We provide a natural extension of the Borda count to the n-dimensional spatial context, an algorithm to find the spatial Borda winner based on the notion of an inverse Borda count, the result that the Borda winner and the Condorcet winner coincide in unidimensional space when all alternatives on a line are feasible, results that show that in multi-dimensional space the Borda winner and the Cond...

The question addressed in this paper is the order of magnitude of the difference between the Borda rule and any given social choice function. A social choice function is a mapping that associates a subset of alternatives to any profile of individual preferences. The Borda rule consists in asking voters to order all alternatives, knowing that the last one in their ranking will receive a score of...

We investigate manipulation of the Borda voting rule, as well as two elimination style voting rules, Nanson’s and Baldwin’s voting rules, which are based on Borda voting. We argue that these rules have a number of desirable computational properties. For unweighted Borda voting, we prove that it is NP-hard for a coalition of two manipulators to compute a manipulation. This resolves a long-standi...

Recent research reveals that many NP-hard voting problems in general become polynomial-time solvable in single-peaked elections. In contrast to these results, we prove for the first time that constructive control by adding/deleting votes for Borda are NP-hard even in single-peaked elections. On the other side, we prove that constructive control by adding/deleting votes/candidates for Borda are ...

Given a preference profile, a social dichotomy function partitions the set of alternatives into a set of approved alternatives and a set of disapproved alternatives. The Borda mean rule approves all alternatives with above-average Borda score, and disapproves alternatives with below-average Borda score. We show that the Borda mean rule is the unique social dichotomy function satisfying neutrali...

Both weighted and unweighted Borda manipulation problems have been proved NP-hard. However, there is no exact combinatorial algorithm known for these problems. In this paper, we initiate the study of exact combinatorial algorithms for both weighted and unweighted Borda manipulation problems. More precisely, we propose O∗((m · 2)) time andO∗(t2m) time combinatorial algorithms for weighted and un...

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...