Soc Choice Welfare Research Articles

Outside options in neutral allocation of discrete resources

Serial dictatorships have emerged as the canonical simple mechanisms in the literature on the allocation of indivisible goods without transfers. They are the only neutral and group-strategy-proof mechanisms in environments in which agents have no outside options and hence no individual rationality constraints (Svensson in Soc Choice Welfare 16:557–567, 1999). Accounting for outside options and individual rationality constraints, our main result constructs the class of group-strategy-proof, neutral, and non-wasteful mechanisms. These mechanisms are also Pareto efficient and we call them binary serial dictatorships. The abundance of the outside option—anybody who wants can opt out to get it—is crucial for our result.

Stable Rules for Electing Committees and Divergence on Outcomes

For three-candidate elections, this paper focuses on the relationships that exist between three stable rules for committee elections and the classical rules from which each of these stable rules are adapted. When selecting committees, a voting rule is said to be stable if it always elects a fixed-size subset of candidates such that there is no candidate in this set that is majority dominated by a candidate outside (Barbera and Coelho in Soc Choice Welfare 31:79–96, 2008; Coelho in Understanding, evaluating and selecting voting rules through games and axioms, 2004). There are some cases where a committee selected by a stable rule may differ from the committee made by the best candidates of the corresponding classical rule from which this stable rule is adapted. We call this the divergence on outcomes. We characterize all the voting situations under which this event is likely to occur. We also evaluate the likelihood of this event using the impartial anonymous culture assumption. As a consequence of our analysis, we highlight a strong connection between three Condorcet consistent rules: the Dodgson rule, the Maximin rule and the Young rule.

Pure Strategy Nash Implementation with Finite Mechanisms

Canonical mechanisms have unattractive features because they have to cover every instances of the implementation problem. This is unavoidable but at the same time it leaves open whether these features can be avoided in all specific cases or even most of them. We focus on one such feature: The infinity of the message space. It has been know since Jackson [A crash course in implementation theory, Soc Choice Welfare 18 (2001) 655-708.] that allowing only finite message spaces is a constraint. What is not known, however, is how bad this constraint is. Not surprisingly it all depends on what is known about the utility representations. What is surprising, though, is that allowing only finite message spaces does not severely limit implementability. In economic environments the constraints are particularly weak.

Orderings based on the banks set: Some new scoring methods for multicriteria decision making

This article introduces new methods for ranking alternatives in multicriteria decision making situations. Each is based on the normative position that the strength of an alternative is inversely related to the number of alternatives that could prevent it from being chosen. The scores discriminate among elements of the Banks set (Banks, Soc Choice Welfare, 1985, 1, 295–306). The new scoring methods are compared to traditional scoring methods and related to the amount of intransitivity (specifically, the size of the top‐cycle) of aggregated preference. The new scores are shown to measure important aspects of alternatives not captured by extant scoring methods and are illustrated in collective choice settings. © 2014 Wiley Periodicals, Inc. Complexity 20: 63–76, 2015

Equal opportunity equivalence in land division

In this paper we look for a solution to a land division problem that could be applied to different types of disputes when the arbitrator has a very limited information about the agents’ preferences. The solution must be fair and efficient under the constraint of the limited information available to the arbitrator. To this scope, we propose to use the concept of equal-opportunity equivalence defined by Thomson (Soc Choice Welfare 11:137–156 1994). We prove the existence of an efficient and equal opportunity equivalent allocation for a land division problem and we present a simple procedure to implement a rule that selects such allocation at each preference profile.

Still more on the Tournament Equilibrium Set

Schwartz (Soc Choice Welfare 3:271–291, 1990) proposed a solution concept (the Tournament Equilibrium Set) for choosing from a tournament and stated some conjectures about this solution. Laffond et al. (Math Sci Hum 123:37–44, 1993) introduced further conjectures and showed the links between some of them. In this short note, we show that one of the conjectures stated by Schwartz (1990) is false. We also complete a result given in Laffond et al. (1993).

On Ehrhart polynomials and probability calculations in voting theory

In voting theory, analyzing the frequency of an event (e.g. a voting paradox), under some specific but widely used assumptions, is equivalent to computing the exact number of integer solutions in a system of linear constraints. Recently, some algorithms for computing this number have been proposed in social choice literature by Huang and Chua (Soc Choice Welfare 17:143–155 2000) and by Gehrlein (Soc Choice Welfare 19:503–512 2002; Rev Econ Des 9:317–336 2006). The purpose of this paper is threefold. Firstly, we want to do justice to Eugene Ehrhart, who, more than forty years ago, discovered the theoretical foundations of the above mentioned algorithms. Secondly, we present some efficient algorithms that have been recently developed by computer scientists, independently from voting theorists. Thirdly, we illustrate the use of these algorithms by providing some original results in voting theory.

An axiomatization of the Nash bargaining solution

I prove that ‘Disagreement Point Convexity’ and ‘Midpoint Domination’ characterize the Nash bargaining solution on the class of two-player bargaining problems and on the class of smooth bargaining problems. I propose an example to show that these two axioms do not characterize the Nash bargaining solution on the class of bargaining problems with more than two players. I prove that the other solutions that satisfy these two properties are not lower hemi-continuous. These different results refine the analysis of Chun (Econ Lett 34:311–316, 1990). I also highlight a rather unexpected link with the result of Dagan et al. (Soc Choice Welfare 19:811–823, 2002).

