Weak Independence and Social Semi‐Orders

This paper provides variants of Arrow's impossibility theorem, which states that there exists no non‐dictatorial aggregation rule satisfying weak Pareto, independence of irrelevant alternatives and collective rationality. In this paper, independence of irrelevant alternatives and collective rationality are simultaneously relaxed. Weak independence is imposed instead of independence of irrelevant alternatives. Social preferences are assumed to satisfy the semi‐order properties of semi‐transitivity and the interval‐order property. We prove that there exists a vetoer when the number of alternatives is greater than or equal to six.     

A note on the independence of irrelevant alternatives in probabilistic choice models

The purpose of this note is to show that there is no necessary relationship between the independence of irrelevant alternatives (IIA) property and stochastic independence of the errors in probabilistic choice models.     

The probability of violating Arrow’s conditions

Arrow’s impossibility theorem shows that all preference aggregation rules (PARs) must violate a specific set of normative conditions (transitivity, Pareto, IIA, nondictatorship) over an unrestricted domain of preference profiles. However, the theorem does not address which PARs are more likely to violate those conditions across preference profiles. We compare the probabilities that thirteen PARs (anti-plurality, Hare, Nanson, plurality, plurality runoff, Simpson–Kramer, Baldwin, Borda, Coombs, Copeland, Dowdall, pairwise majority, and ranked pairs) violate Arrow’s conditions. We prove that Baldwin, Borda, Coombs, Copeland, Dowdall, and ranked pairs are less likely to violate IIA than the first six PARs, and they are less likely to violate Arrow’s conditions jointly. In contrast, pairwise majority never violates IIA but can violate transitivity. Simulations with three alternatives reveal that among the PARs studied, pairwise majority is the most likely to satisfy Arrow’s conditions jointly. Our results suggest pairwise majority violates transitivity with a small probability, while the other PARs violate IIA with much larger probabilities.     

Substitutes and stability for matching with contracts

We consider the matching with contracts framework of Hatfield and Milgrom [20], and we introduce new concepts of bilateral and unilateral substitutes. We show that the bilateral substitutes condition is a sufficient condition for the existence of a stable allocation in this framework. However, the set of stable allocations does not form a lattice under this condition, and there does not necessarily exist a doctor-optimal stable allocation. Under a slightly stronger condition, unilateral substitutes, the set of stable allocations still does not necessarily form a lattice with respect to doctors' preferences, but there does exist a doctor-optimal stable allocation, and other key results such as incentive compatibility and the rural hospitals theorem are recovered.     

Folk theorem with communication

This paper proves a new folk theorem for repeated games with private monitoring and communication, extending the idea of delayed communication in Compte [O. Compte, Communication in repeated games with imperfect private monitoring, Econometrica 66 (1998) 597-626] to the case where private signals are correlated.The sufficient condition for the folk theorem is generically satisfied with more than two players, even when other well-known conditions are not. The folk theorem also applies to some two-players repeated games.     

Majority voting on restricted domains

In judgment aggregation, unlike preference aggregation, not much is known about domain restrictions that guarantee consistent majority outcomes. We introduce several conditions on individual judgments sufficient for consistent majority judgments. Some are based on global orders of propositions or individuals, others on local orders, still others not on orders at all. Some generalize classic social-choice-theoretic domain conditions, others have no counterpart. Our most general condition generalizes Sen's triplewise value-restriction, itself the most general classic condition. We also prove a new characterization theorem: for a large class of domains, if there exists any aggregation function satisfying some democratic conditions, then majority voting is the unique such function. Taken together, our results support the robustness of majority rule.     

Judgment aggregation: (im)possibility theorems

The aggregation of individual judgments over interrelated propositions is a newly arising field of social choice theory. I introduce several independence conditions on judgment aggregation rules, each of which protects against a specific type of manipulation by agenda setters or voters. I derive impossibility theorems whereby these independence conditions are incompatible with certain minimal requirements. Unlike earlier impossibility results, the main result here holds for any (non-trivial) agenda. However, independence conditions arguably undermine the logical structure of judgment aggregation. I therefore suggest restricting independence to “premises”, which leads to a generalised premise-based procedure. This procedure is proven to be possible if the premises are logically independent.     

