Most important decisions in organizations are made by groups of managers or experts. Methods for aggregating preferences and reconciling differences are needed in case decision makers have different viewpoints. Human judgments, including preferences are often vague and cannot be estimated in exact numerical values. This paper proposes a new method under the linguistic framework for heterogeneou...

We introduce the (j, k)-Kemeny rule – a generalization that aggregates weak orders. Special cases include approval voting, the mean rule and Borda mean rule, as well as the Borda count and plurality voting. Why, then, is the winner problem computationally simple for each of these other rules, but NP -hard for Kemeny? We show that winner intractability for the (j, k)-Kemeny rule first appears at...

We say that a preference profile exhibits pairwise consensus around some fixed relation, if whenever relation is closer to it than another one, the Kemeny distance of former not greater its latter. show then this coincides with binary induced by Borda count. also no other scoring rule always selects top ranked alternative which there when such exists.

We introduce the (j, k)-Kemeny rule – a generalization of Kemeny’s voting rule that aggregates j-chotomous weak orders into a k-chotomous weak order. Special cases of (j, k)Kemeny include approval voting, the mean rule and Borda mean rule, as well as the Borda count and plurality voting. Why, then, is the winner problem computationally tractable for each of these other rules, but intractable fo...

We study the problem of Borda Unweighted Coalitional Manipulation, where k manipulators try to manipulate an election on m candidates under the Borda protocol. This problem is known to be NP-hard. While most recent approaches to approximation tried to minimize k, the number of manipulators needed to make the preferred candidate win (thus assuming that the number of manipulators is not limited i...

There are many situations wherein a group of individuals (e.g., voters, experts, sports writers) must produce an ordered list of 'best' alternatives selected from a given group of alternatives (e.g., candidates, proposals, sports teams). Two long established mechanisms that have been used for this task are 'Zermelo's Ranking Method' (1929) and 'Borda's Voting Scheme' (1781). The main purpose of...

How do you aggregate the preferences of multiple agents in a fair manner? This is a question that has occupied researchers for several centuries. Suppose we have k voters who each give their preferences on n candidates. How should the candidates be ranked to best represent the input? Marquis de Condorcet [5] showed that there may not exist a “winner”: a candidate who beats all other candidates ...

population growth as well as development of industry and agriculture has increased the demand and competition over water resources in large watersheds especially in zayandeh rud basin and severely affected on agriculture and environment sectors. hence, providing a best scenario for the allocation of water in this basin is essential. in this study, due to alternating periods of wet, drought and ...