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Social Choice and Welfare

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27.10.2021 | Original Paper

Voting on sanctioning institutions in open and closed communities: experimental evidence

verfasst von: Ramón Cobo-Reyes, Gabriel Katz, Thomas Markussen, Simone Meraglia

Erschienen in: Social Choice and Welfare | Ausgabe 3/2022

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Abstract

We experimentally analyze the effect of endogenous group formation on the type of sanctioning institutions emerging in a society. We allocate subjects to one of two groups. Subjects play a repeated public goods game and vote on the sanctioning system (formal or informal) to be implemented in their group. We compare this environment to one in which subjects are allowed to (i) vote on the sanctioning system and (ii) move between groups. We find that the possibility of moving between groups leads to a larger proportion of subjects voting for formal sanctions. This result is mainly driven by subjects in groups with relatively high initial levels of contribution to the public good, who are more likely to vote for informal sanctions when groups are closed than when they are open.

Vorheriger Artikel Campaign finance and welfare when contributions are spent on mobilizing voters

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A relevant historical example is merchant guilds in Europe (Ogilvie 2011; Dessi and Piccolo 2016). We may view the guilds as a type of (relatively) informal, horizontal institution. Around 1800, as trade and mobility were expanding in the wake of the industrial revolution, many guilds were broken up. To a large extent, they were replaced with government regulation such as patent systems. Hence, this is an example of a move toward more formal, centralized institutions, which coincided with the emergence of a more dynamic, open society.

As discussed below, exceptions include Robbett (2014) and Cobo-Reyes et al. (2019). For a survey of the literature, see Dannenberg and Gallier (2020).

Salmon and Weber (2017) also study an environment in which individuals can move between groups. Their focus is on the effectiveness of alternative rules designed to select the individuals who are allowed to enter a given group. We instead focus on how individuals’ institutional choice varies depending on whether migration is restricted or not. Page et al. (2005) show that individuals are significantly more likely to cooperate in a public goods game when allowed to have a say over with whom they interact. The sorting process in their paper is solely based on previous contributions and, unlike us, the authors do not analyze the role played by different institutional settings.

Ethics approval for experimentation with human subjects was provided by the University of Exeter.

When \(n^{g}\) = 1, the lone subject in a group simply receives her endowment of 50 tokens.

Note that in the experimental instructions (Appendix A) we refer to the IS (respectively, FS) rule-sets as Rule Set 1 (respectively, Rule Set 2).

In MT, subjects are informed about their current group size at the beginning of each period.

For simplicity, we consider a one-period game in our theoretical setting. The finitely repeated multi-period game in our experimental design accounts for the possibility that convergence to an equilibrium may only occur after some iterations of the game.

This analysis is not intended as a validation of alternative theories of social preferences. We have therefore chosen to adopt the framework proposed by Fehr and Schmidt (1999) because of its parsimony.

For the sake of simplicity, we assume that parameters \(\alpha _{_{i}}\) and \(\beta _{_{i}}\) are common knowledge, for \(i=1,...,n\).

As discussed below, we resort to alternative operationalizations of the notions of “high” and “low” contributions in our empirical analysis. These operationalizations are very similar in spirit—though not necessarily identical—to the concepts developed in our theoretical framework.

Note that, compared to the stage game in our experiment, we have slightly modified the timing of play to allow our one-period model to capture the relevant interactions occurring in the laboratory.

For instance, when groups A and B have different “types” (one is “high contribution” and the other is “low contribution”), it can be shown that there exist equilibria in which both groups implement the same type of sanctioning institutions. Although the study of these additional equilibria may be interesting in its own right, we believe that it would not significantly contribute to our understanding of the interaction between individuals’ ability to move across “open” societies and support for sanctioning institutions.

For robustness, we also assess the sensitivity of our results to alternative operationalizations of “high” and “low” contributions. See footnote 19 and the additional results reported in Appendix C.

\(\chi ^{2}(1)=11.25\), \(p=0.00\), for a two-sided test of equality of proportions comparing the share of votes for informal sanctioning institutions—i.e., votes for IS as a percentage of votes cast in all voting periods—averaged across all NMT sessions against the corresponding average share across all MT sessions. A Mann–Whitney test taking each session as an independent observation—i.e., comparing the average proportion of votes for informal sanctions in each of the 10 NMT sessions against the average proportion of votes for IS in each of the 10 MT sessions—yields a similar conclusion: \(z=2.10\), \(p=0.03\), two-tailed.

