Abstract
Compliance with a social norm is a matter of self-enforceability and endogenous motivation to conform which is relevant not just to social norms but also to a wide array of institutions. Here we consider endogenous mechanisms that become effective once the game description has been enriched with pre-play communication allowing impartial agreements on a norm (even if they remain not binding in any sense). Behavioral models understand conformity as the maximization of some “enlarged” utility function properly defined to make room for the individual’s “desire” to comply with a norm reciprocally adhered to by other participants—whose conformity in turn depends on the expectation that the norm will be in fact reciprocally adhered to. In particular this paper presents an experimental study on the “conformity-with-the-ideal preference theory” (Grimalda and Sacconi in Const Polit Econ 16(3):249–276, 2005), based on a simple experimental three person game called the “exclusion game”. If the players participate in a “constitutional stage” (under a veil of ignorance) in which they decide the rule of division unanimously, the experimental data show a dramatic change in the participants’ behavior pattern. Most of them conform to the fair rule of division to which they have agreed in a pre-play communication stage, whereas in the absence of this agreement they behave more egoistically. The paper also argues that this behavior is largely consistent with what Rawls (A theory of justice, Oxford University Press, Oxford, 1971) called the “sense of justice”, a theory of norm compliance unfortunately overlooked by economists and which should be reconsidered after the behaviorist turn in economics.
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Notes
We do not say that the theory is entirely Rawlsian, since it assumes that in the ex ante decision a social contract is subscribed on the Nash bargaining solution of the relevant game, whereas Rawls would have suggested the maximin solution. What we simply say is that the solution given to the norm compliance problem through conformist preferences is strictly consistent with Rawls’ idea of the sense of justice. However, consider that the Nash bargaining solution in a symmetric bargaining situation implies the egalitarian solution which is also consistent with Rawls’ maximin. As Binmore shows, this consistency illustrates an essential feature of the decision under the veil of ignorance, when it is restricted to the payoff space resulting from the symmetric translation of the equilibrium set with respect to the Cartesian axes representing the players’ payoffs (Binmore 2005).
The Nash bargaining solution may be understood as a formal model for the “social contract” that players would agree in an ex ante (possibly hypothetical) collective decision on the rules that should constrain (at least as a matter of “ought”) the allocation of surpluses arising form their interactions (see Sacconi 2000; Binmore 1998, 2005).
This assumption corresponds to Rawls’s assumption of a capacity to form a sense of justice derivable from the lower-level moral sentiments.
See also Grimalda and Sacconi (2005) for details.
Participants were all students at the University of Trento (mainly from economics, law and sociology courses), recruited by responding to ads posted in the various departments.
This is an application of the procedure known as the random lottery incentive system (Starmer and Sugden (1991) and Cubitt et al. (1998)). On adopting this procedure, the round in which the subject has played occupying the G1 or G2 role is selected with a probability of 2/3, which is the same probability of being extracted as G1 or G2 in a one-shot version of the game. Note that, if we look at the third phase of the experiment, using this mechanism we can always compare the choice of each of the players who in that phase have an active role with his/her choice in the first phase.
See Appendix 1 for a detailed description of the voting procedure.
We asked the player to indicate the cell of the payoff matrix in which s/he thought the game would end. In this way we avoided explicitly asking for his/her opinion about the opponent’s willingness to conform with the rule.
When subjects access the third phase they have already played the exclusion game in the first phase. The payoff from that phase (as far as they know at this stage) consists of the equi-probabilistic expectation of the two rounds they have played in the roles of the active players. This expected payoff hence is the status quo from which the gain of playing the third stage must be assessed. The total payoff a participant may earn from the first and third stages will be the sum of how much he expects from the division of the pie at the first stage (E(π1)) and what he will get (π2) from the pie division at the third stage. What actually is allocated to each player at the third stage hence is a surplus, or—to say it differently—the difference between the player total payoff and the expected payoff of the first stage, understood as the player status quo or reservation utility. In order to calculate the Nash product associated to the pie division at the third stage, thus we must account for the surplus accrued to each player for any given outcome by adding to the first stage payoff the amount earned at the third stage specifically less the status quo (i.e., the expected payoff earned at the first stage that cannot be changed at this point in time). The Nash products then become:
\( \mathop \Uppi \limits_{i \in I} \left( {U_{i} (\sigma ) - c_{i} } \right) \)
where U i (σ) = E(π 1) + π 2 and c i = E(π 1) then \( \mathop \Uppi \limits_{i \in I} \left( {E(\pi_{1} ) + \pi_{1} - E(\pi_{i} )} \right) = \mathop \Uppi \limits_{i \in I} (\pi_{1} - 0) \)
By applying this definition we can compute the ‘fairness values’ given by the function corresponding to the various states resulting from playing each strategy combination:
T(4,4) = TMAX = 64
T(3,4) = T(4,3) = 60
T(3,3) = T(3,6) = T(6,3) = 54
T(4,6) = T(6,4) = 48
T(6,6) = TMIN = 0
Hence, from the conformity indexes attached to each outcome of the game, we can compute the individual comprehensive utility values, assuming that in each state the player’s beliefs reciprocally predict exactly the strategy chosen by the opponent. These values are reported in the following matrix:
3
4
6
3
3, 3
3 + (3/4)λ1, 4 + (3/4)λ2
3, 6
4
4 + (3/4)λ2, 3 + (3/4)λ1
4 + λ1, 4 + λ2
4, 6
6
6, 3
6, 4
6, 6
Note that this implies that only a subset of the observations consistent with the theory may have crucial discriminating force amongst different theoretical hypotheses on rational action, and we are mainly interested in producing exactly this kind of evidence. This would also have justified us in placing somewhat more stress on the ethical nature of the second phase decision in order to test the level of conformism in the third phase.
