The probability of the paradox of voting for weak preference orderings

In this paper the probability of the voting paradox for weak orderings is calculated analytically for the three-voter-three-alternative case. It appears that the probability obtained this way is considerably smaller than in the corresponding case for linear orderings. The probability of intransitive majority relations for weak orderings in the 3 × 3 case is calculated as well, both with unconcerned and with concerned voters. Basic in the calculations are three theorems which are formulated in the field of domain conditions and restricted preferences. Received: 18 February 1997 / Accepted: 21 October 1997     

A characterization of strategy-proof voting rules for separable weak orderings

We consider the problem of choosing a subset of a finite set of indivisible objects (public projects, facilities, laws, etc.) studied by Barberà et al. (1991). Here we assume that agents preferences are separable weak orderings. Given such a preference, objects are partitioned into three types, goods, bads, and nulls. We focus on voting rules, which rely only on this partition rather than the full information of preferences. We characterize voting rules satisfying strategy-proofness (no one can ever be better off by lying about his preference) and null-independence (the decision on each object should not be dependent on the preference of an agent for whom the object is a null). We also show that serially dictatorial rules are the only voting rules satisfying efficiency as well as the above two axioms. We show that the separable domain is the unique maximal domain over which each rule in the first characterization, satisfying a certain fairness property, is strategy-proof. I am grateful to Professor William Thomson for helpful comments and suggestions. I also thank Professor John Duggan, Christopher Chambers, and seminar participants in Department of Economics, University of Rochester. I thank anonymous referees for their detailed comments and suggestions that helped me a great deal to develop the earlier version of this paper. All remaining errors are mine.     

Bargaining over a finite set of alternatives

We analyze bilateral bargaining over a finite set of alternatives. We look for "good" ordinal solutions to such problems and show that Unanimity Compromise and Rational Compromise are the only bargaining rules that satisfy a basic set of properties. We then extend our analysis to admit problems with countably infinite alternatives. We show that, on this class, no bargaining rule choosing finite subsets of alternatives can be neutral. When rephrased in the utility framework of Nash (1950), this implies that there is no ordinal bargaining rule that is finite-valued. Professor Sertel passed away on January 25, 2003.     

Choice functions over a finite set: A summary

A choice function picks some outcome(s) from every issue (subset of a fixed set A of outcomes). When is this function derived from one preference relation on A (the choice set being then made up of the best preferred outcomes within the issue), or from several preference relations (the choice set being then the Pareto optimal outcome within the issue, or the union of the best preferred outcomes for each preference relation)? A complete and unified treatment of these problems is given based on three functional properties of the choice function. None of the main results is original.     

The utilitarian criterion,finite sensibility,and the weak majority preference principle

This study is a further analysis of the approach taken by Yew-Kwang Ng to derive the utilitarian criterion. Specific for the model is that individual preferences are finitely sensible. In this framweork an analysis of the consequences on social preferences when different kinds of value premises are imposed is made. It is found that the utilitarian criterion is the unique consequence only for very special choices of the value premise. In addition, uniqueness requires the underlying preferences be cardinal. It is also found that finite sensibility induces approximate cardinalization of preferences.I am grateful to Y.-K. Ng, two anonymous referees and an editor of this journal for helpful and constructive comments on earlier versions of this paper. The research was financially supported by the Swedish Council for Research in the Humanities and Social Sciences     

On the power of poverty orderings

This paper investigates the possibility of increasing the ordering power of additively separable poverty measures beyond the condition of second degree stochastic dominance by considering third degree stochastic dominance. For a fixed poverty line, the ordering power can be significantly enhanced by using the third degree criterion. For a range of poverty lines, the marginal power of the third degree criterion over the second degree depends critically upon the lower bound of the range; if the lower bound poverty line is arbitrarily close to zero, the two criteria coincide. The implications of a strong version of the transfer sensitivity axiom are also considered. Received: 20 November 1995/Accepted: 16 February 1998     

Nash bargaining theory when the number of alternatives can be finite

Nash (1950) considered a domain of convex bargaining problems. We analyse domains including, or even consisting of, finite problems and provide various characterisations of the Nash Bargaining Solution (NBS). In particular, we extend Kaneko's (1980) results. Received: 12 July 1996 / Accepted: 6 February 1997     

Analysis of the response structure to a set of questions with large number of scale points: a new combined metric and categorical approach

In the field of social sciences, certain tasks, such as the identification of typologies and the characterization of groups of individuals according to a set of questions, tend to pose a challenge for researchers. Further complications arise if the chosen rating scale is from 0 to 10, since the responses can be treated either as metric or categorical variables. This paper shows that neither treatment is able on its own to capture all the inherent properties of this type of data, and goes on to propose a bicriteria clustering approach, which captures both perspectives and enables the simultaneous analysis of mixed data using multiple tables.     

