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1.
The structure of fuzzy preferences: Social choice implications 总被引:1,自引:0,他引:1
Gregory Richardson 《Social Choice and Welfare》1998,15(3):359-369
It has been shown that, with an alternative factorization of fuzzy weak preferences into symmetric and antisymmetric components,
one can prove a fuzzy analogue of Arrow's Impossibility Theorem even when the transitivity requirements on individual and
social preferences are very weak. It is demonstrated here that the use of this specification of strict preference, however,
requires preferences to also be strongly connected. In the absence of strong connectedness, another factorization of fuzzy
weak preferences is indicated, for which nondictatorial fuzzy aggregation rules satisfying the weak transitivity requirement
can still be found. On the other hand, if strong connectedness is assumed, the fuzzy version of Arrow's Theorem still holds
for a variety of weak preference factorizations, even if the transitivity condition is weakened to its absolute minimum.
Since Arrow's Impossibility Theorem appeared nearly half a century ago, researchers have been attempting to avoid Arrow's
negative result by relaxing various of his original assumptions. One approach has been to allow preferences – those of individuals
and society or just those of society alone – to be “fuzzy.” In particular, Dutta [4] has shown that, to a limited extent,
one can avoid the impossibility result (or, more precisely, the dictatorship result) by using fuzzy preferences, employing
a particularly weak version of transitivity among the many plausible (but still distinct) definitions of transitivity that
are available for fuzzy preferences.
Another aspect of exact preferences for which the extension to the more general realm of fuzzy preferences is ambiguous is
the factorization of a weak preference relation into a symmetric component (indifference) and an antisymmetric component (strict
preference). There are several ways to do this for fuzzy weak preferences, all of them equivalent to the traditional factorization
in the special case when preferences are exact, but quite different from each other when preferences are fuzzy (see, for example,
[3]).
A recent paper in this journal [1], by A. Banerjee, argues that the choice of definitions for indifference and strict preference,
given a fuzzy weak preference, can also have “Arrovian” implications. In particular, [1] claims that Dutta's version of strict
preference presents certain intuitive difficulties and recommends a different version, with its own axiomatic derivation,
for which the dictatorship results reappear even with Dutta's weak version of transitivity.
However, the conditions used to derive [1]'s version of strict preference imply a restriction on how fuzzy the original weak
preference can be, namely, that the fuzzy weak preference relation must be strongly connected. Without this restriction, I will show that the rest of [1]'s conditions imply yet a third version of strict preference,
for which Dutta's possibility result under weak transitivity still holds. On the other hand, if one accepts the strong connectedness
required in order for it to be valid, I show that [1]'s dictatorship theorem can in fact be strengthened to cover any version of transitivity for fuzzy preferences, no matter how weak, and further, that this dictatorship result holds for any
“regular” formulation of strict preference, including the one originally used by Dutta.
Received: 13 May 1996 / Accepted: 13 January 1997 相似文献
2.
When preferences are single peaked the choice functions that are independent of irrelevant alternatives both in Nash's and in Arrow's sense are characterized. They take the Condorcet winner of the n individual peaks plus at most n-1 fixed ballots (phantom voters). These choice functions are also coalitionally strategy-proof.Next the domain of individual preferences is enlarged to allow for singleplateau preferences: again, Nash's IIA and Arrow's IIA uniquely characterize a class of generalized Condorcet winners choice functions. These are, again, coalitionally strategy-proof. 相似文献
3.
Thomas Schwartz 《Social Choice and Welfare》2001,18(1):1-22
From remarkably general assumptions, Arrow's Theorem concludes that a social intransitivity must afflict some profile of transitive individual preferences. It need not be a cycle, but all others have ties. If we add a modest tie-limit, we get a chaotic cycle, one comprising all alternatives, and a tight one to boot: a short path connects any two alternatives. For this we need naught but (1) linear preference orderings devoid
of infinite ascent, (2) profiles that unanimously order a set of all but two alternatives, and with a slightly fortified tie-limit,
(3) profiles that deviate ever so little from singlepeakedness. With a weaker tie-limit but not (2) or (3), we still get a
chaotic cycle, not necessarily tight. With an even weaker one, we still get a dominant cycle, not necessarily chaotic (every member beats every outside alternative), and with it global instability (every alternative beaten). That tie-limit is necessary for a cycle of any sort, and for global instability too (which does not require a cycle unless alternatives are finite in
number). Earlier Arrovian cycle theorems are quite limited by comparison with these.
