Distribution of coalitional power in randomized multi-valued social choice

This paper considers the distribution of coalitional influence under probabilistic social choice functions which are randomized social choice rules that allow social indifference by mapping each combination of a preference profile and a feasible set to a social choice lottery over all possible choice sets from the feasible set. When there are at least four alternatives in the universal set and ex-post Pareto optimality, independence of irrelevant alternatives and regularity are imposed, we show that: (i) there is a system of additive coalitional weights such that the weight of each coalition is its power to be decisive in every two-alternative feasble set; and (ii) for each combination of a feasible proper subset of the universal set and a preference profile, the society can be partioned in such a way that for each coalition in this partition, the probability of society's choice set being contained in the union of the best sets of its members is equal to the coalition's power or weight. It is further shown that, for feasible proper subsets of the universal set, the probability of society's choice set containing a pair of alternatives that are not jointly present in anyone's best set is zero. Our results remain valid even when the universal set itself becomes feasible provided some additional conditions hold. Received: 10 May 1999/Accepted: 18 June 2000 I would like to thank Professor Prasanta Pattanaik for suggesting to me the line of investigation carried out in this paper. I am solely responsible for any remaining errors and omissions.     

An informationally parsimonious impartial observer theorem

In Harsanyi's impartial observer theorem, an impartial observer determines a social ordering of the lotteries on the set of social alternatives based on a sympathetic but impartial concern for all individuals in society. This ordering is derived from a more primitive ordering on the set of all extended lotteries. An extended lottery is a lottery which determines both the observer's personal identity and the social alternative. We establish a version of Harsanyi's theorem in which the observer is only required to have preferences on the extended lotteries in which there is an equal chance of being any person in society. Received: 19 June 1996 / Accepted: 30 December 1996     

Assent-maximizing social choice

We take a decision theoretic approach to the classic social choice problem, using data on the frequency of choice problems to compute social choice functions. We define a family of social choice rules that depend on the population’s preferences and on the probability distribution over the sets of feasible alternatives that the society will face. Our methods generalize the well-known Kemeny Rule. In the Kemeny Rule, it is known a priori that the subset of feasible alternatives will be a pair. We define a distinct social choice function for each distribution over the feasible subsets. Our rules can be interpreted as distance minimization—selecting the order closest to the population’s preferences, using a metric on the orders that reflects the distribution over the possible feasible sets. The distance is the probability that two orders will disagree about the optimal choice from a randomly selected available set. We provide an algorithmic method to compute these metrics in the case where the probability of a given feasible set is a function only of its cardinality.     

Inefficiencies on linking decisions

It has recently been shown that by linking collective decisions the incentive costs can become negligible and, at the limit, ex ante efficiency can be achieved. In a voting situation this implies that the agents’ intensity of preferences can be taken into account even in the absence of monetary transfers. Rather than considering a limiting result we want to analyse what can be achieved while we consider a finite number of linked decisions. We first characterise the set of implementable mechanisms and show that ex ante efficiency can never be achieved. We then proceed to relax the efficiency requirement and prove that, even when we just require unanimity, the mechanism cannot be sensitive to the agents’ intensity of preference when the domain of preferences is unrestricted.     

Identification of domain restrictions over which acyclic, continuous-valued, and positive responsive social choice rules operate

We consider a social choice problem in various economic environments consisting of n individuals, 4≤n<+∞, each of which is supposed to have classical preferences. A social choice rule is a function associating with each profile of individual preferences a social preference that is assumed to be complete, continuous and acyclic over the alternatives set. The class of social choice rules we deal with is supposed to satisfy the two conditions; binary independence and positive responsiveness. A new domain restriction for the social choice rules is proposed and called the classical domain that is weaker than the free triple domain and holds for almost all economic environments such as economies with private and/or public goods. In this paper we explore what type of classical domain that admits at least one social choice rule satisfying the mentioned conditions to well operate over the domain. The results we obtained are very negative: For any classical domain admitting at least one social choice rule to well operate, the domain consists only of just one profile.     