Strategy-proofness of social welfare functions: The use of the Kemeny distance between preference orderings

The Kemeny distance for preference orderings is used to determine individual rankings of social preferences. Based on this distance function, the strategy-proofness of social welfare functions is examined. Our main result is an impossibility theorem stating that no social welfare function can be strategy-proof, if some additional properties are required.The work on this paper initiated while Walter Bossert was a visitor at the CentER for Economic Research at Tilburg University. The hospitality and the support of CentER and its members are gratefully acknowledged. Ton Storcken's research was supported by a grant from the Cooperation Centre Tilburg and Eindhoven University. An earlier version of the paper was presented at the 1991 Canadian Economic Theory Meeting in Toronto. We thank the participants and especially Ingrid Peters-Fransen for comments. Substantial improvements are due to the suggestions of Bernard Monjardet and two referees.     

The minimal covering set in large tournaments

We prove that in almost all large tournaments, the minimal covering set is the entire set of alternatives. That is, as the number of alternatives gets large, the probability that the minimal covering set of a uniformly chosen random tournament is the entire set of alternatives goes to one. In contrast, it follows from a result of (Fisher and Reeves, Linear Algebra Appl 217:83–85, 1995) that the bipartisan set contains about half of the alternatives in almost all large tournaments.     

Aggregation of preferences with a variable set of alternatives

A social choice correspondence called the Essential set is studied with the help of an axiom called Cloning Consistency. Cloning consistency is the requirement that the formal choice rule be insensitive to the replication of alternatives. The Essential set is the support of the optimal mixed strategies in a symmetric two-party electoral competition game. Received: 24 March 1998/Accepted: 3 March 1999     

An axiomatic characterization of the lexicographic maximin extension of an ordering over a set to the power set

The lexicographic maximin extension of an ordering is an important and widely used tool in social choice theory. We provide an axiomatization of it by means of five axioms. When the basic ordering is linear the following four (independent) axioms are sufficient: (1) Gärdenfors principle; (2) Neutrality; (3) Strong Fishburn monotonicity; and (4) Extension. Our result may also have applications in the theory of individual choice under uncertainty.     

Modeling collecting behavior: The role of set completion

Collecting is a complex behavior that has been studied from a variety of different perspectives. Art objects, stamps, coins, and other established collectibles markets, have been shown over the years to provide some degree of return to the collector in the economics literature. Wonderment over the success of certain collectibles such as Swatch watches and Beanie Babies has received much attention in the popular press. But how does one rationally explain the collecting of matchbook covers, Cracker Jacks toys, belt buckles, salt cellars, Aunt Jemima, etc.? Collecting in the absence of financial gain has received little attention in the economics literature. In the social psychology literature, many individuals are understood to have a natural desire to collect things for various reasons. Financial gain is only one of those reasons. Set completion is another. The reasons for collecting are not always mutually exclusive. For example, a complete set may be worth more in the secondary market, if one exists, than the sum of the individual pieces. This reflects the value of the rarest pieces and the opportunity costs of obtaining them. The model presented in this study explains how set completion motivates collecting behavior, which sheds light on collecting for both financial and nonfinancial reasons. The model accommodates both collectors and noncollectors and illustrates how consumption behavior may vary accordingly. Insight into how manufacturers of collectibles can use this behavior for commercial exploitation is explored.     

国外客车新技术简介

近年来,我国的汽车产业无论是技术还是产量,都获得了突飞猛进的发展,特别是大中型客车,通过技术引进、合资等手段以及国内企业近年来努力所取得的技术进步,已经使客车制造总体水平上了一个新台阶,与欧美和日本等先进国家的差距逐步缩小,可以说已经接近或达到了世界先进水平,特别是机械部分,中国产品与国外产品差距不是太大.而在整车智能化、电子化装备水平上,欧美和日韩等国家的水平要远远高于中国.下面简要介绍一下国外客车的最新技术.     

Generating random weak orders and the probability of a Condorcet winner

We present an algorithm for generating a random weak order of m objects in which all possible weak orders are equally likely. The form of the algorithm suggests analytic expressions for the probability of a Condorcet winner both for linear and for weak preference orders. Received: 6 April 2000/Accepted: 31 January 2001