本文選題：競賽成績評定 + 社會選擇理論��； 參考：《昆明理工大學》2017年碩士論文

【摘要】：隨著我國社會經(jīng)濟的發(fā)展,競技比賽越來越多地出現(xiàn)在我們生活的各個方面。競技比賽一方面可以提高選手的身體素質,另一面可以展現(xiàn)國家的綜合實力,因此具有重要的作用。當前主觀性競技比賽的結果主要通過裁判員對選手的評分來進行評定,由于裁判員的不同評價準則和主觀意愿會一定程度左右比賽的結果,從而降低了競賽成績評定的客觀性。很多學者為了確保競賽的成績具有客觀性,都是從評分制度上進行改革,而沒有考慮到裁判評分標準的一致性問題。然而,對每一位裁判員評分的合理性做出客觀公正的評價,并采取一些有效的管理辦法實施監(jiān)控以保證評分的公正、準確,也是值得研究的課題。因此,本文研究在主觀性競賽中,如何在裁判評分標準不一致時提高競賽結果的公平性。為解決裁判評分標準不一致而導致不同裁判對同一個選手的評分不具備可比較性的問題,本文基于社會選擇理論,根據(jù)裁判員對選手的偏好排序而不是傳統(tǒng)評分來計算競賽結果。通過群體決策和社會選擇理論來構建裁判員對選手的不同偏好關系并計算選手的整體排序。目前已有的成績評定方法幾乎沒有根據(jù)偏好對競賽結果進行排序的,因此,首先需要獲取每個裁判對選手的競賽評分;其次,將選手的分數(shù)轉換成裁判對選手的偏好排序,并建立選手成對偏好矩陣;然后根據(jù)成對偏好矩陣,構建一個有向圖,并計算最強路徑;最后生成最強路徑矩陣,通過比較選手之間的最強路徑,得出選手最終排序。與傳統(tǒng)評分方法相比,Schulze函數(shù)通過考慮裁判員對不同選手之間的偏好關系,構建有向圖并計算最強路徑,從本質上講弱化了排名過程中的操縱性。本文對Schulze函數(shù)用于競賽成績評定的適用性和有效性進行了理論分析和實驗驗證。理論分析對本文提出的Schulze社會選擇函數(shù)是否具備公平性、一致性、單調性和抗操作性進行了證明。結果表明群決策理論中的Schulze函數(shù)體現(xiàn)了多數(shù)準則,不會因個人獨有的偏好改變最終評定結果,可以得到合理的成績評定結果,從而適用于競賽成績評定。實驗驗證了基于Schulze社會選擇函數(shù)的競賽成績評定方法的有效性。最后,根據(jù)本文提出的方法,設計實現(xiàn)了競賽成績評定系統(tǒng),該系統(tǒng)實現(xiàn)了對競賽選手的成績評定和綜合排序功能,并能對所得的競賽評定數(shù)據(jù)進行驗證。驗證模塊包括了成績評定的一致性、單調性等性質和系統(tǒng)性能測試,表明了社會選擇函數(shù)評定方法的有效性和系統(tǒng)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.
【學位授予單位】：昆明理工大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP311.52

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