We characterize the preference domains on which the Borda count satisfies Arrow’s “independence of irrelevant alternatives” condition. Under a weak richness condition, these domains are obtained by fixing one preference ordering and including all its cyclic permutations (“Condorcet cycles”). We then ask on which domains the Borda count is non-manipulable. It turns out that it is non-manipulable...

The application of the theory of partially ordered sets to voting systems is an important development in the mathematical theory of elections. Many of the results in this area are on the comparative properties between traditional elections with linearly ordered ballots and those with partially ordered ballots. In this paper we present a scoring procedure, called the partial Borda count, that ex...

The Borda voting rule is a positional scoring rule where, for m candidates, for every vote the first candidate receives m− 1 points, the second m− 2 points and so on. A Borda winner is a candidate with highest total score. It has been a prominent open problem to determine the computational complexity of UNWEIGHTED COALITIONAL MANIPULATION UNDER BORDA: Can one add a certain number of additional ...

Different kinds of decision rules have been successfully implemented under a linguistic approach. This paper aims the same goal for the Borda count, a well-known procedure with some interesting features. In order to this, two ways of extension from the Borda rule to a linguistic framework are proposed taking into account all the agents’ opinions or only the favorable ones for each alternative w...

Many of the small island democracies of the South Pacific are natural laboratories for constitutional and electoral experimentation, but have tended to be ignored by comparative political science research. This article examines one apparently unknown case of electoral innovation from the region: the use of Borda count voting procedures for elections in the Pacific Island states of Nauru and Kir...

An alternative voting system, referred to as probabilistic Borda rule, is developed and analyzed. The winning alternative under this system is chosen by lottery where the weights are determined from each alternative’s Borda score relative to all Borda points possible. Advantages of the lottery include the elimination of strategic voting on the set of alternatives under consideration and breakin...

Designers routinely rank alternatives in a variety of settings using a staple of comparison, the pairwise comparison. In recent years questions have been raised about the use of such comparisons as a means of calculating and aggregating meaningful preference or choice data. Results on voting have been used to argue that the positional procedure known as the Borda count is the best pairwise voti...

Abstract Of importance when selecting a voting method is whether, on regular basis, its outcomes accurately capture the intent of voters. A surprise that very few procedures do this. Another desired feature for decision approach to assist groups in reaching consensus (Sect. 5). As described, these goals are satisfied only with Borda count. Addressing objectives requires understanding what can g...

Weighted committees allow shareholders, party leaders, etc. to wield different numbers of votes or voting weights as they decide between multiple candidates by a given social choice method. We consider that apply scoring methods such plurality, Borda, antiplurality rule. Many induce the same mapping from committee members’ preferences winning candidates. The respective weight equivalence classe...

General conclusions relating pairwise tallies with positional (e.g., plurality, antiplurality (“vote-for-two”)) election outcomes were previously known only for the Borda Count. While it has been known since the eighteenth century that the Borda and Condorcet winners need not agree, it had not been known, for instance, in which settings the Condorcet and plurality winners can disagree, or must ...