\(\chi ^{2}(1)=30.17\), \(p=0.00\) for a two-tailed test for equality of proportions comparing the average share of votes for IS in the last 3 voting periods of all NMT sessions against the corresponding average share across all MT sessions. The same conclusion holds for a Mann-Whitney test taking each session as an independent observation: \(z=2.33\), \(p=0.02\), two-tailed.

We choose the last three periods that include a voting stage to allow for some learning in the process. Results are the same if we take the last two periods that include a voting stage (\(\chi ^{2}(1)=23.34\), \(p=0.00\), two-tailed equality of proportions test comparing the share of votes for IS across all NMT versus all MT sessions; Mann–Whitney test taking each session as an independent observation: \(z=2.28\), \(p=0.02\), two-tailed) or the last voting stage (\(\chi ^{2}(1)=11.58\), \(p=0.00\); Mann–Whitney test: \(z=2.27\), \(p=0.02\)).

\(\chi ^{2}(1)=5.04\), \(p=0.02\) for a two-sided equality of proportions test comparing the average share of votes for IS in the last 3 voting periods of all NMT sessions against the corresponding percentage averaged across all MT sessions. Mann-Whitney test taking each session as an independent observation: \(z=2.10\), \(p=0.03\), two-tailed.

We replicated the analysis using various absolute—rather than relative—criteria to operationalize “high” and “low” initial contributions. Specifically, we alternatively classify a group as having a “high” initial contribution if the average contribution of its members in the first five periods is: (i) more than half of the endowment (i.e., 25 tokens); (ii) more than 60\(\%\) of the endowment (30 tokens); or (iii) more than 70\(\%\) of the endowment (35 tokens). The findings summarized in Result 1 are not sensitive to the particular operationalization used (see Fig. 6 and Table 5 in Appendix C).

We report the “raw” parameter estimates in Table 6 of Appendix C. These must be transformed to obtain estimates for the marginal effects—i.e., the change in predicted probability associated with changes in the explanatory variables (Greene 2003, p. 667).

As mentioned in Sect. 2, subjects receive information about the average contribution to the public good in their own group, but not in the other group. They are informed about the average payoffs in both groups, though. For completeness, we replicated the analyses replacing High Initial Group Contribution\(_{g(i)}\) with High Initial Group Payoff\(_{g(i)}\); the main findings remain unchanged (see Table 7 in the Appendix).

As is well known, (bias-corrected) fixed effects estimators for panel probit models (e.g., Fernández-Val and Weidner 2016) cannot identify the coefficients of time-invariant covariates. For robustness, we also applied the estimator proposed by Kripfganz and Schwarz (2019) for fixed-effects linear panel models with time-invariant regressors. The results are aligned with those from the random effects probit models (see Table 8 in the Appendix).

These results continue to hold when High Initial Group Contribution\(_{_{g(i)}}\) is defined as a dummy taking the value 1 when the average contribution in i’s group during the first 5 periods of the experiment is greater than a certain fraction—e.g., 50, 60 or 70\(\%\)—of the endowment and 0 otherwise, instead of being measured with respect to the median initial contribution of all groups. See Table 9 in the Appendix.

We repeated the analysis replacing the High Initial Group Payoff \(_{_{h \ne g }}\) dummy with a continuous variable measuring the average payoff (in tokens) of the members of the other group in the first 5 periods of the experiment. The results remain unchanged, i.e. neither the average payoff of the members of group \(h \ne g\) nor its interaction with \(Moving_{i}\) has a statistically significant marginal effect on \(Pr(Vote_{i,t}=1)\).

\(\chi ^{2}(1)=0.01\), \(p=0.90\), for a two-sided equality of proportions test comparing the share of votes for IS averaged across all NMT sessions against the average share across all MT sessions. A Mann–Whitney test taking each “heterogeneous” session as an independent observation yields a similar conclusion: \(z=0.12\), \(p=1.00\), two-tailed.

\(\chi ^{2}(1)=9.11\), \(p=0.00\); Mann-Whitney: z=2.58, p=0.01.

Again, these results remain unchanged if the distinction between “high” and “low” group contributions is based on absolute measures. See Fig. 7 in Appendix C.

For completeness, we also examine subjects’ earnings, which are strongly related to their contributions and punishment decisions. These results are summarized in Appendix C (Fig. 8 and Table 10).

Obviously, the fact that rule-sets are endogenous complicates the attribution of a causal relationship between the institutional setting and subjects’ contribution and punishment decisions. We can nonetheless assess whether there is a systematic association between the type of institutions in place and the average contribution/punishment levels.