Is abstention an escape from Arrow’s theorem?

In a society of variable size, Quesada (Soc Choice Welfare 25(1): 221–226, 2005) establishes the existence of Arrovian social welfare functions which are not dictatorial. We show that this escape from the Arrovian impossibility collapses when a very mild monotonicity condition is introduced.

Mixed Strategies in Games of Capacity Manipulation in Hospital–Intern Markets

We investigate games of capacity manipulation in hospital-intern markets as proposed by Konishi and Unver (Soc Choice Welfare, in press). While Konishi and Unver (Soc Choice Welfare, in press) show that there may not exist a pure-strategy Nash equilibrium in general, there exists a mixed-strategy Nash equilibrium in such a game. We show that every hospital weakly prefers a Nash equilibrium to any “larger” capacity profiles, whether the equilibrium is in pure or mixed strategies. In particular, a Nash equilibrium is weakly preferred by hospitals to the outcome that results from truthful reporting.

Positional Independence in Preference Aggregation: A Remark

In a recent article, Quesada (Soc Choice Welfare 20 363–370, 2003) showed that if, for strict preferences, a unique strongly unanimous Choice Function (CF) is used to aggregate preferences position-wise then the resulting Social Welfare Function (SWF) is dictatorial. We show that this result is still true if one allows the use of different choice functions, one for each position. We also show that allowing choice functions not to be unanimous leads to SCW that are perm-dictatorial or imposed. We also show a way to set a dual problem to the one exposed in Que03, namely only perm-dictatorial and imposed SWFs can be decomposed into several Dual Choice Functions.

The Balinski–Young Comparison of Divisor Methods is Transitive

The ‘favoring small states’ relation of Balinski and Young (Fair representation, 1982) imposes stronger requirements on the nature of seat transfers than the majorization-ordering introduced by Marshall et al. (Soc Choice Welfare 19(4):885–900, 2002). For divisor methods, however, the two relations coincide. As a consequence, when restricted to the class of divisor methods the Balinski and Young relation is transitive.

On the necessary and sufficient conditions for Nash implementation

In a recent work, Ziad (Ziad, A., 1997. A New Necessary Condition for Nash Implementation. To appear in the Journal Of Mathematical Economics) has defined a new condition for the problem of implementation of a social choice correspondence. He has formulated a family of conditions called B k -monotonicity that are necessary for Nash implementation, where k is a natural number that indexes a particular condition. The B k -monotonicity is in general a stronger condition than Maskin monotonicity, but is necessary for implementation. In this note we improve the algorithms proposed by Sjöström (Sjöström, T., 1991. On the necessary and sufficient conditions for Nash implementation. Soc Choice Welfare 8, 333–340) to determine a condition which is necessary and sufficient for implementation. The main result is that in some non implementability cases we do not have to repeat the operation of Sjöström algorithms up to their terminations.

Acyclicity and the dispersion of the veto power

Blair and Pollak (Econometrica (1982) 50: 931–943) prove that, if there are more alternatives than individuals, then, for every arrovian binary decision rule that is acyclic, there is at least one individual who has a veto power over a critical number of pairs of alternatives. If the number of individuals is larger than the number of alternatives, there need not be single vetoers but there could be small coalitions endowed with a similar power. Kelsey (Soc Choice Welfare (1985) 2: 131–137) states precise results in this respect. In this paper, we first give a new and much simpler proof of the main result of Blair and Pollak and complete proofs of the generalization of this result by Kelsey. Then we give a precise answer as to the minimum size of the coalitions that must have a veto power under any acyclic binary decision rule and the minimum number of pairs of alternatives on which these coalitions may exercise their power. We also show that, if the veto power of the coalitions of the minimal size attainable under the last objective is limited to the minimum number of pairs of alternatives, then all larger coalitions have a veto power on all pairs. All the results are obtained by appealing to an acyclicity condition found by Ferejohn and Fishburn (J Econ Theory (1979) 21: 28–45). In the case of symmetric and monotonic binary decision rules, proofs are even easier and illustrate clearly the reasons for the veto power.

The meaning of ?fundamental preferences?

We present the definition and meaning of “fundamental preferences” that are interpersonally comparable, ordinal and endemonistic. We also dispel a number of misunderstandings concerning them. In the article “A cause of preference is not on object of preference” (Soc Choice Welfare (1993) 10: 57–68), Professor Broome misinterprets the notion of “fundamental preferences” in confusing an observer's device for a psychological transformation of the observed (as if an economist studying wealth meant that he becomes wealthy, or if physicians had to be sick — this is well shown in his interpretation of a sentence of mine in p 65 where the crucial switch to the first person is his own). Considering a new set of variables that includes both structural parameters and former variables, hence variables of different kinds, assumes nothing new concerning the observed object; namely, it says neither that the consumption of bread becomes “a cause” of the taste for jam, nor that the individual likes (or dislikes) his own tastes, or anything like this (the accusation of “fantasy”). We shall suggest that certain other views receive a similar treatment in this paper. This misunderstanding is regrettable, since the consideration of fundamental preferences is unavoidable in social ethics, both when one has to compare all-encompassing individual situations, and for the preferences of the hypothetical identical individuals in an Original Position device where they evaluate at once what they might have and what they might be1.