Manipulation and the Pareto rule

This paper examines rules that map preference profiles into choice sets. There are no agendas other than the entire set of alternatives. A rule is said to be “manipulable” if there is a person i, and a preference profile, such that i prefers the choice set obtained when he is dishonest to the one obtained when he is honest. It is “nonmanipulable” if this can never happen. The paper indicates how preferences over choice sets might be sensibly derived from preferences over alternatives, and discusses seven different notions of manipulability associated with seven different assumptions about preferences over sets of alternatives. The paper has two sections of results. In the first I show that the Pareto rule, that is, the rule that maps preference profiles into corresponding sets of Pareto optima, is nonmanipulable in four of the seven senses of manipulability, and manipulable in three of them. In the second section, I examine this conjecture: If an arbitrary rule is nonmanipulable and nonimposed, and if indifference is disallowed, then every choice set must be contained in the set of Pareto optima. The conjecture is true under the strongest definition of nonmanipulability.     

Securing basic well-being for all

The purpose of this article is to examine the possibility of a social choice rule to implement a social policy for “securing basic well-being for all.” The article introduces a new scheme of social choice, called a social relation function (SRF), which associates a reflexive and transitive binary relation over a set of social policies to each profile of individual well-being appraisals and each profile of group evaluations. As part of the domains of SRFs, the available class of group evaluations is constrained by three conditions. Furthermore, the non-negative response (NR) and the weak Pareto condition (WP) are introduced. NR demands giving priority to group evaluation, while treating the groups as formally equal relative to each other. WP requires treating impartially the well-being appraisals of all individuals. In conclusion, this article shows that under some reasonable assumptions, there exists an SRF that satisfies NR and WP.     

Arrovian aggregation in economic environments: how much should we know about indifference surfaces?

Arrow's celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and non-dictatorship principles are violated. In the standard model of division of commodities, we investigate how much information about indifference surfaces is needed to construct social ordering functions satisfying the weak Pareto principle and anonymity. We show that local information such as marginal rates of substitution or the shapes “within the Edgeworth box” is not enough, and knowledge of substantially non-local information is necessary.     

Core is manipulable via segmentation

Any allocation rule that picks only core allocations is manipulable via segmentation. That is, there exists an economy with a coalition of agents such that, once this coalition splits momentarily from the rest of the economy and institutes the allocation rule within itself, no matter which individually rational sub-allocation the complementary coalition picks, when we paste all the agents back together at their new endowments and apply the allocation rule to this “collage” economy, each member of the former coalition will be strictly better off than under direct application of the allocation rule to the original economy.     

Strategy-proof preference aggregation: Possibilities and characterizations

An aggregation rule maps each profile of individual strict preference orderings over a set of alternatives into a social ordering over that set. We call such a rule strategy-proof if misreporting one's preference never produces a different social ordering that is between the original ordering and one's own preference. After describing two examples of manipulable rules, we study in some detail three classes of strategy-proof rules: (i) rules based on a monotonic alteration of the majority relation generated by the preference profile; (ii) rules improving upon a fixed status-quo; and (iii) rules generalizing the Condorcet–Kemeny aggregation method.     

A leximin characterization of strategy-proof and non-resolute social choice procedures

Summary. We characterize strategy-proof social choice procedures when choice sets need not be singletons. Sets are compared by leximin. For a strategy-proof rule g, there is a positive integer k such that either (i) the choice sets g(r) for all profiles r have the same cardinality k and there is an individual i such that g(r) is the set of alternatives that are the k highest ranking in i's preference ordering, or (ii) all sets of cardinality 1 to k are chosen and there is a coalition L of cardinality k such that g(r) is the union of the tops for the individuals in L. There do not exist any strategy-proof rules such that the choice sets are all of cardinality to k where . Received: November 8, 1999; revised version: September 18, 2001     

Collective choice functions on non-convex problems

Collective choice problems on sets in _boxclose_boxclose^n{\frak R}_+^n arise naturally in economics. Such problems have been extensively studied both in the theory of revealed preferences (Peters and Wakker, 1991) and in axiomatic bargaining theory under the assumption of convexity. However, our knowledge of collective choice functions on non-convex problems is still patchy. In this paper I study the existence and characterisation of continuous choice functions on the domain G\Gamma of comprehensive problems. The main result completely characterises rational choice functions that are continuous and satisfy Weak Pareto Optimality: they form the class of Monotone Path Choice Functions on G\Gamma. I also show that any discontinuous rational and weakly Pareto optimal choice function must be non- anonymous.     

Solidarity and Probabilistic Target Rules

We consider a probabilistic approach to collective choice problems where a group of agents with single-peaked preferences have to decide on the level or location of a public good. We show that every probabilistic rule that satisfies Pareto efficiency and "solidarity" (population-monotonicity or replacement-domination) must equal a so-called target rule.     

Preference aggregation with randomized social orderings

We show that every binary and Paretian method for passing from preference profiles to lotteries over preferences is associated with a subadditive function on the set of coalitions of individuals. This function gives the power of each coalition to secure its preference for any x over any y.     

