Social Decision Rules Research Articles

Deliberation and epistemic democracy

• We study how deliberation affects epistemic social choice –both Condorcet Jury and probability pooling. • Each deliberator can discloses some private information to persuade the other agents of her current views. • But her views may also evolve over time, as she learns from other agents (it is a dynamic model). • Agents generally do not disclose all their private information, because of communication costs. • Under certain conditions, the decision reached in equilibrium is the same as with full information pooling. We study the effects of deliberation on epistemic social choice, in two settings. In the first setting, the group faces a binary epistemic decision analogous to the Condorcet Jury Theorem. In the second setting, group members have probabilistic beliefs arising from their private information, and the group wants to aggregate these beliefs in a way that makes optimal use of this information. During deliberation, each agent discloses private information to persuade the other agents of her current views. But her views may also evolve over time, as she learns from other agents. This process will improve the performance of the group, but only under certain conditions; these involve the nature of the social decision rule, the group size, and also the presence of “neutral agents” whom the other agents try to persuade.

Group identification: An integrated approach

Consider social decision rules identifying two or more groups by aggregating individual opinions on who belong to which group. We search for rules respecting cross-group independence in the aggregation process. This independence axiom or its variants, together with other implicit constraints in the two models by Miller (2008) and Cho and Ju (2017), characterize a restricted family of rules; the only “democratic” rule in this family is the liberal rule. Our new framework provides a unified perspective on the main results of the two papers and uncovers implicit constraints in their modeling. Once those constraints are weakened, there emerge a richer family of independent rules including the consent rules (Samet and Schmeidler, 2003). The standard majority rule and many other democratic rules lying between the majority and liberal rules are examples. We also provide a characterization of the consent rules.

The Strong Consistency of Neutral and Monotonic Binary Social Decision Rules

The purpose of this paper is to investigate the strong consistency of neutral and monotonic binary social decision rules. Individuals are assumed to satisfy von Neumann-Morgenstern axioms of individual rationality. The main result of the paper shows that there does not exist any neutral and monotonic non-null non-dictatorial binary social decision rule which is strongly consistent. The relationship between restricted preferences and the existence of strong equilibria is also investigated. It is shown that for every non-dictatorial social decision function satisfying the conditions of independence of irrelevant alternatives, neutrality, monotonicity and weak Pareto-criterion there exists a profile of individual orderings satisfying value-restriction corresponding to which there is no strong equilibrium.

Deliberation and Epistemic Democracy

We study the effects of deliberation on epistemic social choice, in two settings. In the first setting, the group faces a binary epistemic decision analogous to the Condorcet Jury Theorem. In the second setting, group members have probabilistic beliefs arising from their private information, and the group wants to aggregate these beliefs in a way that makes optimal use of this information. During deliberation, each agent discloses private information to persuade the other agents of her current views. But her views may also evolve over time, as she learns from other agents. This process will improve the performance of the group, but only under certain conditions; these involve the nature of the social decision rule, the group size, and also the presence of “neutral agents” whom the other agents try to persuade.

Collective decision making by rational individuals

The patterns and mechanisms of collective decision making in humans and animals have attracted both empirical and theoretical attention. Of particular interest has been the variety of social feedback rules and the extent to which these behavioral rules can be explained and predicted from theories of rational estimation and decision making. However, models that aim to model the full range of social information use have incorporated ad hoc departures from rational decision-making theory to explain the apparent stochasticity and variability of behavior. In this paper I develop a model of social information use and collective decision making by fully rational agents that reveals how a wide range of apparently stochastic social decision rules emerge from fundamental information asymmetries both between individuals and between the decision makers and the observer of those decisions. As well as showing that rational decision making is consistent with empirical observations of collective behavior, this model makes several testable predictions about how individuals make decisions in groups and offers a valuable perspective on how we view sources of variability in animal, and human, behavior.

SOCIAL INFLUENCE STRENGTHENS CROWD WISDOM UNDER VOTING

The advantages of groups over individuals in complex decision-making have long interested scientists across disciplinary divisions. Averaging over a collection of individual judgments proves a reliable strategy for aggregating information, particularly in diverse groups in which statistically independent beliefs fall on both sides of the truth and contradictory biases are cancelled out. Social influence, some have said, narrows variation in individual opinions and undermines this wisdom-of-crowds effect in continuous estimation tasks. Researchers, however, neglected to study social-influence effects on voting in discrete choice tasks. Using agent-based simulation, we show that under voting — the most widespread social decision rule — social influence contributes to information aggregation and thus strengthens collective judgment. Adding to our knowledge about complex systems comprised of adaptive agents, this finding has important ramifications for the design of collective decision-making in both public administration and private firms.

