Are serial Condorcet rules strategy-proof?

Abstract. This paper explores the extent to which majority rule is invulnerable to manipulation by individuals and coalitions, even when majority rule is used to select more than one alternative. The resulting rule may or may not be strategy-proof, depending on the size of the coalitions that can form, and on the nature of the individual preferences over sets of alternatives. No individual can manipulate with respect to a wide family of preferences over sets. The only restriction on the domain of true and revealed individual preferences is that the selection rule is always well defined. Received: 1 November 1999 / Accepted: 7 May 2001 We thank two anonymous referees for suggestions that have significantly improved the paper. We are also grateful to l'Université de Caen for sponsoring a Workshop on Social Choice Theory, where a first draft of this paper was presented in May, 1999, and to the workshop participants for helpful observations. Work on the final version of the paper was done while one of the authors was a guest of the Project on Intergenerational Equity supported by the Ministry of Education, Science, and Technology of Japan. We are grateful to the Ministry and to the project leader, Professor Kotaro Suzumura, for their support.     

Likelihood-based scoring rules for comparing density forecasts in tails

We propose new scoring rules based on conditional and censored likelihood for assessing the predictive accuracy of competing density forecasts over a specific region of interest, such as the left tail in financial risk management. These scoring rules can be interpreted in terms of Kullback-Leibler divergence between weighted versions of the density forecast and the true density. Existing scoring rules based on weighted likelihood favor density forecasts with more probability mass in the given region, rendering predictive accuracy tests biased toward such densities. Using our novel likelihood-based scoring rules avoids this problem.     

Constant scoring rules for choosing one among many alternatives

Quality & Quantity - When a group is to select a decision alternative from a finite set of m ⩾ 3 feasible alternatives, it is often desirable to choose the Condorect (majority)...     

Weighted scoring rules,the impartial culture condition,and homogeneity

The study considers the significance of weight selection for weighted scoring rules on three alternatives. Most research previously done in this area has been based on the assumption of the impartial culture condition. Intuition suggests that if preferences of individuals in a large group are at all distant or different from the impartial culture condition, then the weights selected for a weighted scoring rule become unimportant. It would seem likely in such a situation that one of the alternatives should be a clear front runner and win under almost any weighted scoring rule. A measure of social homogeneity is used in the study to represent the distance between a given set of individuals' preferences and the impartial culture condition. Based on computer simulation analysis, the results indicate that specific weight selection definitely becomes less important as the level of social homogeneity increases. However, the specific weight selection is still found to be of importance for situations with the greatest homogeneity that represent preferences the farthest distance from the condition of impartial culture.     

On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach

For the problem of adjudicating conflicting claims, a rule is consistent if the choice it makes for each problem is always in agreement with the choice it makes for each “reduced problem” obtained by imagining that some claimants leave with their awards and reassessing the situation from the viewpoint of the remaining claimants. We develop a general technique to determine whether a given two-claimant rule admits a consistent extension to general populations, and to identify this extension if it exists. We apply the technique to a succession of examples. I gratefully acknowledge support from NSF under grant SBR-9731431 and SES 0214691, and the comments of Carmen Bevia, Rodrigo Velez, Chun-Hsien Yeh, and a referee.     

The invalidity of the Condorcet Jury Theorem under endogenous decisional skills

The current note clarifies that Condorcet Jury Theorem cannot be generalized to the extended setting where individual decisional skills are not assumed to be exogenous parameters even when these skills are homogeneous. This is true when skills are determined endogenously either by a central planner or, in a decentralized strategic setting, by the decision makers themselves.     

The asymptotic codifference and covariation of log-fractional stable noise

Many econometric quantities such as long-term risk can be modeled by Pareto-like distributions and may also display long-range dependence. If Pareto is replaced by Gaussian, then one can consider fractional Brownian motion whose increments, called fractional Gaussian noise, exhibit long-range dependence. There are many extensions of that process in the infinite variance stable case. Log-fractional stable noise (log-FSN) is a particularly interesting one. It is a stationary mean-zero stable process with infinite variance, parametrized by a tail index α$\alpha$ between 1 and 2, and hence with heavy tails. The lower the value of α$\alpha$, the heavier the tail of the marginal distributions. The fact that α$\alpha$ is less than 2 renders the variance infinite. Thus dependence between past and future cannot be measured using the correlation. There are other dependence measures that one can use, for instance the “codifference” or the “covariation”. Since log-FSN is a moving average and hence “mixing”, these dependence measures converge to zero as the lags between past and future become very large. The codifference, in particular, decreases to zero like a power function as the lag goes to infinity. Two parameters play an important role: (a) the value of the exponent, which depends on α$\alpha$ and measures the speed of the decay; (b) a multiplicative constant of asymptoticity c$c$ which depends also on α$\alpha$. In this paper, it is shown that for symmetric α$\alpha$-stable log-FSN, the constant c$c$ is positive and that the rate of decay of the codifference is such that one has long-range dependence. It is also proved that the same conclusion holds for the second measure of dependence, the covariation, which converges to zero with the same intensity and with a constant of asymptoticity which is positive as well.     