On the Problem of Constructing Rational Preferences

In standard models it is typically taken for granted that preferences are given and defined over the alternatives alone, and the possibility of making a rational choice is a matter of assumption. I generalise this aspect of the economic model so that preferences over alternatives are constructed from given preferences defined over various characteristics of the alternatives under consideration. I characterise the decision problem before investigating what conditions a procedure for aggregating preferences over attributes into preferences over alternatives must satisfy in order for the latter to be rational. I then consider what the implications of these conditions for the procedural rationality of the aggregation process.     

Taxes or Fees? The Political Economy of Providing Excludable Public Goods

This paper provides a positive analysis of public provision of excludable public goods financed by uniform taxes or fees. Individuals differing in preferences decide, using majority rule, the provision level and financing instrument. The decisive voter has median preferences in a tax regime, but generally has above median preferences in a fee regime. Numerical solutions indicate that populations with uniform or left‐skewed distributions of preferences choose taxes, while a majority coalition of high‐ and low‐preference individuals prefer fees when preferences are sufficiently right skewed. Public good provision and welfare under fees exceeds that under taxes in the latter case.     

Misery loves company: Social regret and social interaction effects in choices under risk and uncertainty

Extensive field evidence shows individuals? decisions in settings involving uncertainty depend on their peers? decisions. One hypothesized cause of peer group effects is social interaction effects: an individual?s utility from an action is enhanced by others taking the same action. We employ a series of controlled laboratory experiments to study the causes of peer effects in choice under uncertainty. We find strong peer group effects in the laboratory. Our design allows us to rule out social learning, social norms, group affiliation, and complementarities as possible causes for the observed peer group effects, leaving social interaction effects as the likely cause. We use a combination of theory and empirical analysis to show that preferences including “social regret” are more consistent with the data than preferences including a taste for conformity. We observe spillover effects, as observing another?s choice of one risky gamble makes all risky gambles more likely to be chosen.     

Efficient strategy-proof exchange and minimum consumption guarantees

For exchange economies with classical economic preferences, it is shown that any strategy-proof social choice function that selects Pareto optimal outcomes cannot guarantee everyone a consumption bundle bounded away from the origin. This result demonstrates that there is a fundamental conflict between efficiency and distributional goals in exchange economies if the social choice rule is required to be strategy-proof.     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

PREFERENCES UNDER IGNORANCE

A decision maker (DM) makes choices from different sets of alternatives. The DM is initially ignorant of the payoff associated with each alternative and learns these payoffs only after a large number of choices have been made. We show that, in the presence of an outside option, once payoffs are learned, the optimal choice rule from sets of alternatives can be rationalized by a DM with strict preferences over all alternatives. Under this model, the DM has preferences for preferences while being ignorant of what preferences are “right.”     

Pigouvian pricing and stochastic evolutionary implementation

We study the implementation of efficient behavior in settings with externalities. A planner would like to ensure that a group of agents make socially optimal choices, but he only has limited information about the agents’ preferences, and can only distinguish individual agents through the actions they choose. We describe the agents’ behavior using a stochastic evolutionary model, assuming that their choice probabilities are given by the logit choice rule. We prove that there is a simple price scheme with the following property: regardless of the realization of preferences, a group of agents subjected to the price scheme will spend the vast majority of time in the long run behaving efficiently. The price scheme defines a game that may possess multiple equilibria, but we are able to obtain a unique and efficient selection from this set because of the stochastic nature of the agents’ choice rule. We conclude by comparing the performance of our price scheme with that of VCG mechanisms.     

A new approach to understanding labour supply of disabled people

The main interest of this article is to propose an individual utility maximization model to explain the low participation of disabled people. We account for heterogeneity of preferences and furthermore time of self-caring for disabled individuals is considered as an argument in the utility function. The hours of work decided by disabled individuals are neither homogeneous (they depend on unknown characteristics) nor continuous (discrete choice sets). We use data of 4790 households from the Spanish Survey of Disability, Personal Autonomy and Dependency and find association between time of informal care and labour participation and, consequently, the choice between jobs.     

SEQUENTIAL STOCHASTIC DOMINANCE AND THE ROBUSTNESS OF POVERTY ORDERINGS

When comparing poverty across distributions, an analyst must select a poverty line to identify the poor, an equivalence scale to compare individuals from households of different compositions and sizes, and a poverty index to aggregate individual deprivation into an index of total poverty. A different choice of poverty line, poverty index or equivalence scale can of course reverse an initial poverty ordering. This paper develops easily-checked sequential stochastic dominance conditions that throw light on the robustness of poverty comparisons to these important measurement issues. These general conditions extend well-known results to any order of dominance, to the choice of individual versus family based aggregation, and to the estimation of "critical sets" of measurement assumptions. Our theoretical results are briefly illustrated using data for four countries drawn from the Luxembourg Income Study databases.     

Necessary and sufficient conditions for a resolution of the social choice paradox

We present a restriction on the domain of individual preferences that is both necessary and sufficient for the existence of a social choice rule that is continuous, anonymous, and respects unanimity. The restriction is that the space of preferences be contractible. Contractibility admits a straightforward intuitive explanation, and is a generalisation of conditions such as single peakedness, value restrictedness and limited agreement, which were earlier shown to be sufficient for majority voting to be an acceptable rule. The only restriction on the number of individuals, is that it be finite and at least 2.