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1.
Thomas C. Ratliff 《Social Choice and Welfare》2001,18(1):79-89
In an election without a Condorcet winner, Dodgson's method is designed to find the candidate that is “closest” to being
a Condorcet winner. Similarly, if the head-to-head elections among all candidates do not give a complete transitive ranking,
then Kemeny's Rule finds the “closest” transitive ranking. This paper uses geometric techniques to compare Dodgson's and Kemeny's
notions of closeness and explain how conflict can arise between the two methods.
Received: 19 October 1999/Accepted: 6 December 1999 相似文献
2.
William V. Gehrlein 《Social Choice and Welfare》1998,15(3):351-358
A weighted scoring rule, Rule λ, on three alternative elections selects the winner by awarding 1 point to each voter's first
ranked candidate, λ points to the second ranked candidate, and zero to the third ranked candidate. The Condorcet winner is
the candidate that would defeat each other candidate in a series of pairwise elections by majority rule. The Condorcet efficiency
of Rule λ is the conditional probability that Rule λ selects the Condorcet winner, given that a Condorcet winner exists. Borda
rule (λ=1/2) is the weighted scoring rule that maximizes Condorcet efficiency. The current study considers the conditional
probability that Borda rule selects the Rule λ winner, given that Rule λ elects the Condorcet winner with a large electorate.
Received: 21 August 1996 / Accepted: 7 January 1997 相似文献
3.
Condorcet efficiency: A preference for indifference 总被引:1,自引:0,他引:1
The Condorcet winner in an election is the candidate who would be able to defeat all other candidates in a series of pairwise
elections. The Condorcet efficiency of a voting procedure is the conditional probability that it will elect the Condorcet
winner, given that a Condorcet winner exists. The study considers the Condorcet efficiency of weighted scoring rules (WSR's)
on three candidates for large electorates when voter indifference between candidates is allowed. It is shown that increasing
the proportion of voters who have partial indifference will increase the probability that a Condorcet winner exists, and will
also increase the Condorcet efficiency of all WSR's. The same observation is observed when the proportion of voters with complete
preferences on candidates is reduced. Borda Rule is shown to be the WSR with maximum Condorcet efficiency over a broad range
of assumptions related to voter preferences. The result of forcing voters to completely rank all candidates, by randomly breaking
ties on candidates that are viewed as indifferent, leads to a reduction in the probability that a Condorcet winner exists
and to a reduction in the Condorcet efficiency of all WSR's.
Received: 31 July 1999/Accepted: 11 February 2000 相似文献
4.
On the likelihood of Condorcet's profiles 总被引:1,自引:0,他引:1
Consider a group of individuals who have to collectively choose an outcome from a finite set of feasible alternatives. A
scoring or positional rule is an aggregation procedure where each voter awards a given number of points, w
j, to the alternative she ranks in j
th position in her preference ordering; The outcome chosen is then the alternative that receives the highest number of points.
A Condorcet or majority winner is a candidate who obtains more votes than her opponents in any pairwise comparison. Condorcet
[4] showed that all positional rules fail to satisfy the majority criterion. Furthermore, he supplied a famous example where
all the positional rules select simultaneously the same winner while the majority rule picks another one. Let P
* be the probability of such events in three-candidate elections. We apply the techniques of Merlin et al. [17] to evaluate
P
* for a large population under the Impartial Culture condition. With these assumptions, such a paradox occurs in 1.808% of
the cases.
Received: 30 April 1999/Accepted: 14 September 2000 相似文献
5.
Eivind Stensholt 《Social Choice and Welfare》2010,35(2):291-317
The strategy most damaging to many preferential election methods is to give insincerely low rank to the main opponent of one’s
favourite candidate. Theorem 1 determines the 3-candidate Condorcet method that minimizes the number of noncyclic profiles
allowing the strategic use of a given cyclic profile. Theorems 2, 3 and 4 establish conditions for an anonymous and neutral
3-candidate single-seat election to be monotonic and still avoid this strategy completely. Plurality elections combine these
properties; among the others ‘conditional IRV’ gives the strongest challenge to the plurality winner. Conditional IRV is extended
to any number of candidates. Theorem 5 is an impossibility of Gibbard–Satterthwaite type, describing three specific strategies
that cannot all be avoided in meaningful anonymous and neutral election methods. 相似文献
6.
Condorcet efficiencies under the maximal culture condition 总被引:2,自引:1,他引:1
The Condorcet winner in an election is a candidate that could defeat each other candidate in a series of pairwise majority
rule elections. The Condorcet efficiency of a voting rule is the conditional probability that the voting rule will elect the
Condorcet winner, given that such a winner exists. The study considers the Condorcet efficiency of basic voting rules under
various assumptions about how voter preference rankings are obtained. Particular attention is given to situations in which
the maximal culture condition is used as a basis for obtaining voter preferences.
