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...

In many real world elections, agents are not required to rank all candidates. We study three of the most common methods used to modify voting rules to deal with such partial votes. These methods modify scoring rules (like the Borda count), elimination style rules (like single transferable vote) and rules based on the tournament graph (like Copeland) respectively. We argue that with an eliminati...

The problem of aggregating a set of ordinal rankings of n alternatives has given rise to a number of consensus models. Among the most common of these models are those due to Borda and Kendall, which amount to using average ranks, and the /1 and /2 distance models. A common criticism of these approaches is their use of ordinal rank position numbers directly as the values of being ranked at those...

The POSSIBLE WINNER problem asks whether some distinguished candidate may become the winner of an election when the given incomplete votes are extended into complete ones in a favorable way. POSSIBLE WINNER is NP-complete for common voting rules such as Borda, many other positional scoring rules, Bucklin, Copeland etc. We investigate how three different parameterizations influence the computati...

This issue on the history of social mathematics is a fine occasion for promoting the digital library accumulated by the Bibliothèque nationale de France in Paris (www.gallica.fr) and for displaying beyond the circles of Condorcetian erudition the Condorcet-Borda file related to the mathematics of elections. The two names are well known. Their works, associated with the years 1781 (Borda) and 17...

Abstract: Determination of the best performance parking attendants at Asahan District Transportation Service aims to increase responsibility and high loyalty get satisfactory results award with performance. The assessment officers was carried out by 3 assessors namely traffic engineering management, section, administration staff. problem in assessing is that there no structured system so time q...