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1.
Masashi Umezawa 《Social Choice and Welfare》2009,33(1):151-158
This paper studies coalitional strategy-proofness of social choice correspondences that map preference profiles into sets
of alternatives. In particular, we focus on the Pareto rule, which associates the set of Pareto optimal alternatives with
each preference profile, and examine whether or not there is a necessary connection between coalitional strategy-proofness
and Pareto optimality. The definition of coalitional strategy-proofness is given on the basis of a max–min criterion. We show
that the Pareto rule is coalitionally strategy-proof in this sense. Moreover, we prove that given an arbitrary social choice
correspondence satisfying the coalitional strategy-proofness and nonimposition, all alternatives selected by the correspondence
are Pareto optimal. These two results imply that the Pareto rule is the maximal correspondence in the class of coalitionally
strategy-proof and nonimposed social choice correspondences. 相似文献
2.
Shasikanta Nandeibam 《Social Choice and Welfare》2002,19(3):685-705
We consider probabilistic voting procedures which map each feasible set of alternatives and each utility profile to a social
choice lottery over the feasible set. It is shown that if we impose: (i) a probabilistic collective rationality condition
known as regularity; (ii) probabilistic counterpart of Arrow's independence of irrelevant alternatives and citizens' sovereignty; (iii) a probabilistic positive association condition called monotonicity; then the coalitional power structure under a probabilistic voting procedure is characterized by weak random dictatorship.
Received: 1 March 1999/Accepted: 21 May 2001 相似文献
3.
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. 相似文献
4.
On probabilistic rationalizability 总被引:1,自引:0,他引:1
Shasikanta Nandeibam 《Social Choice and Welfare》2009,32(3):425-437
This paper examines the problem of rationalizability of a choice system without imposing restrictions on the universal set of alternatives and the family of feasible sets. A choice system is the
probabilistic counterpart of a choice function which is basic to much of the theory of individual choice behaviour in economics. We provide a necessary and sufficient condition
for a choice system to be induced by a probability measure on a set of utility functions.
I would like to thank the editor and two anonymous referees for helpful comments. 相似文献
5.
Indraneel Dasgupta 《Social Choice and Welfare》2011,37(4):643-658
We model a general choice environment via probabilistic choice correspondences, with (possibly) incomplete domain and infinite
universal set of alternatives. We offer a consistency restriction regarding choice when the feasible set contracts. This condition,
‘contraction consistency’, subsumes earlier notions such as Chernoff’s Condition, Sen’s α and β, and regularity. We identify a restriction on the domain of the stochastic choice correspondence (SCC), under which contraction
consistency is equivalent to the weak axiom of revealed preference in its most general form. When the universal set of alternatives
is finite, this restriction is also necessary for such equivalence. Analogous domain restrictions are also identified for
the special case where choice is deterministic but possibly multi-valued. Results due to Sen (Rev Econ Stud 38:307–317, 1971) and Dasgupta and Pattanaik (Econ Theory 31:35–50, 2007) fall out as corollaries. Thus, conditions are established, under which our notion of consistency, articulated only in reference
to contractions of the feasible set, suffices as the axiomatic foundation for a general revealed preference theory of choice
behaviour. 相似文献
6.
Norihito Sakamoto 《Social Choice and Welfare》2013,40(4):1033-1045
We consider fair collective choice functions (hereafter fair CCFs) which associate with each profile of extended preference orderings and each set of feasible social states a subset of the set of Pareto efficient and envy-free states for the preference profile. Our main objective is to examine compatibility of fair social choices with collective rationality. We formulate desirable properties of collective rationality, and look for CCFs satisfying them. Next, we show that any fair CCF violates most of collective rationality properties. Moreover, one of our results implies that no fair CCF can be rationalized by a social preference relation. 相似文献
7.
We describe a criterion to evaluate subsets of a finite set of alternatives which are considered as opportunity sets. The axioms for set comparison are motivated within the preference for flexibility framework. We assume the preference over
the universal set of alternatives to be made of two disjoint binary relations. The result is the axiomatic characterization
of a procedure which is formally similar to the leximax ordering, but in our case it incorporates the presence of some uncertainty
about the decision-maker final tastes.