Received: 31 July 1999/Accepted: 15 October 1999 相似文献
4.
Hervé Crès 《Social Choice and Welfare》2001,18(3):507-525
We consider weak preference orderings over a set A
n of n alternatives. An individual preference is of refinement?≤n if it first partitions A
n into ? subsets of `tied' alternatives, and then ranks these subsets within a linear ordering. When ?<n, preferences are coarse. It is shown that, if the refinement of preferences does not exceed ?, a super majority rule (within non-abstaining voters)
with rate 1− 1/? is necessary and sufficient to rule out Condorcet cycles of any length. It is argued moreover how the coarser
the individual preferences, (1) the smaller the rate of super majority necessary to rule out cycles `in probability'; (2)
the more probable the pairwise comparisons of alternatives, for any given super majority rule.
Received: 29 June 1999/Accepted: 25 February 2000 相似文献
5.
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
6.
The object of this paper is to propose a consistency test for an individual involved in collective choice process. Collective choice processes considered in the paper are those that
transform individuals ‘tastes’– which reflect the self-interested view point of the individuals – into (social) ranking of alternatives. In addition to
her tastes, an individual has values about the way by which collective decision should be made. We distinguish two categories of such values. First, there are
end-values that restrict the class of social rankings that the individual considers ethically acceptable. Second there are aggregation-values that specify the way by which the social ranking should depend upon the individuals tastes. The consistency test stands on
an hypothetical operation of universalization of the individual tastes to everyone. Five illustrations of the potential usefulness of our approach for interpreting social
choice theory and welfare economics are proposed. These illustrations deal with utilitarian aggregation in the presence of
income inequality aversion, the so-called ‘ethics of responsibility’ and the aggregation of individual ranking of opportunity
sets based on their freedom of choice. A discussion of the relevance of the consistency test for addressing the problem of
‘laundering’ individual preferences is also provided.
Received: 25 June 1998/Accepted: 16 March 1999 相似文献
7.
Laurent Vidu 《Social Choice and Welfare》1999,16(1):159-167
An Excess-Voting Function relative to a profile π assigns to each pair of alternatives (x,y), the number of voters who prefer x to y minus the number of voters who prefer y to x. It is shown that any non-binary separable Excess-Voting Function can be achieved from a preferences profile when individuals
are endowed with separable preferences. This result is an extension of Hollard and Le Breton (1996).
Received: 16 December 1996 / Accepted: 8 October 1997 相似文献
8.
Olivier Bochet 《Social Choice and Welfare》2007,28(1):111-125
Consider the problem of exact Nash Implementation of social choice correspondences. Define a lottery mechanism as a mechanism in which the planner can randomize on alternatives out of equilibrium while pure alternatives are always chosen in equilibrium. When preferences over alternatives are strict, we show that Maskin monotonicity (Maskin in Rev Econ stud 66: 23–38, 1999) is both necessary and sufficient for a social choice correspondence to be Nash implementable. We discuss how to relax the assumption of strict preferences. Next, we examine social choice correspondences with private components. Finally, we apply our method to the issue of voluntary implementation (Jackon and Palfrey in J Econ Theory 98: 1–25, 2001).I thank Toyo Sakai for his comments on a previous draft. I also thank two anonymous referees and an editor of this journal for helpful comments that improved this paper. A previous version circulated as “A note on Maskin monotonicity”. After the results presented here were obtained, I became aware of a new unpublished paper by Benoit and Ok (2004). The result of Theorem 2 and the discussion that follows is partially similar to their Theorem 1. 相似文献
9.
Connecting and resolving Sen's and Arrow's theorems 总被引:5,自引:0,他引:5
Donald G. Saari 《Social Choice and Welfare》1998,15(2):239-261
It is shown that the source of Sen's and Arrow's impossibility theorems is that Sen's Liberal condition and Arrow's IIA counter
the critical assumption that voters have transitive preferences. But if the procedures are not permitted to treat the transitivity
of individual preferences as a valued input, then we cannot expect rational outputs. Once this common cause for these perplexing
conclusions is understood, these classical conclusions end up admitting quite benign interpretations where it becomes possible
to propose several resolutions.
