ,
925 460FUD france ,
771 0 ,
812 385Presidential democracy FLD argentina ,
712 0 ,
702 356FLD brazil ,
660 0 ,
686 330FLD south korea ,
763 0 ,
800 382FLD usa ,
762 0 ,
796 381HYB turkey ,
500 0 ,
409 350Civil dictatorship AUT china ,
215 0 ,
226 108AUT kazakistan ,
459 0 ,
294 229AUT russia ,
511 0 ,
311 255Military dictatorship AUT iran ,
352 0 ,
238 176Monarchic dictatorship AUT saudi arabia ,
379 0 ,
193 189AUT un.arab em. ,
573 0 ,
276 287
Table 1: Parameters setting for the 20 countries: the Cheibub’s regime classifications(column I); the classification by the Economist (column II, where full democraciesare indicated by FUD, flawed democracies by FLD, hybrid regimes by HYB andauthoritarian ones by AUT); the names of countries (column III); the press freedomindex b k pf (column IV); the democracy index b k d (column V); the asymptotic reducednumber of opinions participating to the dynamics, ¯ N k pf ∼ N · b k pf for N = 500 (columnVI). the political institutions focusing on different aspects: competitive, multi-party po-litical system; universal adult suffrage; regularly contested elections conducted basedon secret ballots, reasonable ballot security and the absence of massive voter fraud;and significant public access of major political parties to the electorate through themedia and generally open political campaigning. The complementary three otherfactors aim at integrating the scale from democracies to dictatorships. More specif-ically, they consist of indicators that are assumed to shorten the distance betweenformal rules and the actual working of systems. The Economist democracy indexallows to collapse the Cheibub’s six-fold classification into four broader groups: fulldemocracies (FUD), flawed democracies (FLD), hybrid regimes (HYB) and author-itarian (AUT).Table 1 summarizes sample composition and parameters setting for the selectedcountries, organized according to the Cheibub classification. Acronymous of theEconomist classification (EC) are also reported for comparison. Values of b k pf and15 igure 3: The opinion spaces of the 20 selected countries as they appear attime T kD , for democratic countries, and at time T kF for authoritarian countries.The different degrees of restriction of the allowed space (in white) due to alimited press freedom are visible. b k D have been normalized in the interval [0 , N kP F ∼ N b kP F for N = 500. The corresponding restricted opinion space allowed for the dynamicsis shown in Figure 3: for each country, censored agents - in the grey area - donot participate to the dynamics, whereas the involved ones - in the white area -converge either towards many clusters (in democracies) or to just a single cluster(in authoritarian regimes).In Table 2, following the procedure explained in section 2.2, we report the same 20countries ordered by decreasing values of b kD together with the corresponding value16 ountry b k d ε k sweden ,
939 0 , finland ,
925 0 , canada ,
922 0 , germany ,
868 0 , uk ,
852 0 , france ,
812 0 , south korea ,
800 0 , japan ,
799 0 , usa ,
796 0 , italy ,
752 0 , country b k d ε k argentina ,
702 0 , india ,
690 0 , brazil ,
686 0 , turkey ,
409 0 , russia ,
311 0 , kazakistan ,
294 0 , un.arab em. ,
276 0 , iran ,
238 0 , china ,
226 0 , saudi arabia ,
193 0 , Table 2: Countries ordered by decreasing values of the democracy index b kD . Foreach country, the corresponding value of the confidence bound ε k is also reported.The threshold value b thD = 0 . ε c = 0 . of the confidence bound ε k calculated according to equations (4) and (5), wherethe threshold value b thD = 0 . Two different scenarios for the presented countries will be now analyzed through ouragent-based simulations: the benchmark scenario without emergency ( e = 0) andan emergency scenario in which different emergency pressure levels will be tested( e > e = 0The benchmark scenario corresponds to no emergency pressure, so that it resultsonly dependent on countries’ parameters. As illustrated before, the model focuseson two key outcomes: gos , as measured by the per capita distance between theoriginal opinions of agents and their final decision, and the tdt , i.e. the timenecessary for the country to converge towards a final decision. First, we need toperform a stability test for both mean gos (a) and mean tdt (b) as a functionof the number of simulation runs over which the averages are computed. Bothconsidered quantities appear to be stable enough already after 1,000 runs, as shownin Figure 4.Table 3 shows the average values of both gos and tdt over 1000 runs. From acomparison with Table 2 we immediately notice that the gos ranking is able to well17 igure 4: Stability test for both Mean gos (a) and Mean tdt (b) as func-tion of the number of simulation runs over which the averages have beenperformed. It clearly appears that both the considered quantities are stableenough already after 1000 runs. reproduce the ranking of the real democracy index b kD , thus confirming the goodnessof the hypothesis at the basis of the hk-p model. Moreover, as expected, on averagelower values of