Quality adjusted life years as expected utilities

Abstract. This article is intended to systematicaly show all the conditions that the Quality Adjusted Life Year (QALY) must satisfy so that it can be interpreted as a von Newman-Morgenstern utility. Such conditions cover two cases. When health states are chronic, we shall be referring to the conditions inferred by Pliskin, Shepard and Weinstein (1980). Likewise, we will devote our attention to commenting on the characterization of Bleichrodt (1996), pointing out that its condition 0 is a bit artificial. In turn, for temporary health states, we will remark that the characterization of Bleichrodt (1995) appears to be incomplete. We shall provide a complete derivation of QALYs. In this way, QALYs can be derived from an individual's preference relation that satisfies the von Newman-Morgenstern axioms by imposing additive independence, absence of contradictory trade-offs and partial symmetry. Moreover, the two last conditions conditions can be replaced by a single condition that we call general symmetry.     

The strategy-proof provision of public goods under congestion and crowding preferences

We examine the strategy-proof provision of excludable public goods when agents care about the number of other consumers. We show that strategy-proof and efficient social choice functions satisfying an outsider independence condition must always assign a fixed number of consumers, regardless of individual desires to participate. A hierarchical rule selects participants and a generalized median rule selects the level of the public good. Under heterogeneity in agents’ views on the optimal number of consumers, strategy-proof, efficient, and outsider independent social choice functions are much more limited and in an important case must be dictatorial.     

Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions

Consider a committee which must select one alternative from a set of three or more alternatives. Committee members each cast a ballot which the voting procedure counts. The voting procedure is strategy-proof if it always induces every committee member to cast a ballot revealing his preference. I prove three theorems. First, every strategy-proof voting procedure is dictatorial. Second, this paper's strategy-proofness condition for voting procedures corresponds to Arrow's rationality, independence of irrelevant alternatives, non-negative response, and citizens' sovereignty conditions for social welfare functions. Third, Arrow's general possibility theorem is proven in a new manner.     

THE BEHAVIOUR OF SOLUTIONS TO BARGAINING PROBLEMS ON THE BASIS OF SOLIDARITY*

The main purpose of this paper is to provide a systematic study of the solidarity‐type axioms for classical convex bargaining problems. As a consequence, we present alternative characterizations for some well‐known solutions in the literature. Instead of using the Monotonicity axiom, the paper provides characterizations of the egalitarian solution and the Kalai–Somorodinsky solution using slightly weaker versions of Nash's original IIA for convex bargaining problems with a fixed population.     

A note on equivalence of consistency and bilateral consistency through converse consistency

In the framework of (set-valued or single-valued) solutions for coalitional games with transferable utility, the three notions of consistency, bilateral consistency, and converse consistency are frequently used to provide axiomatic characterizations of a particular solution (like the core, prekernel, prenucleolus, Shapley value). Our main equivalence theorem claims that a solution satisfies consistency (with respect to an arbitrary reduced game) if and only if the solution satisfies both bilateral consistency and converse consistency (with respect to the same reduced game). The equivalence theorem presumes transitivity of the reduced game technique as well as difference independence on payoff vectors for two-person reduced games.     

An Afriat Theorem for the collective model of household consumption

We provide a nonparametric ‘revealed preference’ characterization of rational household behavior in terms of the collective consumption model, while accounting for general individual preferences that can be non-convex. Our main result is the Collective Afriat Theorem, which parallels the well-known Afriat Theorem for the unitary model. First, it provides a characterization of collectively rational consumption behavior in terms of collective Afriat inequalities. Next, it implies the Collective Axiom of Revealed Preference (CARP) as a testable necessary and sufficient condition for data consistency with collective rationality. Finally, the theorem has some interesting testability implications. With only a finite set of observations, the nature of consumption externalities (positive or negative) in the intra-household allocation process is non-testable. The same non-testability conclusion holds for privateness (with or without externalities) or publicness of consumption. By contrast, concavity of individual utility functions (representing convex preferences) turns out to be testable. In addition, monotonicity is testable for the model that assumes all household consumption is public.     