Received: 2 April 1996 / Accepted: 15 October 1996 相似文献
10.
David A. Smith 《Social Choice and Welfare》1999,16(4):639-661
All social choice functions are manipulable when more than two alternatives are available. I evaluate the manipulability
of the Borda count, plurality rule, minimax set, and uncovered set. Four measures of manipulability are defined and computed
stochastically for small numbers of agents and alternatives.
Social choice rules derived from the minimax and uncovered sets are found to be relatively immune to manipulation whether
a sole manipulating agent has complete knowledge or absolutely no knowledge of the preferences of the others. The Borda rule
is especially manipulable if the manipulating agent has complete knowledge of the others.
Received: 5 January 1996/Accepted: 31 July 1998 相似文献
11.
T. Groseclose 《Social Choice and Welfare》2007,28(2):321-335
I examine a model of majority rule in which alternatives are described by two characteristics: (1) their position in a standard,
left-right dimension, and (2) their position in a good-bad dimension, over which voters have identical preferences. I show
that when voters’ preferences are single-peaked and concave over the first dimension, majority rule is transitive, and the majority’s preferences are identical to the median voter’s.
Thus, Black’s (The theory of committees and elections, 1958) theorem extends to such a “one and a half” dimensional framework.
Meanwhile, another well-known result of majority rule, Downs’ (An economic theory of democracy, 1957) electoral competition
model, does not extend to the framework. The condition that preferences can be represented in a one-and-a-half-dimensional
framework is strictly weaker than the condition that preferences be single-peaked and symmetric. The condition is strictly
stronger than the condition that preferences be order-restricted, as defined by Rothstein (Soc Choice Welf 7:331–342;1990). 相似文献
12.
We develop a theory of representation of interdependent preferences that reflect the widely acknowledged phenomenon of keeping up with the Joneses (i.e. of those preferences which maintain that well-being depend on “relative standing” in the society as well as on material
consumption). The principal ingredient of our analysis is the assumption that individuals desire to occupy a (subjectively)
better position than their peers. This is quite a primitive starting point in that it does not give any reference to what
is actually regarded as “status” in the society. We call this basic postulate negative interdependence, and study its implications. In particular, combining this assumption with some other basic postulates that are widely used
in a number of other branches of the theory of individual choice, we axiomatize the relative income hypothesis, and obtain
an operational representation of interdependent preferences.
Received: 7 December 1998/Accepted: 24 August 1999 相似文献
13.
Martin Eiliv Sandbu 《Social Choice and Welfare》2008,31(4):589-619
Much work in social choice theory takes individual preferences as uninvestigated inputs into aggregation functions designed
to reflect considerations of fairness. Advances in experimental and behavioural economics show that fairness can also be an
important motivation in the preferences of individuals themselves. A proper characterisation of how fairness concerns enter
such preferences can enrich the informational basis of many social choice exercises. This paper proposes axiomatic foundations
for individual fairness-motivated preferences that cover most of the models developed to rationalise observed behaviour in
experiments. These models fall into two classes: Outcome-based models, which see preferences as defined only over distributive
outcomes, and context-dependent models, which allow rankings over distributive outcomes to change systematically with non-outcome
factors. I accommodate outcome-based and context-sensitive fairness concerns by modelling fairness-motivated preferences as
a reference-dependent preference structure. I first present a set of axioms and two theorems that generate commonly used outcome-based models as special cases. I then
generalise the axiomatic basis to allow for reference-dependence, and derive a simple functional form in which the weight
on each person’s payoff depends on a reference vector of how much each person deserves. 相似文献
14.
James Schummer 《Social Choice and Welfare》1996,14(1):47-56
Strategy-proofness has been shown to be a strong property, particularly on large domains of preferences. We therefore examine the existence
of strategy-proof and efficient solutions on restricted, 2-person domains of exchange economies. On the class of 2-person exchange economies in which agents
have homothetic, strictly convex preferences we show, as Zhou (1991) did for a larger domain, that such a solution is necessarily
dictatorial. As this proof requires preferences exhibiting high degrees of complementarity, our search continues to a class of linear
preferences. Even on this “small” domain, the same negative result holds. These two results are extended to many superdomains,
including Zhou’s.
Received: 9 June 1995/Accepted: 8 January 1996 相似文献
15.