The primal route to the turnpike and asymptotic stability

Asymptotic turnpike theorems in the case where the future is discounted are traditionally derived under the assumptions that a utility function is twice differentiable and that is Hessian is negative definite. Replacing these assumptions by a weaker one. I give a proof of the theorem simpler than existing ones.     

The structure of exactly strongly consistent social choice functions

For ? an anonymous exactly strongly consistent social choice function (ESC SCF) and x an alternative, define $\text{b}{}_{\mathrm{x}}\text{=b(}{}^{\mathrm{f}}\text{)}{}_{\mathrm{x}}$ to be the size of a minimal blocking coalition for x. By studying the correspondence between ? and $\text{{b(}{}^{\mathrm{f}}\text{)}{}_{\mathrm{x}}\text{}}$, we establish the existence, uniqueness and monotonicity of ESC SCF's. We also prove the following conjecture of B. Peleg: A non–constant anonymous ESC SCF depends on the knowledge of every player's full preference profile.     

A Note on the Probability of Having a Strong Condorcet Winner

In an election, a strong Condorcet winner is a candidate who is top-ranked by more than 50% of the voters. The purpose of this note is to provide some algebraic representations for the probability of having a strong Condorcet winner in three-candidate elections. Three alternative procedures for generating voting situations are considered: the Impartial Culture condition, the Impartial Anonymous Culture condition and the Maximal Culture condition. It turns out that the conclusions we obtain strongly depend on the way for generating voting situations.     

Optimal portfolio choice and consistent performance

Consistent financial performance is the key element to success in asset management. We use a dynamic wealth constraint to represent the consistent performance requirement, which takes into account the entire historical records as a benchmark so that the wealth always stays at or above the benchmark. The optimal policy under this wealth constraint is characterized, and several implications are presented in this paper. This consistent performance constraint could be an appealing tool to be implemented in a volatile market and have rich practical implications.     

地产市场的"情"和"义"

又到春暖花开时.清冷已近一年的中国地产市场在牛年春天的暖阳里开始显露复苏的迹象,并似有"重拾昨日辉煌"的气势.……     

The asymptotic distribution of a class of nonparametric test statistics

Zusammenfassung In dieser Arbeit wird das asymptotische Verhalten einer Klasse von verteilungsfreien Statistiken, welche nicht-lineare Funktionen des Rangvektors sind, untersucht. Es ergibt sich, da? unter sehr allgemeinen Bedingungen die Grenzverteilung eine (evtl. unendliche) Summe von gewichteten, unabh?ngigenx ²-Verteilungen ist. Die Theorie der Wahrscheinlichkeitsma?e aufHilbertschen R?umen und das Konzept der „schwachen Konvergenz“ solcher Ma? erweisen sich dabei als sehr brauchbare Hilfsmittel.

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Research supported by the National Science Foundation under Grant No. GP-3816 and GP-6859. This work is based on the authors Ph. D. Dissertation, University of Minnesota.     

“质价相符”相对论

<正>物业服务的价是具体的、理性的、能量化的;而物业服务的质是抽象的、感性的、难量化的。当需求得到满足时,就算是花再高的价,感觉值,就有质,因此物业服务质价相符是相对的。非保障性住房物业服务价格放开(以下简称价格放开),对物业管理行业来讲是利好消息,这一政策实施落地,无疑将会促进市场的繁荣,让物业管理真正回归市场化。但在实行过程中,也难免会给物业服务     

The dynamics of public opinion under majority rules

This note explains the process of public opinion formation via a locally interactive, space-time analysis. The model we use is a special case of the general framework for modelling social interaction proposed in Blume and Durlauf (2001). In the reduced form of the model we study how each individual, when faced with the choice of one, out of two, opinions, tends to conform to the opinion held by the majority of her neighbours. We consider different, symmetric and asymmetric, majority rules. Depending on the specific behavioral rule, the aggregate process of opinion formation may display contagion on one specific opinion, or consensus among all individuals in the population, or co-existence of both opinions. Whenever consensus obtains, we observe the formation of homogeneous areas ( clusters) that seem almost stationary along the dynamics. The authors wish to thank A. Postelwaite and two anonymous referees for very helpful suggestions.