Received: 20 January 1999/Accepted: 20 October 1999 相似文献
8.
Ryo-ichi Nagahisa 《Social Choice and Welfare》1996,13(4):383-395
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. 相似文献
9.
Arrow's Theorem, in its social choice function formulation, assumes that all nonempty finite subsets of the universal set of alternatives is potentially a feasible set. We demonstrate that the axioms in Arrow's Theorem, with weak Pareto strengthened to strong Pareto, are consistent if it is assumed that there is a prespecified alternative which is in every feasible set. We further show that if the collection of feasible sets consists of all subsets of alternatives containing a prespecified list of alternatives and if there are at least three additional alternatives not on this list, replacing nondictatorship by anonymity results in an impossibility theorem.Most of the research for this article was completed while we were participants in the Public Choice Institute held at Dalhousie University during the summer of 1984. We wish to record here our thanks to the Institute Director, E.F. McClennen, and its sponsors, the Council for Philosophical Studies, the U.S. National Science Foundation, and the Social Science and Humanities Research Council of Canada. We are grateful to our referees for their comments and the Center for Mathematical Studies in Economics and Management Science at Northwestern University, where Weymark was a visitor during 1985–86, for secretarial assistance. 相似文献
10.
We say that a social choice function (SCF) satisfies Top-k Monotonicity if the following holds. Suppose the outcome of the SCF at a preference profile is one of the top k-ranked alternatives for voter i. Let the set of these k alternatives be denoted by B. Suppose that i’s preference ordering changes in such a way that the set of first k-ranked alternatives remains the set B. Then the outcome at the new profile must belong to B. This definition of monotonicity arises naturally from considerations of set “improvements” and is weaker than the axioms of strong positive association and Maskin Monotonicity. Our main results are that if there are two voters then a SCF satisfies unanimity and Top-2 or Top-pair Monotonicity if and only if it is dictatorial. If there are more than two voters, then Top-pair Monotonicity must be replaced by Top-3 Monotonicity (or Top-triple Monotonicity) for the analogous result. Our results demonstrate that connection between dictatorship and “improvement” axioms is stronger than that suggested by the Muller–Satterthwaite result (Muller and Satterthwaite in J Econ Theory 14:412–418, 1977) and the Gibbard–Sattherthwaite theorem. 相似文献
11.
Shasikanta Nandeibam 《Social Choice and Welfare》2011,37(4):633-641
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. 相似文献
12.
Carmelo Rodríguez-Álvarez 《Social Choice and Welfare》2007,29(2):175-199
Duggan and Schwartz (Soc Choice and Welfare 17: 85–93, 2000) have proposed a generalization of the Gibbard–Satterthwaite Theorem to multivalued social choice rules.
They show that only dictatorial rules are strategy-proof and satisfy citizens sovereignty and residual resoluteness. Citizens sovereignty requires that each alternative is chosen at some preference profile. Residual resoluteness compels
the election to be single-valued when the preferences of the voters are “similar”. We propose an alternative proof to the
Duggan and Schwartz’s Theorem. Our proof highlights the crucial role of residual resoluteness. In addition, we prove that
every strategy-proof and onto social choice correspondence concentrates the social decision power in the hands of an arbitrary group of voters. Finally,
we show that this result still holds in a more general framework in which voters report their preferences over sets of alternatives. 相似文献
13.
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. 相似文献
14.
The vulnerability of four social choice functions to coalitional manipulation of preferences 总被引:2,自引:1,他引:1
The vulnerability of a social choice function to coalitional manipulation of preferences is defined as the proportion of voting situations in which the social choice function can be manipulated by a coalition of individuals. In this paper, we provide exact relations giving the vulnerability of four specific social choice functions (plurality rule, anti-plurality rule, plurality with runoff, anti-plurality with runoff) in three-alternative elections. Plurality with runoff appears to be less vulnerable than the other three rules. 相似文献
15.