Hervé Moulin 《Social Choice and Welfare》1999,16(2):279-320
Each one of n users consumes an idiosyncratic commodity produced in indivisible units. The n commodities are jointly produced by a central facility and total cost must be shared by the users.
A “sequential stand alone mechanism” shares costs incrementally according to a fixed ordering of the users: the first user
always pays stand alone cost, the second pays the stand alone cost of the first two users minus that of the first and so on.
If the second derivatives of costs are of a constant sign, such a method yields a unique strong equilibrium at every profile
of convex preferences in the game where each user chooses his own demand. This equilibrium, in turn, defines a coalition strategy-proof
social choice function.
Under decreasing marginal costs and submodular costs, the sequential stand alone mechanisms are almost characterized by these
properties; the only exception is the binary demand case (each agent consumes zero or one unit) where a rich family of cost
sharing methods (the Shapley value among them) yields a coalition strategy-proof equilibrium selection. Under increasing marginal
costs and supermodular costs, coalition strategy-proofness characterizes a richer family of cost sharing methods: they give
out one unit at a time while charging marginal costs, with the users taking turns according to a sequence fixed in advance.
These methods contain serial cost sharing as a limit case.
Received: 8 July 1997/Accepted: 22 January 1998 相似文献
16.
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
17.
S. Fuchs-Seliger 《Social Choice and Welfare》1986,3(3):161-176
The purpose of this paper is to explore duality in the theory of social choice. As application Arrow's Impossibility Theorem and another impossibility theorem using the notion of positive responsiveness are chosen. It will be seen that we can establish notions and theorems which are symmetric to the original ones. However, if we establish impossibility theorems when rational behaviour is described by budget correspondences and not by choice correspondences, we need not assume that every subset of X (a family of alternatives) with cardinality 2 is a budget set. Therefore the dual theorems also may hold for families of competitive budget sets. It will also be shown that although the underlying preferences on X need not be acyclic, local decisiveness on budget sets may lead to global decisiveness on these sets. 相似文献
18.
John Duggan 《Social Choice and Welfare》1997,14(4):471-478
Hansson (1969) sets forth four conditions satisfied by no generalized social welfare function (GSWF), a mapping from profiles
of individual preferences to arbitrary social preference relations. Though transitivity is not imposed on social preferences,
one of Hansson’s conditions requires that socially maximal alternatives always exist. Of course, this condition is not satisfied
by the majority GSWF. We prove a generalization of Hansson’s theorem that requires the existence of maximal alternatives only
in very special cases. Our result applies to the majority GSWF and a large class of other GSWFs that sometimes produce no
maximal alternatives.
Received: 10 July 1995/Accepted: 4 March 1996 相似文献
19.
Independent Decisiveness and the Arrow theorem 总被引:7,自引:0,他引:7
Vincenzo Denicolò 《Social Choice and Welfare》1998,15(4):563-566
I show that the condition of Independence of Irrelevant Alternatives in Arrow's impossibility theorem can be weakened into
Relational Independent Decisiveness. The condition of Relational Independent Decisiveness is essentially a translation of
Sen's Independent Decisiveness into the traditional Arrovian framework. I also show by example that Relational Independent
Decisiveness is indeed weaker than Arrow's Independence of Irrelevant Alternatives.
Received: 30 October 1996 / Accepted: 22 May 1997 相似文献
20.
This paper re-examines the so-called ‘chairman’s paradox‘ that was first noticed by Farquharson in his path breaking tract
on sophisticated voting, Theory of Voting (1969). The Chairman’s paradox is concerned with the case of a three member committee in which a particular player who has
a regular and a tie-breaking vote – the ‘chairman’ – not only will do worse in specific instances under the plurality procedure
for three alternatives than if he did not have such a vote, but will also do worse overall. That is, the chairman’s a priori probability of success (‘getting what one wants’) for all possible games with linear (strict) preference orders is lower than that of the two regular members. It is demonstrated that this result, which comes
about if voters act strategically rather than sincerely, is not as robust as it has been thought to be. By merely replacing
the standard assumption of linear preference orders with weak preference orders, which allow for indifference, we can escape from the paradox for the canonical case of three players and
three alternatives. With weak preference orders, the a priori success of the chairman is now greater than that of the other two players. We also point to a new paradox of sophisticated voting. 相似文献