gos are associated to higher values of tdt . This is, in general,the case of real democratic countries, where the political debate guarantees finaldecisions closer to opinions, but requiring more time to reach them. The oppositeoccurs for dictatorships, whose values of gos are higher but tdt is much lower:in fact, real authoritarian regimes are typically quick to decide, but opinions haveno status. However, it is interesting to notice that, immediately after the jumpin tdt from dictatorships to democracies (from 5.6 to 11.52), we found a smallgroup of strong democracies, with a very small gos but also with a relatively low tdt , compared with the other democracies: this is a typical non linear outcome ofthe hk-p model, which favors a quick aggregation of small clusters in the debatephase of countries with a very high democracy index (i.e. a small confidence bound)while hinders a rapid convergence in big clusters for democracies with a b kD (cid:39) b thD (i.e. with a confidence bound just below the critical threshold (cid:15) c ), thus enhancingtheir tdt . We think that this emergent properties of our model well captures thereal behavior of flawed democracies, whose bureaucratic apparatus slows down thepolitical decision-making processes.It is therefore evident the necessity to combine both gos and tdt informationinto a unique synthetic index, in order to build a global ranking which could takeinto account all the above considerations. To this aim we calculate the gos / tdt ountry gos sweden , finland , canada , germany , uk , france , south korea , usa , italy , un.arab em. , japan , argentina , russia , turkey , brazil , kazakistan , saudi arabia , india , iran , china , country tdt saudi arabia , china , iran , un.arab em. , kazakistan , russia , turkey , sweden , finland , canada , germany , uk , india , france , japan , usa , south korea , argentina , italy , brazil , country g/t gos tdt finland ,
91 135 ,
65 12 , germany ,
08 152 ,
85 13 , sweden ,
73 135 ,
15 11 , canada ,
77 147 ,
43 12 , south korea ,
94 175 ,
40 14 , usa ,
01 176 ,
25 14 , france ,
01 173 ,
66 14 , italy ,
01 180 ,
75 15 , uk ,
10 169 ,
03 13 , japan ,
47 181 ,
86 14 , brazil ,
50 193 ,
30 15 , argentina ,
80 188 ,
41 14 , india ,
10 202 ,
34 14 , turkey ,
77 192 ,
12 5 , un.arab em. ,
71 181 ,
67 4 , russia ,
63 189 ,
01 5 , kazakistan ,
86 194 ,
01 4 , iran ,
71 202 ,
90 4 , saudi arabia ,
54 200 ,
53 4 , china ,
14 213 ,
90 4 , Table 3:
Rankings of averages over 1000 runs. gos (left panel), tdt (midpanel), and g/t ratio (right panel - gos and tdt are repeated for readingconvenience). g/t ), i.e. the cost in terms of distance between original opinion and finaldecision for each time decision unit. In other words, how costly is to be quick. Val-ues range between 10 .
91 to 14 .
10 for democracies, while dictatorships range from32 .
77 to 45 .
14. The introduction of this index, combined with previous informa-tion, allows to identify the existence of four different groups of countries: efficientstrong democracies (Finland, Germany, Sweden, Canada) with low gos and tdt (compared to other democracies) and with low g/t ; slow flawed democracies (theremaining democratic countries, from South Korea to India), with quite high gos and tdt , but low g/t ; strong dictatorships (Iran, Sudi Arabia, China), charac-terized by small tdt and the highest values of gos and g/t ; light dictatorships(Kazakistan, Russia, United Arab Emirates and Turkey), with a tdt comparablewith that of strong dictatorships but with a relatively smaller gos and g/t . Thesituation is summarized in Figure 5, which shows a 3D plot where each one of theconsidered 20 countries is reported like a point as function of the three main indi-cators of performance of the hk-p model, gos , tdt and their ratio g/t , averagedover 1000 runs. We obtain four groups, highlighted with ellipsoidal curves for betteridentification, which we have labelled as strong and light autocracies (characterizedby a small tdt but high values for both gos and g/t ); slow light democracies (withquite high gos and tdt , but low g/t ); efficient strong democracies (with low gos and g/t and also a lower tdt than other democracies). Notice that the distribu-tion of countries in such groups is in a good agreement with the classification ofEconomist presented in Table 1. e > gos which could over-compensate the benefits ofspeed. But what does it happen when systems in which decisions occur are stressedby some kind of emergency pressure? In order to test such a condition we introducedifferent levels of emergency pressure, ranging from 10% to 80%. As previouslyexplained, the way in which emergency pressure works in our model is by addinga further restriction to the allowed opinion space, which enhances the weight ofcensored agents in the global opinion shift.Figure 6 shows the emergency responses of the 20 countries in terms of gos asfunction of an increasing level of emergency pressure. Countries are organized in20 igure 5: A 3D plot where each of the considered 20 countries is reported likea point as