Strategy-proof social choice

This paper surveys the literature on strategy-proofness from a historical perspective. While I discuss the connections with other works on incentives in mechanism design, the main emphasis is on social choice models. This article has been prepared for the Handbook of Social Choice and Welfare, Volume 2, Edited by K. Arrow, A. Sen and K. Suzumura

Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results

We define different concepts of group strategy-proofness for social choice functions. We discuss the connections between the defined concepts under different assumptions on their domains of definition. We characterize the social choice functions that satisfy each one of them and whose ranges consist of two alternatives, in terms of two types of basic properties.

Scoring rules on dichotomous preferences

In this paper, we study individual incentives to report preferences truthfully for the special case when individuals have dichotomous preferences on the set of alternatives and preferences are aggregated in form of scoring rules. In particular, we show that (a) the Borda Count coincides with Approval Voting on the dichotomous preference domain, (b) the Borda Count is the only strategy-proof scoring rule on the dichotomous preference domain, and (c) if at least three individuals participate in the election, then the dichotomous preference domain is the unique maximal rich domain under which the Borda Count is strategy-proof.

The Instrumental voter goes to the news-agent: demand for information, election closeness, and the media

This paper studies the impact of instrumental voting on information demand and mass media behaviour during electoral campaigns. If voters act instrumentally then information demand should increase with the closeness of an election. Mass media are modeled as profit-maximizing firms that take into account information demand, the value of customers to advertisers and the marginal cost of customers. Information supply should be larger in electoral constituencies where the contest is expected to be closer, there is a higher population density, and customers are on average more profitable for advertisers. The impact of electorate size is theoretically undetermined. These conclusions are then tested with comfortable results on data from the 1997 general election in Britain.

Spatial competition between two candidates of different quality: the effects of candidate ideology and private information

This paper examines competition in a spatial model of two-candidate elections, where one candidate enjoys a quality advantage over the other candidate. The candidates care about winning and also have policy preferences. There is two-dimensional private information. Candidate ideal points as well as their tradeoffs between policy preferences and winning are private information. The distribution of this two-dimensional type is common knowledge. The location of the median voter's ideal point is uncertain, with a distribution that is commonly known by both candidates. Pure strategy equilibria always exist in this model. We characterize the effects of increased uncertainty about the median voter, the effect of candidate policy preferences, and the effects of changes in the distribution of private information. We prove that the distribution of candidate policies approaches the mixed equilibrium of Aragones and Palfrey (2002a), when both candidates' weights on policy preferences go to zero.

The effect of candidate quality on electoral equilibrium: an experimental study

When two candidates of different quality compete in a one dimensional policy space, the equilibrium outcomes are asymmetric and do not correspond to the median. There are three main effects. First, the better candidate adopts more centrist policies than the worse candidate. Second, the equilibrium is statistical, in the sense that it predicts a probability distribution of outcomes rather than a single degenerate outcome. Third, the equilibrium varies systematically with the level of uncertainty about the location of the median voter. We test these three predictions using laboratory experiments, and find strong support for all three. We also observe some biases and show that they canbe explained by quantal response equilibrium.

Free triples, large indifference classes and the majority rule

We present a new domain of preferences under which the majority relation is always quasi-transitive and thus Condorcet winners always exist. We model situations where a set of individuals must choose one individual in the group. Agents are connected through some relationship that can be interpreted as expressing neighborhood, and which is formalized by a graph. Our restriction on preferences is as follows: each agent can freely rank his immediate neighbors, but then he is indifferent between each neighbor and all other agents that this neighbor "leads to". Hence, agents can be highly perceptive regarding their neighbors, while being insensitive to the differences between these and other agents which are further removed from them. We show quasi-transitivity of the majority relation when the graph expressing the neighborhood relation is a tree. We also discuss a further restriction allowing to extend the result for more general graphs. Finally, we compare the proposed restriction with others in the literature, to conclude that it is independent of any previously discussed domain restriction.

Voting by committees with exit

We study the problem of a society choosing a subset of new members from a finite set of candidates (as in Barberà, Sonnenschein, and Zhou, 1991). However, we explicitly consider the possibility that initial members of the society (founders) may want to leave it if they do not like the resulting new society. We show that, if founders have separable (or additive) preferences, the unique strategy-proof and stable social choice function satisfying voters' sovereignty (on the set of candidates) is the one where candidates are chosen unanimously and no founder leaves the society.

Voting by committees under constraints

We consider social choice problems where a society must choose a subset from a set of objects. Specifically, we characterize the families of strategy-proof voting procedures when not all possible subsets of objects are feasible, and voters' preferences are separable or additively representable.