This comparison considers only the average contributions from period 6 onward of each session. By contrast, average contributions are statistically indistinguishable between treatments in the first 5 periods of the experiment, when institutions and group affiliations are fixed (Mann–Whitney test: \(z=1.28\), \(p=0.20\), two-tailed, taking each session as an independent observation).

Arguably, the discrepancies between the results and Hypothesis 2.a could be explained by the fact that the repeated nature of the interactions in our experiment is not fully captured by the simplified one-period model on which our hypothesis is based.

“Raw” parameter estimates—representing the effect of the predictors on the uncensored latent variables—are reported in Appendix C (Table 11).

The results are generally similar using the two-step method proposed by Honoré and Kesina (2017) to estimate fixed-effects censored regression models with time-invariant explanatory variables (Table 12 in Appendix C).

It is worth noting that, as shown in Fig. 4 average contributions are quite high in FS (and systematically higher than in IS). Hence, there is relatively “little room” for further increases. This may help explain the insignificant marginal effect of Punishment Received\(_{i,t-1}\) on Contribution\(_{i, t}\) in FS.

Anti-social punishment may be present in IS (cf. e.g. Herrmann et al. 2008; Ertan et al. 2009), but is ruled out—by definition—in FS.

“Raw” parameter estimates—representing the effect of the predictors on the uncensored latent variables—are reported in Appendix C (Table 13). The substantive results are similar using Honoré and Kesina (2017)’s fixed-effects estimator (Table 14).

This is also observed in Fig. 9 in Appendix C, which displays the punishment directed towards subjects in IS who contribute more than the group average, as a share of the total punishment in each period.

The average number of tokens sent per instance of anti-social punishment is 9.07 in MT and 7 in NMT (Mann-Whitney test: \(z=0.34\), \(p=0.73\), two-tailed).

Evidence pointing in this direction is provided by Weber (2006). The author finds that slow growth in group size has a positive effect on coordination.

\(\chi ^{2}(1)\)=64.98, p=0.00, for a two-sided equality of proportions test comparing the number of moves from IS to FS to those in the other direction, as a proportion of the total number of group switches across all the periods and sessions in which the two groups implement different rule-sets. We also conducted a Wilcoxon signed rank test taking each of these (102) period-sessions as the unit of analysis; differences are again statistically significant: z = 8.63, p = 0.00.

A possible explanation for this result is that IS is implemented because it functions relatively well. If this is the case, since IS is a relatively efficient institution with respect to FS, it tends to attract more subjects. Figure 10 in the Appendix complements this analysis by plotting the share of participants located in a group with IS in each period. This would be the consequence of the combination of voting and migration decisions.

Parameter estimates are reported in Appendix C (Table 15). Since these specifications do not include time-invariant predictors, we also fitted two-way (subject and period) fixed-effects probit models using the method developed by Fernández-Val and Weidner (2016). The main results remain qualitatively similar (see Table 16).

For a similar result, see Cobo-Reyes et al. (2019).

This outcome may occur either because the conditions in Lemma 1—and in Proposition 5 in Fehr and Schmidt (1999)—are violated, or because individuals coordinate on an equilibrium involving relatively low contributions to the public good.

In this proof, we focus on the case in which only one individual moves from group B to group A. It is straightforward to generalize the proof to the case in which more than one individual move from group B to group A.

It is easy to show that this behavior is an equilibrium of the sub-game in which both groups implement IS. To complete the description of the equilibrium, it is enough to add that, when both groups implement IS, a movement by more than one of group B’s initial members leads to a breakdown of cooperation in both groups.

Recall that group B is defined as “low contribution”. We are therefore assuming that the decrease in the number of members leads to a new equilibrium in which cooperation is “high”. Provided that the outgoing member is not a “conditionally cooperative enforcer”, this statement is in line with Lemma 1 (see (7)).

It is easy to show that this behavior is an equilibrium of the sub-game in which both groups implement IS. To complete the description of the equilibrium behavior in this sub-game, it is enough to add that a movement by more than one of group B’s initial members leads to a breakdown of cooperation in both groups.

As it will be clear from the proof, there exist equilibria in which both groups implement FS and individuals move between groups.

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Titel: Voting on sanctioning institutions in open and closed communities: experimental evidence
verfasst von: Ramón Cobo-Reyes
Gabriel Katz
Thomas Markussen
Simone Meraglia
Publikationsdatum: 27.10.2021
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 3/2022
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-021-01363-6

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