Strategy-proofness on restricted separable domains

We study a problem in which a group of voters must decide which candidates are elected from a set of alternatives. The voters’ preferences on the combinations of elected candidates are represented by linear orderings. We propose a family of restrictions of the domain of separable preferences. These subdomains are generated from a partition that identifies the friends, enemies and unbiased candidates for each voter. We characterize the family of social choice functions that satisfy strategy-proofness and tops-onlyness properties on each of the subdomains. We find that these domain restrictions are not accompanied by an increase in the family of social choice functions satisfying the two properties.     

Efficiency and truthfulness with Leontief preferences. A note on two-agent,two-good economies

In exchange economies where agents have private information about their preferences, strategy-proof and individually rational social choice functions are in general not efficient. We provide a restricted domain, namely the set of preferences representable by Leontief utility functions, where there exist mechanisms which are strategy-proof, efficient and individually rational. In two-agent, two-good economies we are able to provide an even stronger result. We characterize the class of efficient and individually rational social choice functions, which are fully implementable in truthful strategies.Received: 28 April 2003, Accepted: 23 June 2003, JEL Classification: D51, D71The author thanks Matthew Jackson, Jordi Massó and James Schummer for fruitful discussions, William Thomson for many valuable comments on an earlier version. A particular thank to Salvador Barberá for his fundamental help.     

Strategy-proof fuzzy aggregation rules

We investigate the structure of fuzzy aggregation rules which, for every permissible profile of fuzzy individual preferences, specify a fuzzy social preference. We show that all fuzzy aggregation rules which are strategy-proof and satisfy a minimal range condition are dictatorial. In other words, there is an individual whose fuzzy preferences determine the entire fuzzy social ranking at every profile in the domain of the aggregation rule. To prove this theorem, we show that all fuzzy aggregation rules which are strategy-proof and satisfy the minimal range condition must also satisfy counterparts of independence of irrelevant alternatives and the Pareto criterion. There has been hardly any treatment of the manipulability problem in the literature on social choice with fuzzy preferences.     

Circular domains

I introduce the notion of circular domains and prove that on any circular domain there is no strategy-proof and nondictatorial social choice function. Moreover, I show that on any proper subset of a minimal circular domain, there exists a group strategy-proof and essential social choice function. These results together detect the minimal size of the domains over which the incompatibility arises with respect to pairs of democratic-incentive requirements (nondictatorial, strategy-proof) and (essential, group strategy-proof).     

An alternative direct proof of Gibbard’s random dictatorship theorem

We present an alternative proof of the Gibbards random dictatorship theorem with ex post Pareto optimality. Gibbard(1977) showed that when the number of alternatives is finite and larger than two, and individual preferences are linear (strict), a strategy-proof decision scheme (a probabilistic analogue of a social choice function or a voting rule) is a convex combination of decision schemes which are, in his terms, either unilateral or duple. As a corollary of this theorem (credited to H. Sonnenschein) he showed that a decision scheme which is strategy-proof and satisfies ex post Pareto optimality is randomly dictatorial. We call this corollary the Gibbards random dictatorship theorem. We present a proof of this theorem which is direct and follows closely the original Gibbards approach. Focusing attention to the case with ex post Pareto optimality our proof is more simple and intuitive than the original Gibbards proof.Received: 15 October 2001, Accepted: 23 May 2003, JEL Classification: D71, D72Yasuhito Tanaka: The author is grateful to an anonymous referee and the Associate editor of this journal for very helpful comments and suggestions. And this research has been supported by a grant from the Zengin Foundation for Studies on Economics and Finance in Japan.     

Probabilistic strategy-proof rules over single-peaked domains

It is proved that every strategy-proof, peaks-only or unanimous, probabilistic rule defined over a minimally rich domain of single-peaked preferences is a probability mixture of strategy-proof, peaks-only or unanimous, deterministic rules over the same domain. The proof employs Farkas’ Lemma and the max-flow min-cut theorem for capacitated networks.     

The structure of decision schemes with cardinal preferences

This paper replacesGibbard’s (Econometrica 45:665-681, 1977) assumption of strict ordinal preferences by themore natural assumption of cardinal preferences on the set pure social alternatives and we also admit indifferences among the alternatives. By following a similar line of reasoning to the Gibbard-Satterthwaite theoremin the deterministic framework, we first show that if a decision scheme satisfies strategy proofness and unanimity, then there is an underlying probabilistic neutrality result which generates an additive coalitional power function. This result is then used to prove that a decision scheme which satisfies strategy proofness and unanimity can be represented as a weak random dictatorship. A weak random dictatorship assigns each individual a chance to be a weak dictator. An individual has weak dictatorial power if the support of the social choice lottery is always a subset of his/her maximal utility set. In contrast to Gibbard’s complete characterization of randomdictatorship, we also demonstrate with an example that strategy proofness and unanimity are sufficient but not necessary conditions for a weak random dictatorship.     