function of the three main indicators of performance of the hk-p model, gos , tdt and their ratio g/t , averaged over 1000 runs. Through acomparison with Table 3 it is easy to identify each single country (see text formore details). Four clusters of countries can be clearly distinguished, whichwe have labelled as: strong and light autocracies (characterized by a small tdt but high values for both gos and g/t ); slow light democracies (withquite high gos and tdt , but low g/t ); efficient strong democracies (with low gos and g/t and also a lower tdt than other democracies). igure 6: Emergency response of the 20 countries in terms of gos as functionof an increasing level of alarm. Countries are organized in four groups, from(a) to (d), ordered according to decreasing gos values. Averages are over1000 runs. four groups, from (a) to (d), according to decreasing gos values.Regardless of regimes, moving from low towards high emergency pressure levelsall countries in each group show convergent trajectories toward a common point witha higher gos value. This means that, under the effect of increasing emergency levels,there exists a progressive shift of democracies towards the higher degree of distortionsof preferences typical of dictatorship regimes. A visual inspection of Figure 7, whichillustrates the behavior of the gos distributions cumulated for democracy countriesand for dictatorial ones, confirms the dynamic of this convergent shift as a responseto the increasing emergency pressure.The second outcome to look at is the emergency response in terms of tdt , asshown in Figure 8. It is clearly visible that emergency pressure forces tdt to reducein the case of democracies, while it seems to be irrelevant in the case of dictatorships,which evidently already operated as in emergency conditions. However, althoughspeed to converge does not change for these authoritarian regimes, as previouslyobserved emergency still increase the distance between opinions and final decisions.Analogously to what illustrated before, Figure 9 shows the behavior of the tdt distributions, cumulated for democracy countries and for dictatorial ones, underan increasing emergency pressure. In this case, a small progressive tendency ofdemocracies to reduce time to decide can be appreciated, but the distance fromdictatorships remains persistent even at the maximum emergency level.22 igure 7:
Behaviour of the gos distributions, cumulated for democratic coun-tries and for authoritarian ones, against an increasing level of emergencypressure. It is evident the progressive shift of democracies towards the highdegree of distortion of preferences typical of authoritarian regimes under theeffect of the increasing level of emergency.
Figure 8:
Emergency response of the 20 countries in terms of tdt as functionof an increasing level of alarm. Countries are organized in four groups, from(a) to (d), ordered according to decreasing tdt values. Averages are over1000 runs. igure 9: Behavior of the tdt distributions, cumulated for democratic coun-tries and for authoritarian ones, against an increasing level of emergency pres-sure. Again, democracies tend to approach the short decision time windowscharacteristic of authoritarian regimes as the emergency increases.
Moving to the synthesis index, the average g/t ratio confirms the movementof democracies under emergency pressure toward dictatorships. Ranging from 10percent to 80 percent of emergency pressure, Table 4 displays the g/t ratio for allcountries in the sample. Despite the ranking does not change, differences amongcountries are affected and democracies converge to position close to dictatorship.
In the previous sub-sections we tested a modified version of the Hegselmann andKrause (2002) model to analyze how regimes (democracy vs. dictatorship) differ-ently react to emergency pressure. Two different perspectives were investigated:democratic representativeness, i.e. the degree of free circulation of ideas, and timeefficiency, i.e. the time necessary to converge to a final policy decision. Our findingssuggest a trade-off between preference representativeness and time delay: the moredemocratic a country is, the slower the ratio between the global opinion shift perunit of time spent to converge to a final decision ( g/t ). However, irrespective ofregimes, countries tend to converge to similar values of this ratio under emergencypressure.This appears to be happened in the case of the covid -19 pandemic, which weconsider here as a typical example of emergency situation, moreover affecting manycountries in the world in comparable intervals of time. On January 5 the WorldHealth Organization ( who ) published its first flagship technical publication con-24 ountry e = 0% e = 10% e = 20% e = 30% e = 50% e = 80% finland ,
91 12 ,
00 12 ,
891 13 ,
83 15 ,
17 18 , germany ,
08 12 ,
17 13 ,
01 13 ,
96 15 ,
49 19 , sweden ,
73 12 ,
49 13 ,
40 14 ,
04 15 ,
52 19 , canada ,
77 12 ,
59 13 ,
46 14 ,
17 15 ,
65 19 , south korea ,
94 12 ,
70 13 ,
47 14 ,
19 15 ,
80 19 , usa ,
01 12 ,
79 13 ,
57 14 ,
41 15 ,
88 20 , france ,