Sets of alternatives as Condorcet winners

We characterize sets of alternatives which are Condorcet winners according to preferences over sets of alternatives, in terms of properties defined on preferences over alternatives. We state our results under certain preference extension axioms which, at any preference profile over alternatives, give the list of admissible preference profiles over sets of alternatives. It turns out to be that requiring from a set to be a Condorcet winner at every admissible preference profile is too demanding, even when the set of admissible preference profiles is fairly narrow. However, weakening this requirement to being a Condorcet winner at some admissible preference profile opens the door to more permissive results and we characterize these sets by using various versions of an undomination condition. Although our main results are given for a world where any two sets – whether they are of the same cardinality or not – can be compared, the case for sets of equal cardinality is also considered. Received: 15 March 2001/Accepted: 31 May 2002 This paper was written while Barış Kaymak was a graduate student in Economics at Boğazi?i University. We thank ?ağatay Kayı and İpek ?zkal-Sanver who kindly agreed to be our initial listeners. The paper has been presented at the Economic Theory seminars of Bilkent, Ko? and Sabancı Universities as well as at the Fifth Conference of the Society for the Advancement of Economic Theory, July 2001, Ischia, Italy and at the 24^th Bosphorus Workshop on Economic Design, August 2001, Bodrum, Turkey. We thank Fuad Aleskerov, İzak Atiyas, ?zgür Kıbrıs, Semih Koray, Gilbert Laffond, Bezalel Peleg, Murat Sertel, Tayfun S?nmez, Utku ünver and all the participants. Remzi Sanver acknowledges partial financial support from İstanbul Bilgi University and the Turkish Academy of Sciences and thanks Haluk Sanver and Serem Ltd. for their continuous moral and financial support. Last but not the least, we thank Carmen Herrero and two anonymous referees. Of course we are the sole responsible for all possible errors.     

Almost all social choice rules are highly manipulable,but a few aren't

Explores, for several classes of social choice rules, the distribution of the number of profiles at which a rule can be strategically manipulated. In this paper, we will do comparative social choice, looking for information about how social choice rules compare in their vulnerability to strategic misrepresentation of preferences.I am indebted to Universidad Internacional Menendez Pelayo for an invitation to present an early version of this paper at a June, 1989 conference at Valencia, Spain. Thanks for comments go to the participants of that conference, especially Salvador Barbera; also for comments at seminars at Syracuse University and the University of Rochester.     

A Social Choice Lemma on Voting Over Lotteries with Applications to a Class of Dynamic Games

We prove a lemma characterizing majority preferences over lotteries on a subset of Euclidean space. Assuming voters have quadratic von Neumann–Morgenstern utility representations, and assuming existence of a majority undominated (or “core”) point, the core voter is decisive: one lottery is majority-preferred to another if and only if this is the preference of the core voter. Several applications of this result to dynamic voting games are discussed.This paper was completed after Jeff Banks’s death. John Duggan is deeply indebted to him for his friendship and his collaboration on this and many other projects.     

Aggregation of individuals' preference intensities into social preference intensity

A result of John Harsanyi concerns the aggregation of individuals' preferences into social preferences. The result states that if the individuals in a society and the society as a whole have preference relations that compare probability distributions on a set of outcomes, and the preference relations satisfy expected-utility conditions and Pareto conditions, then a utility function for the social preference relation is a positive affine function of utility functions for the individuals' preference relations. This paper presents an analogous result for preference relations that denote intensity of preference, i.e., preference relations that compare exchanges of outcomes. This approach avoids the difficulties of requiring that the individuals in the society have common beliefs regarding uncertainty. Received: 14 October 1996 / Accepted: 4 September 1997     

Motivational crowding out effects in charitable giving: Experimental evidence

This paper tests motivational crowding out in the domain of charitable giving. A novelty is that our experiment isolates alternative explanations for the decline of giving, such as strategic considerations of decision-makers. Moreover, preference elicitation allows us to focus on the reaction of donors characterized by different degrees of intrinsic motivation. In the charitable-giving setting subjects donate money to the German “Red Cross” in two consecutive donations. The first dictator game is modified, i.e., donors face with equal probability an ex post reimbursement or a subsequent payment. The second game is a standard dictator game. We find that after an ex post change in the price of giving of the first donation, substantially more donors with a high degree of intrinsic motivation decrease donations than subjects with a low degree of intrinsic motivation and donors who did not experience a price effect. In a replication study we find support for these results for subjects who have previously participated in at least one economic experiment.     