Centralized allocation in multiple markets

We provide a characterization result for the problem of centralized allocation of indivisible objects in multiple markets. Each market may be interpreted either as a different type of object or as a different period. We show that every allocation rule that is strategy-proof, Pareto-efficient and nonbossy is a sequential dictatorship. The result holds for an arbitrary number of agents and for any preference domain that contains the class of lexicographical preferences.     

Increasing sales by introducing non‐salable items

Rationality implies that adding ‘irrelevant’ and, in particular, inferior alternatives to the opportunity set cannot increase the choice probability of some other alternative. In this study, we propose a novel approach that can rationalize an intended addition of such alternatives because it strictly increases the choice probability of some existing alternative. The driving force behind the existence and extent of such an increase is the random nature of individual preferences, that implies intransitivity, and the random nature of the applied choice procedures. We study the case of a firm interested in increasing the sales of some of its existing products by introducing a new and inferior (non‐salable) product. Our main results focus on the feasibility and potential advantage of a successful such strategy. We first establish necessary and sufficient conditions for an increase in the sale probability and then derive the maximal possible absolute and relative increase in this probability, when the firm has extremely limited information on the characteristics of the consumers. We then derive analogous results, assuming that the existing line of products consists of just two items and that the firm has accurate information on the consumers' stochastic preferences over the existing products. These later results are illustrated using some experimental evidence. The applicability of the approach is finally briefly discussed in the context of branding policy. Copyright © 2006 John Wiley & Sons, Ltd.     

Researching with whom? Stability and manipulation

This paper explores the existence of stable research teams, when the preferences of each agent depend on the set of researchers who are collaborating. We introduce a property over researchers’ preferences, called top responsiveness, guaranteeing the existence of stable research teams configurations. We also provide a stable mechanism, induced by the so-called top covering algorithm, which is strategy-proof when researchers preferences satisfy top responsiveness. Furthermore, we find that, in this framework, the top covering mechanism is the only strategy-proof mechanism that always selects stable allocations.     

Consistency in Measures of Social Homogeneity: A Connection with Proximity to Single Peaked Preferences

A survey of work is presented that is related to the relationship between measures of social homogeneity and probability that a Pairwise Majority Rule Winner (PMRW), or Condorcet Winner, exists. Little evidence has been reported to support the notion of a strong relationship between these two factors. Exact probability representations are derived to show that it is possible to find a parameter that is directly observable from voter profiles that can be systematically changed, so that an expected decrease in social homogeneity will lead to a counterintuitive increase in the expected probability that a PMRW exists. Using a different observable profile parameter that reflects a rough measure of the proximity of profiles to completely single-peaked preferences adds a sufficient degree of consistency among voters' preferences to produce the expected outcome.     

Nonparametric Bayesian modelling of monotone preferences for discrete choice experiments

Discrete choice experiments are widely used to learn about the distribution of individual preferences for product attributes. Such experiments are often designed and conducted deliberately for the purpose of designing new products. There is a long-standing literature on nonparametric and Bayesian modelling of preferences for the study of consumer choice when there is a market for each product, but this work does not apply when such markets fail to exist as is the case with most product attributes. This paper takes up the common case in which attributes can be quantified and preferences over these attributes are monotone. It shows that monotonicity is the only shape constraint appropriate for a utility function in these circumstances. The paper models components of utility using a Dirichlet prior distribution and demonstrates that all monotone nondecreasing utility functions are supported by the prior. It develops a Markov chain Monte Carlo algorithm for posterior simulation that is reliable and practical given the number of attributes, choices and sample sizes characteristic of discrete choice experiments. The paper uses the algorithm to demonstrate the flexibility of the model in capturing heterogeneous preferences and applies it to a discrete choice experiment that elicits preferences for different auto insurance policies.     

Modeling voter choice to predict the final outcome of two-stage elections

Most election forecasting research to date has been conducted in the context of single-round elections. However, more than 40 countries in the world employ a two-stage process, where actual voting data are available between the first and the second rounds to help politicians understand their position in relation to each other and to voter preferences and to help them predict the final outcome of the election. In this study we take advantage of the theoretical foundation on voter behavior from the political science literature and the recent methodological advances in choice modeling to develop a Nested Logit Factor Model of voter choice which we use to predict the final outcome of two stage elections and gain insights about the underlying political landscape. We apply the proposed model to data from the first stage and predict the final outcome of two stage elections based on the inferences made from the first stage results. We demonstrate how our proposed model can help politicians understand their competitive position immediately after the first round of actual voting and test its predictive accuracy in the run-off election across 11 different state governorship elections.     

