孔多塞效率：加权巴克林vs加权得分和博尔达

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences Pub Date : 2025-05-01 DOI:10.1016/j.mathsocsci.2025.102420

D. Marc Kilgour , Jean-Charles Grégoire , Angèle M. Foley

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引用次数: 0

摘要

我们想知道，在排序投票、单赢家选举中，与巴克林相关的程序能在多大程度上识别孔多塞的获胜者。巴克林程序可以有广泛的加权向量和阈值；例如，一种方法应用Borda权重，类似于加权计分选举中的Borda Count。通过模拟，我们估计了加权巴克林选举和加权得分选举在选民数量变得非常大时的最大孔多塞效率；这些措施当然取决于选票的基本分配情况。对于公正的匿名文化分布，当有3个候选人时，加权Bucklin比加权得分表现出更高的孔多塞效率，但当有4个候选人时则不如加权得分，当有5个或6个候选人时基本相等。我们还比较了他们在公正的文化分布下（同样好）和一维空间模型下（加权的Bucklin通常更好，有时好得多）。

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Condorcet efficiency: Weighted Bucklin vs. weighted scoring and Borda

We ask how good Bucklin-related procedures can be at identifying Condorcet winners in ranked-ballot, single-winner elections. Bucklin procedures can have a wide range of weighting vectors and thresholds; one, for example, applies Borda weights, analogous to the Borda Count in weighted scoring elections. Using simulation, we estimate the maximum Condorcet efficiency of both weighted Bucklin and weighted scoring elections as the number of voters becomes very large; these measures depend of course on the underlying distribution of ballots. For the impartial anonymous culture distribution, weighted Bucklin exhibits higher Condorcet efficiency than weighted scoring when there are 3 candidates, but is not as good when there are 4 candidates, and about equal when there are 5 or 6. We also compare them under the impartial culture distribution (equally good), and under a one-dimensional spatial model (weighted Bucklin is usually better, sometimes much better).

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来源期刊

Mathematical Social Sciences 数学-数学跨学科应用

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

59 days

期刊介绍： The international, interdisciplinary journal Mathematical Social Sciences publishes original research articles, survey papers, short notes and book reviews. The journal emphasizes the unity of mathematical modelling in economics, psychology, political sciences, sociology and other social sciences. Topics of particular interest include the fundamental aspects of choice, information, and preferences (decision science) and of interaction (game theory and economic theory), the measurement of utility, welfare and inequality, the formal theories of justice and implementation, voting rules, cooperative games, fair division, cost allocation, bargaining, matching, social networks, and evolutionary and other dynamics models. Papers published by the journal are mathematically rigorous but no bounds, from above or from below, limits their technical level. All mathematical techniques may be used. The articles should be self-contained and readable by social scientists trained in mathematics.