Received: 4 February 1998/Accepted: 13 April 1998 相似文献
7.
A nail-biting election 总被引:1,自引:1,他引:0
In the first competitive election for President of the Social Choice and Welfare Society, the (official) approval-voting
winner differed from the (hypothetical) Borda count winner, who was also the Condorcet winner. But because the election was
essentially a toss-up, it is impossible to say who should have won. The election for Council was more true to form of other professional-society elections, with the winners identical,
and even their rankings almost duplicative, under both voting systems.
Received: 11 April 2000/Accepted: 26 March 2001 相似文献
8.
By using geometry, a fairly complete analysis of Kemeny's rule (KR) is obtained. It is shown that the Borda Count (BC) always
ranks the KR winner above the KR loser, and, conversely, KR always ranks the BC winner above the BC loser. Such KR relationships
fail to hold for other positional methods. The geometric reasons why KR enjoys remarkably consistent election rankings as
candidates are added or dropped are explained. The power of this KR consistency is demonstrated by comparing KR and BC outcomes.
But KR's consistency carries a heavy cost; it requires KR to partially dismiss the crucial “individual rationality of voters”
assumption.
Received: 5 February 1998/Accepted: 26 May 1999 相似文献
9.
Kaoru Ueda 《Social Choice and Welfare》2002,19(3):613-626
In this paper we discuss the issue of when oligopolization in collective rent-seeking occurs, that is, when some groups retire
from rent-seeking. A complete characterization of the pure-strategy Nash equilibrium in a collective rent-seeking game among
m (≥2) heterogeneous groups is derived. The conditions of oligopolization are derived by using this result and related to the
works of Nitzan [9, 10] and Hillman and Riley [3]. Also, the subgame perfect equilibrium of a simple two-stage collective
rent-seeking game (Lee [7]) is fully characterized. In this game, it is confirmed that no group retires from the contest in
the second stage and oligopolization never occurs. An example of the two-stage collective rent-seeking game with monitoring
costs is devised to show the possibilities of oligopolization.
Received: 21 September 1999/Accepted: 27 March 2001 相似文献
10.
The concept of coalition proof Nash equilibrium was introduced by Bernheim et al. [5]. In the present paper, we consider
the representation problem for coalition proof Nash equilibrium: For a given effectivity function, describing the power structure
or the system of rights of coalitions in society, it is investigated whether there is a game form which gives rise to this
effectivity function and which is such that for any preference assignment, there is a coalition proof Nash equilibrium.
It is shown that the effectivity functions which can be represented in coalition proof Nash equilibrium are exactly those
which satisfy the well-known properties of maximality and superadditivity. As a corollary of the result, we obtain necessary
conditions for implementation of a social choice correspondence in coalition proof Nash equilibrium which can be formulated
in terms of the associated effectivity function.
Received: 24 June 1999/Accepted: 20 September 2000 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.
Olivier Hudry 《Social Choice and Welfare》1999,16(1):137-143
Given a tournament T, a Banks winner of T is the first vertex of any maximal (with respect to inclusion) transitive subtournament of T; a Copeland winner of T is a vertex with a maximum out-degree. In this paper, we show that 13 is the minimum number of vertices that a tournament
must have so that none of its Copeland winners is a Banks winner: for any tournament with less than 13 vertices, there is
always at least one vertex which is a Copeland winner and a Banks winner simultaneously.
Received: 2 May 1997 / Accepted: 30 September 1997 相似文献
13.
The notion of keeping distances, introduced by N. Baigent in [2], avoids the need to introduce topological concepts when
defining Social Welfare Functions with requirements analogous to those established by Chichilnsky in [3]. In the following
study we propose an extension of the results of Baigent, in a non topological framework, to a much broader class of metrics
which enables the case of infinite agents to be considered in a natural fashion.
Received: 14 June 1999/Accepted: 4 November 1999 相似文献
14.
In voting, the main idea of the distance rationalizability framework is to view the voters’ preferences as an imperfect approximation to some kind of consensus. This approach, which is deeply rooted in the social choice literature, allows one to define (“rationalize”) voting rules via a consensus class of elections and a distance: a candidate is said to be an election winner if she is ranked first in one of the nearest (with respect to the given distance) consensus elections. It is known that many classic voting rules can be distance-rationalized. In this article, we provide new results on distance rationalizability of several Condorcet-consistent voting rules. In particular, we distance-rationalize the Young rule and Maximin using distances similar to the Hamming distance. It has been claimed that the Young rule can be rationalized by the Condorcet consensus class and the Hamming distance; we show that this claim is incorrect and, in fact, this consensus class and distance yield a new rule, which has not been studied before. We prove that, similarly to the Young rule, this new rule has a computationally hard winner determination problem. 相似文献
15.