This paper characterizes strategy-proof social choice functions (SCFs), the outcome of which are multiple public goods. Feasible
alternatives belong to subsets of a product set . The SCFs are not necessarily “onto”, but the weaker requirement, that every element in each category of public goods A
k
is attained at some preference profile, is imposed instead. Admissible preferences are arbitrary rankings of the goods in
the various categories, while a separability restriction concerning preferences among the various categories is assumed. It
is found that the range of the SCF is uniquely decomposed into a product set in general coarser than the original product set, and that the SCF must be dictatorial on each component B
l
. If the range cannot be decomposed, a form of the Gibbard–Satterthwaite theorem with a restricted preference domain is obtained. 相似文献
16.
Bairj Donabedian 《Sociological Theory》2003,21(2):175-190
This paper proposes criteria for distinguishing those types of social forms that are susceptible to lawlike explanation from those that are susceptible to interpretive accounts. The main criterion concerns the rankability of choice alternatives. The choice process is modeled as having two subprocesses. The first subprocess is a rational one in which unacceptable decision alternatives are eliminated, reducing the universe of alternatives to the set of interchangeably acceptable options, termed the admissible set. In the second subprocess, an arbitrary choice is made from the admissible set. In rational‐choice settings, the admissible set consists of just one element, the optimum. However, this is clearly not the only possibility, as the example of language, with its plurality of interchangeable phonemic options, bears witness. The fundamental concept: At one extreme—the extreme of language—the admissible set is large and the arbitrary‐choice subprocess dominates the rational‐choice subprocess. At the other extreme—the extreme of rational‐choice theory—the admissible set consists of a single element and the rational‐choice subprocess dominates the arbitrary‐choice subprocess. Social law has its proper home in those territories of human activity where the admissible set is small; social interpretation has its proper home in those regions where the admissible set is large. 相似文献
17.
Extended preferences and freedom of choice 总被引:2,自引:0,他引:2
The common choice theory in economics is based on the assumption that an individual is defined in terms of a binary preference
relation. This preference relation is defined over alternatives without taking into account menu dependence and, in particular,
freedom of choice or, more generally, the set that contains the alternatives. In this study we clarify the nature and the
significance of freedom of choice which may positively or negatively affect the individual's welfare. Our proposed extended
preference relation of the individual takes into account both the particular alternative and the opportunity set that he faces.
This extended relation does not induce ranking of opportunity sets. Its restriction to a particular opportunity set is the
paradigmatic preference relation and it can capture the dependence of preferences on freedom of choice. Our main result establishes
the inconsistency between dependence of extended preferences on freedom of choice and the existence of a utility that represents
the paradigmatic preference relation and any of its restrictions.
Received: 30 December 1997/Accepted: 6 September 1999 相似文献
18.
We study classes of voting situations where agents may exhibit a systematic inability to distinguish between the elements
of certain sets of alternatives. These sets of alternatives may differ from voter to voter, thus resulting in personalized
families of preferences. We study the properties of the majority relation when defined on restricted domains that are the
cartesian product of preference families, each one reflecting the corresponding agent’s objective indifferences, and otherwise
allowing for all possible (strict) preference relations among alternatives. We present necessary and sufficient conditions
on the preference domains of this type, guaranteeing that majority rule is quasi-transitive and thus the existence of Condorcet
winners at any profile in the domain, and for any finite subset of alternatives. Finally, we compare our proposed restrictions
with others in the literature, to conclude that they are independent of any previously discussed domain restriction. 相似文献
19.
Sets of alternatives as Condorcet winners 总被引:1,自引:0,他引:1
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 24th 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. 相似文献
20.
Arrow's axioms for social welfare functions are shown to be inconsistent when the set of alternatives is the nonnegative
orthant in a multidimensional Euclidean space and preferences are assumed to be either the set of analytic classical economic
preferences or the set of Euclidean spatial preferences. When either of these preference domains is combined with an agenda
domain consisting of compact sets with nonempty interiors, strengthened versions of the Arrovian social choice correspondence
axioms are shown to be consistent. To help establish the economic possibility theorem, an ordinal version of the Analytic
Continuation Principle is developed.
Received: 4 July 2000/Accepted: 2 April 2001 相似文献