Pairwise Strategy-Proofness and Self-Enforcing Manipulation

"Strategy-proofness" is one of the axioms that are most frequently used in the recent literature on social choice theory. It requires that by misrepresenting his preferences, no agent can manipulate the outcome of the social choice rule in his favor. The stronger requirement of "group strategy-proofness" is also often employed to obtain clear characterization results of social choice rules. Group strategy-proofness requires that no group of agents can manipulate the outcome in their favors. In this paper, we advocate "effective pairwise strategy-proofness." It is the requirement that the social choice rule should be immune to unilateral manipulation and "self-enforcing" pairwise manipulation in the sense that no agent of a pair has the incentive to betray his partner. We apply the axiom of effective pairwise strategy-proofness to three types of economies: public good economy, pure exchange economy, and allotment economy. Although effective pairwise strategy-proofness is seemingly a much weaker axiom than group strategy-proofness, effective pairwise strategy-proofness characterizes social choice rules that are analyzed by using different axioms in the literature.

Individual versus group strategy-proofness: when do they coincide?

A social choice function is group strategy-proof on a domain if no group of agents can manipulate its final outcome to their own benefit by declaring false preferences on that domain. Group strategy-proofness is a very attractive requirement of incentive compatibility. But in many cases it is hard or impossible to find nontrivial social choice functions satisfying even the weakest condition of individual strategy-proofness. However, there are a number of economically significant domains where interesting rules satisfying individual strategy-proofness can be defined, and for some of them, all these rules turn out to also satisfy the stronger requirement of group strategy-proofness. This is the case, for example, when preferences are single-peaked or single-dipped. In other cases, this equivalence does not hold. We provide sufficient conditions defining domains of preferences guaranteeing that individual and group strategy-proofness are equivalent for all rules defined on theStrategy-proofness, Group strategy-proofness, k-size strategy-proofness, Sequential inclusion, Single-peaked preferences, Single-dipped preferences, Separable preferences.

Strategy-proofness of social choice functions and non-negative association property with continuous preferences

We consider the relation between strategy-proofness of resolute (single-valued) social choice functions and its property which we call Non-negative association property (NNAP) when individual preferences over infinite number of alternatives are continuous, and the set of alternatives is a metric space. NNAP is a weaker version of Strong positive association property (SPAP) of Muller and Satterthwaite(1977). Barbera and Peleg(1990) showed that strategy-proofness of resolute social choice functions implies Modified strong positive association property (MSPAP). But MSPAP is not equivalent to strategy-proofness. We shall show that strategy-proofness and NNAP are equivalent for resolute social choice functions with continuous preferences.continuous preferences

The Relation between Monotonicity and Strategy-Proofness

The Muller-Satterthwaite Theorem (Muller and Satterthwaite, 1977) establishes the equivalence between Maskin monotonicity and strategy-proofness, two cornerstone conditions for the decentralization of social choice rules. We consider a general model that covers public goods economies as in Muller and Satterthwaite (1977) as well as private goods economies. For private goods economies we use a weaker condition than Maskin monotonicity that we call unilateral monotonicity. We introduce two easy-to-check domain conditions which separately guarantee that (i) unilateral/Maskin monotonicity implies strategy-proofness (Theorem 1) and (ii) strategy-proofness implies unilateral/Maskin monotonicity (Theorem 2). We introduce and discuss various classical single-peaked domains and show which of the domain conditions they satisfy (see Propositions 1 and 2 and an overview in Table 1). As a by-product of our analysis, we obtain some extensions of the Muller-Satterthwaite Theorem as summarized in Theorem 3. We also discuss some new "Muller-Satterthwaite domains" (e.g.,Proposition 3).Muller-Satterthwaite Theorem; restricted domains; rich domains; single-peaked domains; strategy-proofness; unilateral/Maskin monotonicity

Generalized monotonicity and strategy-proofness for non-resolute social choice correspondences

Recently there are several works which analyzed the strategy-proofness of non-resolute social choice rules such as Duggan and Schwartz (2000) and Ching and Zhou (2001). In these analyses it was assumed that individual preferences are linear, that is, they excluded indifference from individual preferences. We present an analysis of the strategy-proofness of non-resolute social choice rules when indifference in individual preferences is allowed. Following to the definition of the strategy-proofness by Ching and Zhou (2001) we shall show that a generalized version of monotonicity and the strategy-proofness are equivalent. It is an extension of the equivalence of monotonicity and the strategy-proofness for resolute social choice rules with linear individual preferences proved by Muller and Satterthwate (1980) to the case of non-resolute social choice rules with general individual preferences.generalized monotonicity

Strictly strategy-proof auctions

A strictly strategy-proof mechanism is one that asks agents to use strictly dominant strategies. In the canonical one-dimensional mechanism design setting with private values, we show that strict strategy-proofness is equivalent to strict monotonicity plus the envelope formula, echoing a well-known characterisation of (weak) strategy-proofness. A consequence is that strategy-proofness can be made strict by an arbitrarily small modification, so that strictness is 'essentially for free'

Strategy-Proof and Anonymous Rule in Queueing Problems: A Relationship between Equity and Efficiency

In this paper, we consider a relationship between equity and efficiency in queueing problems. We show that under strategy-proofness, anonymity in welfare implies queue-efficiency. Furthermore, we also give a characterization of the equally distributed pairwise pivotal rule, as the only rule that satisfies strategy-proofness, anonymity in welfare and budget-balance.Queueing Problems, Strategy-Proofness, Anonymity in welfare, Efficiency

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.strategy-proofness, reshuffling invariance, monotonicity, intertwined domains

A Characterization of the Randomized Uniform Rule

We consider the problem of allocating several units of an indivisible object among the agents with single-peaked and risk-averse utility functions. We introduce equal probability for the best, and show that the randomized uniform rule is the only randomized rule satisfying strategy-proofness, Pareto optimality, and equal probability for the best. This is an alternative characterization of the result of Ehlers and Klaus (2004).The Randomized Uniform Rule, Single-Peaked Utility Functions, Equal Probability for the Best, Strategy-Proofness, Indivisibility

Strategy-Proofness and Single-Crossing

This paper analyzes strategy-proof collective choice rules when individuals have single-crossing preferences on a finite and ordered set of social alternatives. It shows that a social choice rule is anonymous, unanimous and strategy-proof on a maximal single-crossing domain if and only if it is an extended median rule with n - 1 fixed ballots located at the end points of the set of alternatives. As a by-product, the paper also proves that strategy-proofness implies the tops-only property. And it offers a strategic foundation for the so called "single-crossing version" of the Median Voter Theorem, by showing that the median ideal point can be implemented in dominant strategies by a direct mechanism in which every individual reveals his true preferences.Strategy-proofness; single-crossing; median voter; positional dictators