For the details on this test see for example Siegel and Castellan (1988).
For a more detailed description of subjects’ choice across the three phases see Appendix 2.
This hypothesis is supported by the replies to the debriefing questionnaire.
As suggested by an anonymous referee, our explanation of subjects’ compliance seems to be compatible with the theory of the role of cheap talk in fostering coordination devised by Farrel and Rabin (1996), but also, we would add, with the Lewis’s (1969) hypothesis that informal agreement can facilitate the convergence of players’ expectations in coordination problems. Note, however, that in this article we do not deal with the problem of the selection among pre-existing multiple equilibria. According to conformist preferences theory, the agreement activates the deontological component of player’s preferences, and this activation is a necessary condition for the existence of a particular equilibrium. In our experiment, without the agreement the {“ask for 4”, “ask for 4”} equilibrium would not exist. At the same time, as it is typical in the context of psychological games, the existence of an equilibrium depends on the emergence of beliefs compatible with it. If players hold reciprocal beliefs compatible with the stretegy combination {“ask for 4”, “ask for 4”} then that strategy combination will be the psychological equilibrium of the exclusion game. But if their reciprocal beliefs are compatible with the play of the strategy combination {“ask for 6”, “ask for 6”}, then the psychological equilibrium of the exclusion game will be {“ask for 6”, “ask for 6”}. What the experimental evidence suggests is that the agreement seems to have an important role also in the emergence of these beliefs, and this would be in line with Farrel and Rabin (1996).
This made it impossible to identify the members of a particular group by exploiting the information about the outcome of the voting procedure.
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Acknowledgments
This work is based on the experimental evidence collected by Sacconi and Faillo (2005). In this paper the reader will find a new quantitative analysis and a more general theoretical interpretation of the results of the original experiment. This paper is part of two larger research projects: “Social capital, corporate social responsibility and local development” supported by the PAT, and “CSR and corporate governance” supported by the MIUR. Help from both the institutions is gratefully acknowledged.
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Appendices
Appendix 1
1.1 Voting procedure
Subjects were randomly assigned to five groups with three members (identified with the numbers from 1 to 5). Each member could read the number of his/her group on his/her computer screen but could not interact with the other members, nor identify them. The experimenter distributed a form like the one in Fig. 6.
Form for the general principle selection
The subjects were asked to fill in the “ID” and “Group’s number” boxes and to select their preferred principle by ticking one of the two boxes in the “Player’s choice” column. The experimenters collected the forms and checked the votes, writing on each player’s form the choices of the other members of the group. If the members of some groups did not reach unanimous agreement, the experimenter again distributed the forms to all the subjects.Footnote 16 Members of the groups that did not reach agreement were asked to vote again, while the others had to wait. The experimenter collected the forms, checked the votes and repeated the same procedure until all the groups had reached agreement. The maximum number of trials allowed was five.
After the voting for selection of the general principle, new forms like the ones in Figs. 7 and 8 were distributed. These stated particular division rules deduced from the general principle. Each subject received a form stating the rules deduced from the principle selected in the previous stage. The voting procedure was the same as the one adopted for the principles selections, but the maximum number of trials was now ten.
Form for the selection of rule deduced from principle 1
Form for the selection of rule deduced from principle 2
At the end of the voting procedure, the experimenter inserted the rule selected in a form that appeared on the screen of each subject.
Appendix 2
2.1 The dynamics of subjects’ choice
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Sacconi, L., Faillo, M. Conformity, reciprocity and the sense of justice. How social contract-based preferences and beliefs explain norm compliance: the experimental evidence. Const Polit Econ 21, 171–201 (2010). https://doi.org/10.1007/s10602-009-9080-x
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DOI: https://doi.org/10.1007/s10602-009-9080-x