A Data Envelopment Model for Aggregating Preference Rankings

This paper presents a general model for aggregating votes from a preferential ballot. The thrust of the model is to accord each candidate a fair assessment in terms of his overall standing vis-a-vis first place, second place, …, kth place votes. The form of the model is a combined index Σ_{j = 1}^kW_jv_ij where v_ij is the number of the jth place votes received by the ith candidate. The weights W_j are assumed to form a monotonically decreasing sequence with W_j − W_{j + 1} ≥ d(j, ε). These constraints correspond to the assurance region (AR) side constraints in the DEA framework. The properties of the model are examined in terms of this discrimination intensity function d, and in the special case that d(j, ε) = ε, our model is shown to be equivalent to the consensus models of Borda and Kendall.