Francesco De Sinopoli 《Social Choice and Welfare》2000,17(4):655-672
In this paper we show in the context of voting games with plurality rule that the “perfect” equilibrium concept does not
appear restrictive enough, since, independently of preferences, it can exclude at most the election of only one candidate.
Furthermore, some examples show that there are “perfect” equilibria that are not “proper”. However, also some “proper” outcome
is eliminated by sophisticated voting, while Mertens' stable set fully satisfies such criterium, for generic plurality games.
Moreover, we highlight a weakness of the simple sophisticated voting principle. Finally, we find that, for some games, sophisticated
voting (and strategic stability) does not elect the Condorcet winner, neither it respects Duverger's law, even with a large
number of voters.
Received: 16 March 1999/Accepted: 25 September 1999 相似文献
16.
Markus Schulze 《Social Choice and Welfare》2011,36(2):267-303
In recent years, the Pirate Party of Sweden, the Wikimedia Foundation, the Debian project, the “Software in the Public Interest”
project, the Gentoo project, and many other private organizations adopted a new single-winner election method for internal
elections and referendums. In this article, we will introduce this method, demonstrate that it satisfies, e.g., resolvability,
Condorcet, Pareto, reversal symmetry, monotonicity, and independence of clones and present an O(C^3) algorithm to calculate the winner, where C is the number of alternatives. 相似文献
17.
John C. McCabe-Dansted Geoffrey Pritchard Arkadii Slinko 《Social Choice and Welfare》2008,31(2):311-330
It is known that Dodgson’s rule is computationally very demanding. Tideman (Soc Choice Welf 4:185–206, 1987) suggested an
approximation to it but did not investigate how often his approximation selects the Dodgson winner. We show that under the
Impartial Culture assumption the probability that the Tideman winner is the Dodgson winner converges to 1 as the number of
voters increase. However we show that this convergence is not exponentially fast. We suggest another approximation—we call
it Dodgson Quick—for which this convergence is exponentially fast. Also we show that the Simpson and Dodgson rules are asymptotically
different. 相似文献
18.
In this paper we introduce harmonic analysis (Fourier series) as a tool for characterizing the existence of Nash equilibria
in two-dimensional spatial majority rule voting games with large electorates. We apply our methods both to traditional proximity
models and to directional models. In the latter voters exhibit preferences over directions rather than over alternatives,
per se. A directional equilibrium can be characterized as a Condorcet direction, in analogy to the Condorcet (majority) winner
in the usual voting models, i.e., a direction which is preferred by a majority to (or at least is not beaten by) any other
direction. We provide a parallel treatment of the total median condition for equilibrium under proximity voting and equilibrium
conditions for directional voting that shows that the former result is in terms of a strict equality (a knife-edge result
very unlikely to hold) while the latter is in terms of an inequality which is relatively easy to satisfy. For the Matthews
[3] directional model and a variant of the Rabinowitz and Macdonald [7] directional model, we present a sufficiency condition
for the existence of a Condorcet directional vector in terms of the odd-numbered components of the Fourier series representing
the density distribution of the voter points. We interpret our theoretical results by looking at real-world voter distributions
and direction fields among voter points derived from U.S. and Norwegian survey data.
Received: 7 July 1995 / Accepted: 14 May 1996 相似文献
19.
William V. Gehrlein 《Social Choice and Welfare》2006,26(1):191-208
Niemi (Am Polit Sci Rev 63:488–497, 1969) proposed a simple measure of the cohesiveness of a group of n voters’ preferences that reflects the proximity of their preferences to single-peakedness. For three-candidate elections, this measure, k, reduces to the minimum number of voters who rank one of the candidates as being least preferred. The current study develops closed form representations for the conditional probability, PASW(n,IAC|k), that all weighted scoring rules will elect the Condorcet winner in an election, given a specified value of k. Results show a very strong relationship between PASW(n,IAC|k) and k, such that the determination of the voting rule to be used in an election becomes significantly less critical relative to the likelihood of electing the Condorcet winner as voters in a society have more structured preferences. As voters’ preferences become more unstructured as measured by their distance from single-peakedness, it becomes much more likely that different voting rules will select different winners.A preliminary version of this paper was presented at the European Public Choice Society Conference in Berlin, Germany, April 15–18, 2004. 相似文献
20.
Different scoring rules can result in the selection of any of the k competing candidates, given the same preference profile, (Saari DG 2001, Chaotic elections! A mathematician looks at voting. American Mathematical Society, Providence, R.I.). It is also possible that a candidate, and even a Condorcet winning candidate, cannot be selected by any scoring rule, (Saari DG 2000 Econ Theory 15:55–101). These findings are balanced by Saari’s result (Saari DG 1992 Soc Choice Welf 9(4):277–306) that specifies the necessary and sufficient condition for the selection of the same candidate by all scoring rules. This condition is, however, indirect. We provide a sufficient condition that is stated directly in terms of the preference profile; therefore, its testability does not require the verdict of any voting rule. 相似文献