DUALITY WITH SECTOR‐SPECIFIC EXTERNALITIES UNDER SOCIAL CONSTANT RETURNS*

We develop dual approaches to quantity and price relationships of production in a general multisectoral model with sector‐specific externalities. The production of each good exhibits socially constant returns to scale but privately decreasing returns. We find that the Stolper‐Samuelson theorem holds for factor intensity ranking from the social perspective and that the Rybczynski theorem holds for factor intensity ranking from the private perspective. The price‐output dual fails to hold in general. Moreover, we re‐establish the Heckscher‐Ohlin theorem in the two‐sector case, as well as the factor endowment–factor price and price‐output comparative statics in the high‐dimension case under proper conditions.     

The role of independence in the Green-Lin Diamond-Dybvig model

Green and Lin study a version of the Diamond-Dybvig model with a finite number of agents, independence (independent determination of each agent's type), and sequential service. For special preferences, they show that the ex ante first-best allocation is the unique equilibrium outcome of the model with private information about types. Via a simple argument, it is shown that uniqueness of the truth-telling equilibrium holds for general preferences—and, in particular, for a constrained-efficient allocation whether first-best or not. The crucial assumption is independence.     

Preparing Africa for the twenty-first century: Lessons from constitutional economics

In the 1960s, when most African countries gained independence, they had an opportunity to select new political and economic institutions to promote growth and development. After more than three decades of political autonomy, it now appears that the opportunity made possible by decolonization was wasted and never fully utilized to promote sustainable development in the continent. As a result, after more than thirty years of independence, most of Africa remains poor and highly deprived. Political economy in the continent is characterized by opportunism, promoted by political coalitions whose primary objective is to subvert the rules to generate benefits for themselves. The end of the Cold War and the subsequent cessation of superpower rivalry, in addition to the demise of apartheid in South Africa, has provided policy makers in Africa another opportunity to choose new institutions to lead Africans into the twenty-first century. Public choice and constitutional economics provide guidelines that can be utilized to develop efficient and self-enforcing institutions to enhance development and effect significant increases in social welfare in Africa in the next century.     

A subjective model of experimentation

Typically an experiment is defined by a set of possible signals and a likelihood function, and both are specified exogenously—they are taken to be observable by the analyst. This paper renders them subjective by showing that they may be derived from suitable choice behavior. This is done in the context of an axiomatic representation theorem for preference on a suitable domain.     

On the independence from irrelevant alternatives in probabilistic choice models

Probabilistic choice models often invoke a behavioral assumption referred to as the independence from irrelevant alternatives. The implications of this condition have not been fully developed in probabilistic choice contexts. It is well known that nonpathological preferences may not exhibit the independence from irrelevant alternatives, which is apparently an assumption of convenience; and the obvious question is then whether the assumption is very restrictive. This paper addresses this question. A common model of probabilistic choice is constructed. A measure of the likelihood that independence from irrelevant alternatives holds is seen to arise naturally in this model. Given this measure, it is demonstrated that the condition will almost always fail to hold.     

Aggregation of binary evaluations with abstentions

A general model of aggregation of binary evaluations over interrelated issues, introduced by Wilson and further studied by Rubinstein and Fishburn and by the authors, is extended here to allow for abstentions on some of the issues. It is shown that the same structural conditions on the set of feasible evaluations that lead to dictatorship in the model without abstentions, lead to oligarchy in the presence of abstentions. Arrow's impossibility theorem for social welfare functions, Gibbard's oligarchy theorem for quasi-transitive social decision functions, as well as some apparently new theorems on preference aggregation, are obtained as corollaries.     

The robustness of the independent private value model in Bayesian mechanism design

Summary. In a Bayesian model of group decision-making, dependence among the agents' types has been shown to have a beneficial effect on the design of incentive compatible mechanisms that achieve the efficient choice associated with complete information. This effect is shown here to depend as much upon the use of large monetary transfers among the agents as it does upon dependence: if the transfers are bounded in magnitude, then nonexistence in the case of independence of an efficient, incentive compatible, ex ante budget-balanced and interim individually rational mechanism is robust to the introduction of a small amount of dependence among types. This robustness result supports the use of the simplifying assumption of independence in mechanism design. Received: October 28, 1996; revised version: May 28, 1997