群體對候選人投票排序時處理相同排名的方法

A procedure to discriminate candidates in tie of a group voting system.

吳奇鴻(Chi-Hung Wu)

指導教授 ： 劉復華

國立交通大學/管理學院/工業工程與管理系所/碩士(2009年)

https://doi.org/10.6842/NCTU.2009.01110

摘要

本研究之目的為分析一種普遍的投票結果。針對不可量化指標，由一群評審對若干候選人加以排序，每位評審先對候選人加以排序，彙總排序的結果，得知每位候選人在各項名次的得票次數。使用資料包絡分析法來處理投票後的資料，可求得各名次的權重，以這組權重來計算各候選人的得票加權總分，再以此總分做為排序。若有總分相同時，則為同排名。此現象在實務上造成困擾，本研究之目的乃處理同排名之問題及著重於區辨排名後該如何分配資源給該若干同排名者。以上述的排名模式為第一階段，本研究再增第二階段之處理程序，提出兩種方法來將因總分相同而排名相同的候選人加以排序。第一個是利用同排名之間總合分數最大差距(gap)的觀念；第二個是利用求取最小可將兩者總合分數區分差距，將相同排名的候選人分出高下。並且避免兩大缺點，即是 ε 設定的問題與非高效者的改變不會影響到高效者的排序。

關鍵字

資料包絡分析 ； 共同權重 ； 排序 ； 投票系統

並列摘要

This research is aimed to develop a procedure to analyze the voting result of a voting group. We focus on the indices that can not be quantified. Each voter of the group ranks several candidates in his/her preference order. The first phase of our procedure is employing previous developed model that determines a set of weights for the places in the order therefore the candidates could be ordered according to their aggregated scores. The model is unable to discriminate the candidates in tie with the aggregated score. In this research, we propose to append a decision process as the second phase that consists of a nonlinear mathematical programming model to discriminate candidates in tie. We propose two methods. In the first method, we maximize the gaps of aggregate scores among same ranking units; in the second method, we select the minimum gap that can distinguish same ranking units. And in order to avoid two drawbacks. The first drawback is how to establish Archimedean infinitesimal constant. The second drawback is the inefficient may change the order of efficient candidates.

並列關鍵字

data envelopment analysis ； common weights ； ranking ； voting

參考文獻

Adler, N., Friedman, L. & Sinuany-Stern, Z., 2002. Review of ranking methods in the data envelopment analysis context. European Journal of Operational Research, pp.249-265.

Andersen, P. & Petersen, N.C., 1993. A procedure for ranking efficient units in data envelopment analysis. Management Science, pp.1261-1264.

Charnes, A., Cooper, W.W. & Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research, pp.429-444.

Cook, W.D. & Kress, M., 1990. A data envelopment model for aggregating preference rankings. Management Science, pp.1302-1310.

Doyle, J. & Green, R., 1994. Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the Operational Research Society, pp.567-578.