Stable coalition structures with fixed decision scheme

This paper studies the stability of a finite local public goods economy in horizontal differentiation, where a jurisdiction's choice of the public good is given by an exogenous decision scheme. In this paper, we characterize the class of decision schemes that ensure the existence of an equilibrium with free mobility (that we call Tiebout equilibrium) for monotone distribution of players. This class contains all the decision schemes whose choice lies between the Rawlsian decision scheme and the median voter with mid-distance of the two median voters when there are ties. We show that for non-monotone distribution, there is no decision scheme that can ensure the stability of coalitions. In the last part of the paper, we prove the non-emptiness of the core of this coalition formation game

On Strategy-proofness and symmetric single-peakedness

We characterize the class of strategy-proof social choice functions on the domain of symmetric single-peaked preferences. This class is strictly larger than the set of generalized median voter schemes (the class of strategy-proof and tops-only social choice functions on the domain of single-peaked preferences characterized by Moulin (1980)) since, under the domain of symmetric single-peaked preferences, generalized median voter schemes can be disturbed by discontinuity points and remain strategy-proof on the smaller domain. Our result identifies the specific nature of these discontinuities which allow to design non-onto social choice functions to deal with feasibility constraints.

Preference intensities and risk aversion in school choice: a laboratory experiment

We experimentally investigate in the laboratory two prominent mechanisms that are employed in school choice programs to assign students to public schools. We study how individual behavior is influenced by preference intensities and risk aversion. Our main results show that (a) the Gale-Shapley mechanism is more robust to changes in cardinal preferences than the Boston mechanism independently of whether individuals can submit a complete or only a restricted ranking of the schools and (b) subjects with a higher degree of risk aversion are more likely to play "safer" strategies under the Gale-Shapley but not under the Boston mechanism. Both results have important implications for the efficiency and the stability of the mechanisms.

Two necessary conditions for strategy-proofness: on what domains are they also sufficient?

A social choice function may or may not satisfy a desirable property depending on its domain of definition. For the same reason, different conditions may be equivalent for functions defined on some domains, while different in other cases. Understanding the role of domains is therefore a crucial issue in mechanism design. We illustrate this point by analyzing the role of different conditions that are always related, but not always equivalent to strategy-proofness. We define two very natural conditions that are necessary for strategy-proofness: monotonicity and reshuffling invariance. We remark that they are not always sufficient. Then, we identify a domain condition, called intertwinedness, that ensures the equivalence between our two conditions and that of strategy-proofness. We prove that some important domains are intertwined: those of single-peaked preferences, both with public and private goods, and also those arising in simple models of house allocation. We prove that other necessary conditions for strategy-proofness also become equivalent to ours when applied to functions defined on intertwined domains, even if they are not equivalent in general. We also study the relationship between our domain restrictions and others that appear in the literature, proving that we are indeed introducing a novel proposal.

Eurozone Crisis and Social Models: What We Can Learn from Italy and Spain. CES Papers - Open Forum #20, 2013-2014

This paper considers the role of social model features in the economic performance of Italy and Spain during the run-up to the Eurozone crisis, as well as the consequences of that crisis, in turn, for the two countries social models. It takes issue with the prevailing view - what I refer to as the “competitiveness thesis” - which attributes the debtor status of the two countries to a lack of competitive capacity rooted in social model features. This competitiveness thesis has been key in justifying the “liberalization plus austerity” measures that European institutions have demanded in return for financial support for Italy and Spain at critical points during the crisis. The paper challenges this prevailing wisdom. First, it reviews the characteristics of the Italian and Spanish social models and their evolution in the period prior to the crisis, revealing a far more complex, dynamic and differentiated picture than is given in the political economy literature. Second, the paper considers various ways in which social model characteristics are said to have contributed to the Eurozone crisis, finding such explanations wanting. Italy and Spain ́s debtor status was primarily the result of much broader dynamics in the Euro- zone, including capital flows from richer to poorer countries that affected economic demand, with social model features playing, at most, an ancillary role. More aggressive reforms responding to EU demands in Spain may have increased the long term social and economic costs of the crisis, whereas the political stalemate that slowed such reforms in Italy may have paradoxically mitigated these costs. The comparison of the two countries thus suggests that, in the absence of broader macro-institutional reform of the Eurozone, compliance with EU dictates may have had perverse effects.

Work values, endogenous sentiments and redistribution

We examine the interactions between individual behavior, sentiments and the social contract in a model of rational voting over redistribution. Agents have moral "work values". Individuals' self-esteem and social consideration of others are endogenously determined comparing behaviors to moral standards. Attitudes toward redistribution depend on self-interest and social preferences. We characterize the politico-economic equilibria in which sentiments, labor supply and redistribution are determined simultaneously. The equilibria feature different degrees of "social cohesion" and redistribution depending on pre-tax income inequality. In clustered equilibria the poor are held partly responsible for their low income since they work less than the moral standard and hence redistribution is low. The paper proposes a novel explanation for the emergence of different sentiments and social contracts across countries. The predictions appear broadly in line with well-documented differences between the United States and Europe.