Does majoritarian approval matter in selecting a social choice rule? An exploratory panel study

This study is an attempt to empirically detect the public opinion concerning majoritarian approval axiom. A social choice rule respects majoritarian approval iff it chooses only those alternatives which are regarded by a majority of “voters” to be among the “better half” of the candidates available. We focus on three social choice rules, the Majoritarian Compromise, Borda’s Rule and Condorcet’s Method, among which the Majoritarian Compromise is the only social choice rule always respecting majoritarian approval. We confronted each of our 288 subjects with four hypothetical preference profiles of a hypothetical electorate over some abstract set of four alternatives. At each hypothetical preference profile, two representing the preferences of five and two other of seven voters, the subject was asked to indicate, from an impartial viewpoint, which of the four alternatives should be chosen whose preference profile was presented, which if that is unavailable, then which if both of the above are unavailable, and finally which alternative should be avoided especially. In each of these profiles there is a Majoritarian Compromise-winner, a Borda-winner and a Condorcet-winner, and the Majoritarian Compromise-winner is always distinct from both the Borda-winner and the Condorcet-winner, while the Borda- and Condorcet-winners sometimes coincide. If the Borda- and Condorcet-winners coincide then there are two dummy candidates, otherwise only one, and dummies coincide with neither of the Majoritarian Compromise-, Borda- or Condorcet-winner. We presented our subjects with various types of hypothetical preference profiles, some where Borda respecting majoritarian approval, some where it failed to do so, then again for Condorcet, some profiles it respected majoritarian approval and some where it did not. The main thing we wanted to see was whether subjects’ support for Borda and Condorcet was higher when this social choice rule respected majoritarian approval than it did not. Our unambiguous overall empirical finding is that our subjects’ support for Borda and Condorcet was significantly stronger as they respect majoritarian approval.     

Living with unfairness: The limits of equal opportunity in a market economy

Equality of opportunity is often presented as a criterion which reconciles egalitarianism with principles of freedom and responsibility. This paper distinguishes between the principle of starting-line equality, which requires that everyones initial opportunities, assessed in relation to what is publicly known ex ante, are equal, and the principle that equal efforts should yield equal ex post rewards. It argues that the first principle is compatible with allocation of resources through markets but, because of the division of knowledge, the second is not. If we want the opportunities which markets give us, we have to accept ex post unfairness. Earlier versions of this paper were presented at a workshop on the measurement of freedom at the London School of Economics, and at a conference on non-welfarist issues in normative economics at the University of Caen. I thank participants at those meetings, and particularly Tania Burchardt, Marco Mariotti and Franz Prettenthaler, for comments. My work on this paper was supported by the Leverhulme Trust.     

On randomized rationality

In contrast to the traditional notion of rationalizability of stochastic choice which requires the preference relations to be strict, we propose a notion of rationalizability without requiring the preference relations to be strict. Our definition is based on the simple hypothesis of a two-stage choice process: stage (i) a preference relation R is drawn according to a probability assignment; stage (ii) an alternative is picked from each feasible set according to a uniform lottery over the R-greatest set in it. We provide a necessary and sufficient condition for rationalizability of stochastic choice. Since our framework is general enough to subsume the traditional case, our result also provides an alternative characterization of the traditional notion of rationalizability. We also show the equivalence between the two notions of rationalizability in a specific case.     

A fundamental structure of strategy-proof social choice correspondences with restricted preferences over alternatives

I prove that under each strategy-proof and unanimous social choice correspondence, there is at least one agent who is decisive. Because the result is established on a weak requirement on preferences over sets, the existence of a decisive agent is an underlying feature of most strategy-proof and unanimous social choice correspondences. Moreover, I consider a restriction on the space of preferences over alternatives. I prove that circular sets of preferences over alternatives are sufficient for the existence of a decisive agent.     