A multi-criteria approach for assigning weights in voting systems

Following a new analytical orientation, this paper proposes an approach for investigating group versus individual trade-offs in general voting situations. From specific particularizations of a general family of p-norms, three social decision rules have been derived. These rules trigger three different systems of weights in the voting system. Once the three rules were obtained and the rationale underlying them justified, a compromise framework integrating all the rules was formulated. The compromise framework is computationally based on goal programming. In this way, it is possible to establish directly trade-offs and balance compromise solutions between the three social rules. Thus, not only is the weighted voting system formulated within a theoretically sound framework, but the applicability of the approach to real political situations is also more flexible and pragmatic.

The Liberal Ethics of Non-Interference

This article analyses the liberal ethics of non-interference in social choice. It examines a liberal principle that captures non-interfering views of society and is inspired by John Stuart Mill’s conception of liberty. The principle expresses the idea that society should not penalize individuals after changes in their situation that do not affect others. The article highlights an impossibility for liberal approaches: every social decision rule that satisfies unanimity and a general principle of non-interference must be dictatorial. This raises some important issues for liberal approaches in social choice and political philosophy.

Identifying Groups in a Boolean Algebra

We study the problem of determining memberships to the groups in a Boolean algebra. The Boolean algebra is composed of basic groups (e.g., “J” and “K”) and the other groups that are derived from basic groups through the conjunction, disjunction, or negation operations (e.g., “J and K”, “J or K”, “not J”, etc.). All groups, basic and derived, are to be identified simultaneously based on the opinions of the potential members. Our main results are characterizations of (social decision) rules by means of independence axioms that are variants of Arrow’s independence of irrelevant alternatives. We report that any of these independence axioms, together with other fairly mild axioms, implies simple decision schemes that focus on a single fixed vote for every membership decision. These rules are characterized earlier in the binary and multinary group identification models by Miller (2008) and Cho and Ju (2015). We unify these two models and their main results. Our extended setup uncovers implicit constraints in the earlier studies. Dropping these constraints, as we propose, leads to quite a rich spectrum of rules. Among them are the consent rules by Samet and Schmeidler (2003).

Metric rationalization of social welfare functions

Metric rationalization of social decision rules has been intensively investigated when the social outcome is a nonempty subset of alternatives. The present paper proposes a similar framework for social welfare functions (SWFs)—that is when each social outcome is a ranking of alternatives. A metric rationalizable SWF reports as an approximation of the unanimity consensus the relative ranking of any pair of alternatives as in the closest profile where individuals all agree on those alternatives, the closeness being measured with respect to a metric on profiles. Two notions of unanimity are in consideration: top unanimity on an alternative holds when individuals all agree that it is top ranked while pairwise unanimity on a pair occurs when individuals all prefer an alternative to another. Without strong requirements on metrics, characterizations provided in both cases show that metric rationalizations of SWFs are essentially equivalent to the Pareto principle for SWFs. Furthermore, two interesting classes of metric rationalizable SWFs–multi-valued scoring SWFs and pairwise scoring SWFs–are each uniquely identified by means of some appropriate and appealing properties on metrics among which decomposability, neutrality and monotonicity are known.

Optimal Apportionment

This paper provides a theoretical foundation that supports the degressive proportionality principle in apportionment problems, such as the allocation of seats in a federal parliament. The utility assigned by an individual to a constitutional rule is a function of the frequency with which each collective decision matches the individual’s own will. The core of the argument is that, if the function is concave, then classical utilitarianism at the social level recommends decision rules that exhibit degressive proportionality with respect to the population size.

Majority and minority influence in group negotiation: The moderating effects of social motivation and decision rules.

In organizational groups, often a majority has aligned preferences that oppose those of a minority. Although such situations may give rise to majority coalitions that exclude the minority or to minorities blocking unfavorable agreements, structural and motivational factors may stimulate groups to engage in integrative negotiation, leading to collectively beneficial agreements. An experiment with 97 3-person groups was designed to test hypotheses about the interactions among decision rule, the majority's social motivation, and the minority's social motivation. Results showed that under unanimity rule, minority members block decisions, thus harming the group, but only when the minority has proself motivation. Under majority rule, majority members coalesce at the minority's expense, but only when the majority has a proself motivation. Implications for negotiation research and group decision making are discussed.

Balanced Bayesian mechanisms

In the transferable utility case, a number of authors have identified conditions on beliefs that guarantee the existence of Bayesian incentive compatible mechanisms with balanced transfers. We present a new, easy to interpret, condition and we show that it is (strictly) more general than all the other conditions found in the literature. We also study conditions guaranteeing the Bayesian implementability of all social decision rules with balanced budget mechanisms.

