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Social Choice and Welfare

Erschienen in:

18.01.2017 | Original Paper

Conformity in voting

verfasst von: Bernardo Moreno, María del Pino Ramos-Sosa

Erschienen in: Social Choice and Welfare | Ausgabe 3/2017

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Abstract

A group of agents has to decide whether to accept or reject a proposal. Agents vote in favor of or against the proposal and, if the number of agents in favor is greater than a certain threshold, the proposal is accepted. Conformist agents vote based on not only their opinion but also the votes of other agents. Independent agents consider only their own opinions. If all agents are conformists and vote simultaneously, there are undominated Nash equilibria in which the decision is different from that obtained if all agents vote for their opinions. Next, we provide the number of independent agents sufficient to obtain, in any equilibrium, the decision obtained when all agents vote for their opinions. This number depends on the total number of agents, the threshold, and the conformity measure. If agents vote sequentially, the voting behavior of conformist agents does not affect the decision.

Vorheriger Artikel Revealed preferences with plural motives: axiomatic foundations of normative assessments in non-utilitarian welfare economics

Nächster Artikel Strategic schools under the Boston mechanism revisited

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In the sequential version of the game, in Sect. 5, the equilibrium concept used is that of subgame perfect Nash equilibrium.

We assume that external advisors or consultants have incentives only for being sincere and representing the interests of their employers; they receive no gain by deviating from that behavior.

We acknowledge that it could be very natural to think that when agents have different groups to conform to, they prefer to conform to those whose messages coincide with their own opinions. Our results hold under this assumption.

See Sobel (2005) for a study of interdependent preferences applied to the ultimatum game case in which agents’ preferences also depend on the consumption of others.

Section 5 analyzes a sequential version of the game.

Note that our property of selfishness is related to the notion of selfish preferences used in Sobel (2005), which refers to the preferences that do not directly depend on the messages of others.

Moreno and Ramos-Sosa (2015) opens the door to more general versions of conformity. Agents may pay attention to some specific subsets of agents. Those subsets of agents could be either groups of experts, or a leader, or, as Kenneth Shepsle proposed to the authors, an agent may want to conform to some agents and not to others. Note that in these cases, the identity of the agents plays an important role.

An anonymous referee proposes to us another version of conformity in which agents want to conform to as many agents as possible. In Sect. 4, we show how this alternative version of conformity relates to that proposed in this study.

For every preference profile, the alternative selected by any q-truthful social choice function specifies the decision and vote of each agent. Alternatively, any q-truthful social choice function could specify the decision and number of agents voting for each option. The former could be related to an open ballot scenario whereas the latter is more related to a secret ballot scenario in which the decision is made public once all agents have voted. Our results remain valid under this alternative definition of a q-truthful social choice function.

A more realistic scenario would be one in which the preference relations of the agents are unknown. We assume complete information as a first step before analysing the implications of incomplete information in future research.

Note that for any profile different from \(\succeq ^{0}\), any weakly undominated Nash equilibrium implements the \(1-\)truthful social choice function.

Note that for any profile different from \(\succeq ^{1},\) any weakly undominated Nash equilibrium implements the \(n-\)threshold rule.

We thank the anonymous referee who advised us to refer to these preference profiles as problematic and to adopt a criterion stating when a preference profile is more problematic than another.

We assume that these external advisors have incentives only to be sincere and to represent the interests of their employers, and receive no gain by deviating from that behavior.

We acknowledge that in a more general model, conformist agents may not observe the message of independent agents before they send their messages. For instance, conformist agents may know the number of independent agents but do not know their identities. This is an interesting scenario that we leave for further research.

Admittedly, an exact number of independent agents could also be obtained for any given \((h_{1},\ldots ,h_{n})\) but we consider that the symmetric case is a focal point.

We thank an anonymous referee for proposing this alternative way of modeling conformity.

The proof when n is odd and \(q=\frac{n+1}{2}\) is included in Moreno and Ramos-Sosa (2015).

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Titel: Conformity in voting
verfasst von: Bernardo Moreno
María del Pino Ramos-Sosa
Publikationsdatum: 18.01.2017
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 3/2017
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-016-1023-7

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