在大型競賽之中，評審們負責審閱參賽者的資料並依表現將其排名。若每位評審都有足夠的時間及精力審查所有的參賽者，則參賽者的最終排名即是所有評審排名之平均，因為這組參賽者的排名可代表所有評審的意見，故在本研究中將之稱為「詳盡排名」。
但在大型比賽中，數量眾多的參賽者使評審無法在短時間內將之一一審查並排出名次，故為減輕評審負擔，參賽者們會被分成幾個小組，而每位評審只需負責審查其中一組。因為每位評審只審查過一部份的參賽者，故參賽者的最終排名也從所有評審的平均改為部分評審的平均。本研究之重點在於在不增加評審負擔，也就評審們依然只需審查部分參賽者的情況下，如何使評審透過有效率的合作，將參賽者排出與「詳盡排名」最接近的名次。
本篇研究所提出的評分程序稱為「協同排序法」，此程序包含了多個階段；在一個階段中，所有的參賽者被分成許多小組，而一個小組由一位評審來排名。在結束一階段評比後，每位參賽者將會根據先前的排名順序重新分配到新的小組，透過重新分組，能夠將參賽者依照實力更均勻地分配在不同的小組裡中。
實驗的結果顯示，當300位參賽者被分配到3個小組的情況下，利用「協同排序法」經過3階段的評審後，平均每位參賽者排名誤差為4.18；然而，若採用原始方式審查，也就是不再重新分組，則平均每位參賽者排名誤差將高達11.88。此外，在實際的運用協同排序法時，「詳盡排名」是未知的，此研究也提供了估計參賽者排名誤差的方法。

關鍵字：排名、大規模競賽、分組、申請入學

In a competition, a number of evaluators are responsible for reviewing and ranking a group of participants. After reviewing all participants by each evaluator, the final ranking result is obtained by averaging all evaluator’s ranking, which is called “exhaustive ranking”. However, if the number of participants is large, an evaluator is not able to review all participants. Thus, the participants have to be divided into several subgroups, and an evaluator only needs to review a subgroup. The final ranking result is therefore determined by the partial evaluations by various evaluators. The focus of this study is, without increasing the efforts of evaluators, how to determine a ranking as close to exhaustive ranking as possible under the condition that an evaluator can only review a portion of all participants.
The proposed evaluation procedure is called cooperative ranking methods that involve a number of iterations. In an iteration, all participants are divided into a number of subgroups and each subgroup is reviewed by an evaluator. After being evaluated in previous iterations, a participant could be re-assigned to a different subgroup based on the result of previous iterations. By utilizing the previous evaluation results, the participants would be evenly assigned to different subgroups.
The experiment results show that in a competition of 300 participants who are divided into three subgroups, the average error in ranking position of a participant is 4.18 in three iterations by applying the proposed evaluation method. On the other hand, a traditional approach that does not adopts regrouping, the average error is as high as 11.88. In addition, in actual application of the proposed evaluation procedure whose exhaustive ranking is unknown, the method to estimate the error in ranking position is also proposed in this study.
Keywords: ranking, large scale competition, regroup, cooperative, group.

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