Social Motives in Integrative Negotiation: The Mediating Influence of Procedural Fairness

Although a large body of research has examined the influence of social motives on integrative negotiation, little is known about how social motives affect procedural fairness judgments in negotiation. In two experiments concerned with small group negotiation, we manipulated group members' social motives (pro-social vs. egoistic), and measured joint negotiation outcomes and procedural fairness. Experiment 1 showed that, compared to group members with an egoistic motivation, those with a pro-social motive experienced more procedural fairness, which was partly responsible for the higher joint outcomes they obtained. In Experiment 2, we manipulated social motives and decision rule. Results showed that pro-social groups experienced more procedural fairness than egoistic groups when a majority rule was applied, but not when a unanimity rule was applied.

Social decision rules are not immune to conflict

Social decision rules are not immune to conflict

Explicit form of neutral social decision rules for basic rationality conditions

The paper deals with aggregation operators F:( R 1) n→ R 2 which satisfy the classical requirements of binariness (independence), neutrality to alternatives, non-imposition, and which transform any n-tuple of individual relations of the given class R 1 into a collective relation of the given class R 2 . We consider as R 1 and R 2 the classes: L of linear orders, W of weak orders, S of semiorders, I of interval orders, P of partial orders, T of transitive relations, A of acyclic relations. For all 27 possible pairs R 1, R 2∈{ L, W, S, I , P, T, A} such that R 1⊆ R 2 , we bring the explicit form of operators ( R 1) n→ R 2 . The results are obtained on the basis of the following approach. Using a logical form of operators, we associate to each F a so-called ordinal binary relation ρ F on R n (for any x , y ∈ R n one is uniquely determined by signs of coordinate differences x i − y i , 1≤ i≤ n). We prove that if R 2 satisfies some mild conditions then F maps W n into R 2 if and only if ρ F∈ R 2 . So the description of the operators W n→ R 2 amounts to the description of the ordinal relations of R 2 . The approach can be adapted to some classes R 1≠ W .

64% Majority rule in Ducal Venice: Voting for the Doge*

A recent result of Caplin and Nalebuff (1988) demonstrates that, under certain conditions on individual preferences and their distribution across society, super-majority rule performs well as a social decision rule. If the required super-majority is chosen appropriately, the rule yields a unique winner and voter cycles cannot occur. The voting procedure for electing a Doge in medieval Venice, developed in 1268, employed a super-majority requirement agreeing with the Caplin and Nalebuff formula. We present a brief history of the Venetian political institutions, show how the rule was employed, and argue that it contributed to the remarkable centuries-long political stability of Venice.

Structure of neutral and monotonic binary social decision rules with quasi-transitive individual preferences

The paper investigates the structure of neutral and monotonic binary social decision rules with unrestricted domain under the assumption that individual weak preference relations are reflexive, connected, and quasi-transitive. Among other results, neutral and monotonic binary social decision rules on this domain are characterized for alternative social rationality assumptions.

Characterization of monotonicity and neutrality for binary Paretian social decision rules

Abstract It is shown that a necessary and sufficient condition for a binary Paretian social decision rule to be neutral and monotonic is that it satisfies Pareto quasi-transitivity.

Posterior Implementability in a Two-Person Decision Problem

When a decision rule is implemented using a Bayesian incentive compatible mechanism in which the messages are publicly observable, the players' information is augmented by their observation of each others' strategies. In this paper we study the set of Bayesian implementable decision rules which have the further property that the information conveyed in the process of their implementation does not invalidate the optimality of the players' strategies. We call such rules posterior implementable. We concentrate on a two-person problem with two possible decisions, and, for this problem, we obtain a complete characterization of the set of posterior implementable decision rules. Our main result entails that a posterior implementable social decision rule can take essentially only two values throughout the range of observations of the two players. The domains over which each of these two outcomes is realized can be characterized by the fact that the boundary between them is a step function satisfying a certain set of equations. The motivation for studying posterior implementable rules is that they represent the outcomes of a two-stage cooperative process. In the first stage, communication takes place but no binding commitments can be made. The second stage consists of ratifying (signing) the agreement obtained at the first stage. At this state, no further information is conveyed. Both parties must be satisfied with the nonbinding commitments obtained at the first stage, so that these actions are actually carried out. Possible applications of this theory are given. A constructive method for finding the posterior implementable rules is presented and the set of such rules is contrasted, in an example, with the full set of Bayesian implementable rules.