Risky social choice with incomplete or noisy interpersonal comparisons of well-being

In this study, we develop a model of social choice over lotteries, where people’s psychological characteristics are mutable, their preferences may be incomplete, and incomplete or noisy interpersonal comparisons of well-being are possible. Formally, we suppose individual preferences are described by a von Neumann-Morgenstern (vNM) preference order on a space of lotteries over psychophysical states; the social planner must construct a vNM preference order on lotteries over social states. First, we consider a model where the individual vNM preference order is incomplete (so not all interpersonal comparisons are possible). Then, we consider a model where the individual vNM preference order is complete, but unknown to the planner, and thus modelled by a random variable. In both cases, we obtain characterizations of a utilitarian social welfare function.     

The original Borda count and partial voting

In a Borda count, bc, M. de Borda suggested the last preference cast should receive 1 point, the voter’s penultimate ranking should get 2 points, and so on. Today, however, points are often awarded to (first, second,..., last) preferences cast as per (n, n?1, ..., 1) or more frequently, (n ?1, n?2,..., 0). If partial voting is allowed, and if a first preference is to be given n or n ? 1 points regardless of how many preferences the voter casts, he/she will be incentivised to rank only one option/candidate. If everyone acts in this way, the bc metamorphoses into a plurality vote... which de Borda criticized at length. If all the voters submit full ballots, the outcome—social choice or ranking—will be the same under any of the above three counting procedures. In the event of one or more persons submitting a partial vote, however, outcomes may vary considerably. This preliminary paper suggests research should consider partial voting. The author examines the consequences of the various rules so far advocated and then purports that M. de Borda, in using his formula, was perhaps more astute than the science has hitherto recognised.     

Trust and risk revisited

A trustor faces a risky choice in the trust game when he acts upon his belief regarding the chances of betrayal by the trustee. Despite intensive research there is no clear evidence for a link between lottery risk preferences and risk involved in trusting others. We argue that this is due to crucial differences between the risk measurements in the two settings. Trusting is giving up control to a human while lottery risk arises from a mechanistic randomization device. We propose a risky trust game that experimentally measures risk in the same context as the standard trust game, but nevertheless reduces the trust decision to objective risk. Our results show that transfers in the trust game can indeed be explained by individual risk attitudes elicited with the risky trust game, while lottery risk preferences have no explanatory power.     

Generalizing the Gibbard–Satterthwaite theorem: partial preferences,the degree of manipulation,and multi-valuedness

The Gibbard–Satterthwaite (GS) theorem is generalized in three ways: First, it is proved that the theorem is still valid when individual preferences belong to a convenient class of partial preferences; second, it is shown that every non-dictatorial surjective social choice function (SCF) is not only manipulable, but it can be manipulated in such a way that some individual obtains either his best or second best alternative; third, we prove a variant of the theorem where the outcomes of the SCF are subsets of the set of alternatives of an a priori fixed size. In addition, all results are proved not only for finite, but also for countably infinite sets of alternatives.     

Equity, continuity, and myopia: A generalization of Diamond’s impossibility theorem

 We consider social preferences over infinite horizon intergenerational consumption paths. We use the Mackey topology to define continuity of social preferences. Our main objective is to generalize one of Diamond’s impossibility theorems. First, we show that the trivial preference relation is the only asymmetric social preference relation satisfying equity and continuity. Second, we compare Campbell’s impossibility theorem with ours. Finally we use an order-based notion of myopia and establish another impossibility result. Received: 26 August 1994/Accepted: 5 June 1996     

Nash implementation via hyperfunctions

Hyperfunctions are social choice rules which assign sets of alternatives to preference profiles over sets. Therefore, they are more general objects compared to standard (social choice) correspondences. In fact, every correspondence can be expressed in terms of an equivalent hyperfunction. We give a partial characterization of Nash-implementable hyperfunctions and explore the conditions under which correspondences have Nash-implementable equivalent hyperfunctions. While the strength of these conditions depends on the axioms used to extend preferences over alternatives to sets, they are at most as strong as the conjunction of Maskin monotonicity with the no veto power condition. Thus, our approach expands the set of Nash-implementable social choice rules. In fact, social choice rules such as the majority rule and the top cycle are Nash-implementable through their equivalent hyperfunctions, while they are not Maskin-monotonic, and thus, not Nash-implementable in the standard framework.

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