基于社会选择理论的竞赛成绩评定方法研究

发布时间：2018-04-14 05:36

本文选题：竞赛成绩评定 + 社会选择理论　；参考：《昆明理工大学》2017年硕士论文

【摘要】：随着我国社会经济的发展,竞技比赛越来越多地出现在我们生活的各个方面。竞技比赛一方面可以提高选手的身体素质,另一面可以展现国家的综合实力,因此具有重要的作用。当前主观性竞技比赛的结果主要通过裁判员对选手的评分来进行评定,由于裁判员的不同评价准则和主观意愿会一定程度左右比赛的结果,从而降低了竞赛成绩评定的客观性。很多学者为了确保竞赛的成绩具有客观性,都是从评分制度上进行改革,而没有考虑到裁判评分标准的一致性问题。然而,对每一位裁判员评分的合理性做出客观公正的评价,并采取一些有效的管理办法实施监控以保证评分的公正、准确,也是值得研究的课题。因此,本文研究在主观性竞赛中,如何在裁判评分标准不一致时提高竞赛结果的公平性。为解决裁判评分标准不一致而导致不同裁判对同一个选手的评分不具备可比较性的问题,本文基于社会选择理论,根据裁判员对选手的偏好排序而不是传统评分来计算竞赛结果。通过群体决策和社会选择理论来构建裁判员对选手的不同偏好关系并计算选手的整体排序。目前已有的成绩评定方法几乎没有根据偏好对竞赛结果进行排序的,因此,首先需要获取每个裁判对选手的竞赛评分;其次,将选手的分数转换成裁判对选手的偏好排序,并建立选手成对偏好矩阵;然后根据成对偏好矩阵,构建一个有向图,并计算最强路径;最后生成最强路径矩阵,通过比较选手之间的最强路径,得出选手最终排序。与传统评分方法相比,Schulze函数通过考虑裁判员对不同选手之间的偏好关系,构建有向图并计算最强路径,从本质上讲弱化了排名过程中的操纵性。本文对Schulze函数用于竞赛成绩评定的适用性和有效性进行了理论分析和实验验证。理论分析对本文提出的Schulze社会选择函数是否具备公平性、一致性、单调性和抗操作性进行了证明。结果表明群决策理论中的Schulze函数体现了多数准则,不会因个人独有的偏好改变最终评定结果,可以得到合理的成绩评定结果,从而适用于竞赛成绩评定。实验验证了基于Schulze社会选择函数的竞赛成绩评定方法的有效性。最后,根据本文提出的方法,设计实现了竞赛成绩评定系统,该系统实现了对竞赛选手的成绩评定和综合排序功能,并能对所得的竞赛评定数据进行验证。验证模块包括了成绩评定的一致性、单调性等性质和系统性能测试,表明了社会选择函数评定方法的有效性和系统的高效性。
[Abstract]:With the development of our social economy, more and more competitive competitions appear in all aspects of our life.On the one hand, competitive competition can improve the players' physical quality, on the other hand, it can show the comprehensive strength of the country, so it plays an important role.At present, the result of subjective competitive competition is mainly evaluated by the referee's score. Because the referee's different evaluation criteria and subjective will will influence the result of the competition to some extent, it reduces the objectivity of the evaluation of the competition result.In order to ensure the objectivity of the results of the competition, many scholars have reformed the scoring system without considering the consistency of the judges' scoring standards.However, making an objective and fair evaluation of the rationality of each referee's score and adopting some effective management methods to ensure the fairness and accuracy of the scoring are also worthy of study.Therefore, this paper studies how to improve the fairness of competition results in subjective competitions.In order to solve the problem that different referees do not have comparable scores on the same player due to inconsistent standards, this paper based on the theory of social choice.The results of the competition are calculated according to the referee's preference for the player rather than the traditional score.Through the theory of group decision and social choice, the referees' different preferences to the players are constructed and the overall ranking of the players is calculated.At present, there is almost no ranking of the result of the competition according to the preference, so, first of all, it is necessary to obtain the competition score of each referee on the contestant; secondly, to convert the score of the player into the preference ranking of the referee to the player.Then a digraph is constructed according to the pair preference matrix and the strongest path is calculated. Finally the strongest path matrix is generated and the final ranking is obtained by comparing the strongest paths between players.Compared with the traditional scoring method, Schulze function constructs digraph and calculates the strongest path by considering the referees' preference to different players, which essentially weakens the maneuverability in the ranking process.In this paper, the applicability and validity of the Schulze function in the evaluation of competition results are analyzed theoretically and experimentally.The theoretical analysis proves whether the Schulze social selection function has fairness, consistency, monotonicity and anti-maneuverability.The results show that the Schulze function in the group decision theory embodies the majority criterion and can not change the final evaluation result because of the individual's unique preference, and can get a reasonable result, which can be applied to the evaluation of competition results.The effectiveness of the evaluation method based on Schulze social selection function is verified by experiments.Finally, according to the method proposed in this paper, a competition score evaluation system is designed and implemented. The system realizes the performance evaluation and comprehensive sorting function of the contestants, and can verify the competition evaluation data.The verification module includes the consistency of performance evaluation, monotonicity and system performance testing, which shows the effectiveness of the social selection function evaluation method and the high efficiency of the system.
【学位授予单位】：昆明理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP311.52

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