On the performance of voting systems in spatial voting simulations

We study the performance of voting systems in terms of minimizing the overall social disutility of making a collective choice in an univariate voting space with ideological voting and perfect information. In order to obtain a distribution of the performance indicator for each of the 12 systems chosen for this study—Baldwin’s Method, Black’s Method, The Borda Count, Bucklin’s Grand Junction System, Coombs’ Method, Dodgson’s System, Instant Run-Off Voting, Plurality, Simpson’s MinMax, Tideman’s Ranked Pairs, Schulze’s Beatpath Method, and Two-Round Majority—we simulate elections using an Agent-Based Computational approach under several different distributions for voters and candidates positioning, with up to 15 available candidates. At each iteration, voters generate complete and strict ordinal utility functions over the set of available candidates, based on which each voting system computes a winner. We define the performance of a system in terms of its capability of choosing among the available candidates the one that minimizes aggregate voter disutility. As expected, the results show an overall dominance of Condorcet completion methods over the traditional and more widely used voting systems, regardless of the distributions of voter and candidate positions.     

On probability models in voting theory

This paper illustrates the use of probability models to study properties of voting rules. In particular, a simple occupancy distribution and its limiting Dlrichlet form are introduced, corresponding to simplifying assumptions about voters' preferences. We use as illustrations the occurrence probability of the Condorcet Paradox, a vintage problem in social choice theory, along with the related concept of Condorcet efficiency, a measure of goodness for voting rules. Further examples include properties of a lottery rule and the vulnerability of certain voting rules to strategic manipulation. Prospects for future work are indicated.     

Optimal lottery

This article proposes an equilibrium approach to lottery markets in which a firm designs an optimal lottery to rank-dependent expected utility (RDU) consumers. We show that a finite number of prizes cannot be optimal, unless implausible utility and probability weighting functions are assumed. We then investigate the conditions under which a probability density function can be optimal. With standard RDU preferences, this implies a discrete probability on the ticket price, and a continuous probability on prizes afterwards. Under some preferences consistent with experimental literature, the optimal lottery follows a power-law distribution, with a plausibly extremely high degree of prize skewness.     

On the relationship between economic development and political democracy

A politico-economic model is defined, in which consumers, at date 0, decide how much to invest in a firm (and how much of its stock to purchase), whose production possibilities are determined by the outcome of an election, to be held at date 1. At date 1, consumers vote on the level of pollution the firm shall be allowed to emit. There are incomplete markets; the states of the world are the two possible electoral outcomes at date 1, each associated with the victory of a particular party. In turn, the parties represent poor and rich voters; voters’ interests at date 1 are determined by the investments they have made at date 0. Because parties are uncertain about a parameter of voter preferences, the electoral (Nash) equilibrium at date 1 is not median-voter: there are two possible policies (pollution levels), occurring with probabilities that can be calculated. A full equilibrium of the model is an economic equilibrium with incomplete markets at date 0 and a political equilibrium at date 1, each of which induces the other. In a fictional ‘benevolent dictatorship,’ elections are called off, and the dictator announces a pollution policy which is the expected outcome of the would-be elections. By substituting the expected value of a lottery for a lottery, the utilities of citizens, who are risk-averse, increase. There are, however, costs to dictatorship, in the form of the absence of civil liberties. For any economic environment, it is possible to compute the equilibria under democracy and benevolent dictatorship, and to evaluate what coalition of the population prefers one to the other. In this way, the benevolent dictatorship is a benchmark against which to measure the costs of democracy. We examine to what extent the support for democracy, contrasted with benevolent dictatorship, grows among the population as economic development occurs. Development is simulated in five different ways, and it is not unambiguously the case that it induces a growing social preference for democracy. I have benefitted from discussions with A. Alesina and M. Quinzii, from the comments of S. Barbera at the International Economic Association conference on democracy and development (1992), from the comments of Michael Winston at the NBER political economy conference (1992), and from comments by participants at these conferences and at several university seminars.     

The construction of choice: a computational voting model

Social choice models usually assume that choice occurs among exogenously given and non-decomposable alternatives. On the contrary, choice is often among objects that are constructed by individuals or institutions as complex bundles made up of many interdependent components. In this paper we present a model of object construction in majority voting and show that, in general, by appropriately changing these bundles, different social outcomes may be obtained, depending upon initial conditions and agenda; that intransitive cycles and median voter dominance may be made to appear or disappear; and that decidability may be ensured by increasing manipulability or viceversa.     

A Note on Additive Separability and Latent Index Models of Binary Choice: Representation Results*

The standard binary choice model in econometrics has the choice determined by a latent index crossing a threshold. The latent index is almost always assumed to be additively separable in observable and unobservable regressors, and most commonly linear in all regressors. This note provides a class of non‐separable latent index functions which will have equivalent representations as additively separable or linear index functions. These results demonstrate that assuming a linear or additively separable latent index function is less restrictive than previously recognized.