Abstract
Ranked voting data arise when voters select and rank more than one candidate with an order of preference. Cook et al.[1] introduced data envelopment analysis (DEA) to analyze ranked voting data. Obata et al.[2] proposed a new method that did not use information obtained from inefficient candidates to discriminate efficient candidates. Liu et al.[3] ranked efficient DMUs on the DEA frontier with common weights. They proposed a methodology to determine one common set of weights for the performance indices of all DMUs. Then, these DMUs were ranked according to the efficiency score weighted by the common set of weights. In this paper, we use one common set of weights for ranked voting data.
Highlights
In the recent papers, we have considered ranked voting data which are obtained when voters select and rank more than one candidate
Let a be the minimum of set ai | i 1,..., m we can obtain another feasible common set of weights wj leads to a smaller objective function, and this contradicts the assumption
The results showed that the score of A is maximum at w 1 and the normalized preference score was z
Summary
We have considered ranked voting data which are obtained when voters select and rank more than one candidate. By using data envelopment analysis (DEA) [4], Cook et al.[1] have proposed a method for estimating preference scores without imposing any fixed weights on outputs. The resulting score Z0* is the preference score of the candidate This model obtains favorable weights that are different for each DMU. Liu et al [3] ranked efficient DMUs using common weight but the object of this paper is ranked voting in the method of Obata et al [2] with common weight; we use Liu et al [3] method.
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