01 12 ,
84 13 ,
65 14 ,
47 16 ,
03 20 , italy ,
01 12 ,
93 13 ,
80 14 ,
67 16 ,
47 20 , uk ,
10 12 ,
93 13 ,
81 14 ,
95 16 ,
80 20 , japan ,
47 13 ,
02 13 ,
97 15 ,
07 17 ,
77 21 , brazil ,
50 13 ,
16 14 ,
41 15 ,
63 17 ,
84 21 , argentina ,
80 13 ,
18 14 ,
77 16 ,
49 18 ,
03 21 , india ,
10 15 ,
96 16 ,
97 17 ,
56 18 ,
82 22 , turkey ,
77 33 ,
72 34 ,
43 35 ,
06 36 ,
63 36 , un.arab em. ,
71 38 ,
20 39 ,
28 40 ,
43 41 ,
91 42 , russia ,
63 38 ,
67 39 ,
50 40 ,
49 42 ,
36 42 , kazakistan ,
86 39 ,
77 40 ,
50 41 ,
38 42 ,
67 44 , iran ,
71 43 ,
24 43 ,
763 44 ,
18 45 ,
06 44 , saudi arabia ,
54 45 ,
17 45 ,
55 45 ,
42 45 ,
71 44 , china ,
14 45 ,
45 45 ,
91 46 ,
63 47 ,
13 46 , Table 4:
Average g/t ratio of Countries over 1000 runs with different levelsof emergency pressure, ranging from 10% to 80%. Despite the ranking doesnot change, differences among different countries are affected and democraciesconverge to positions close to dictatorships, as shown also in figures. igure 10: The Kaplan-Meier survival estimates for delay response to emer-gency pressure are plotted for 143 countries, grouped in four regimes followingthe Economist classification. tained a risk assessment on the status of patients and the public health response onthe cluster of pneumonia cases in Wuhan as reported by China. Two months later,on March 11, the who declared covid -19 a pandemic, pointing to the over 118,000cases of the coronavirus illness in over 110 countries and the sustained risk of fur-ther global spread. The worry for risk arose containment measures which becamegradually more stringent according to emergency pressure. By 26 March, 1.7 billionpeople worldwide were under some form of lockdown, the more extreme containmentmeasure, which increased to 3.9 billion people by the first week of April. However,the speed with which countries adopted lockdown was different.Let us assume the time interval between the first confirmed case and lockdownto be a proxy for delay response to emergency pressure. Using data from Oxford covid -19 Government Response Tracker, edited by the University of Oxford, Figure10 displays the Kaplan-Meier survival estimates for such a delay for 143 countries.Following the Economist classification, data have been aggregated in four regimes -which can be roughly identified with the four groups of countries recognized in Figure5 - and show that plurality of opinions and variety in levels of government may havehad a role in determining different temporal replies also in applying emergencymeasures.In order to better understand results, it could be useful to split delay time intwo sub-period: before and after 50 days.26t clearly appears that, before 50 days, full democracies are later than otherregimes to lockdown, while hybrid regimes, what Cheibub et al. (2010) called civildictatorships, are quicker to join a given percentage of closure. In particular, con-sidering the negative slope of the first part of the four curves in Figure 10 as pro-portional to the average g/t of the corresponding group of countries (under a givenemergency pressure level), we can put in relationship their rapidity in adopting thelockdown, and the consequent distortion of preferences, with the average gos perunit of tdt found in our simulations (see Table 4), which is always smaller for (fullor flawed) democracies and higher for (strong or light) dictatorships.Then, in the long term, regimes collapsed to the same value, but full democraciesconfirmed to be the longer. This is, again, what we expected from our simulation.In summary, democracy is time-costly, but emergency pressure, as measured by thedistance from the first case, forces countries to be quick, taking solutions similar tothose adopted by more authoritarian countries.Such conclusions shed light on the fact that emergencies challenge all institutionalconfigurations and exacerbate limits of their physiologic structure. All regimes ex-hibit wide differences in the management of critical situations, leading to a quitestable ranking. Our results underline that the political efficiency does not necessar-ily imply the reduction of the democratic representation: indeed, countries wherethe social consciousness is high and the free expression of opinions is the normalityseem to have some advantage and perform better in our simulations. Nonetheless, insome cases, less efficient democracies experience smaller advantages with respect toauthoritarian regimes, which however seem to exhibit a reduction of freedom moreproportional than the time reduction gained in terms of decision time. We claimthat despite our results cannot be considered as definitive and descriptive of thewhole complex picture of political action of Governments, it gives a robust intuitionon the existence of both more or less efficient democracies, i.e., more or less po-litically mature, and more or less enlightened dictatorial regimes. This makes ourresults realistic and show that the existence of emergencies may unveil fragilities ofinstitutional systems.
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