Condorcet and Borda in 1784. Misfits and Documents
نویسنده
چکیده
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 1784 (Condorcet), are often mentioned, but are less well known. (See Iain McLean’s and Arnold Urken’s articles in this issue for the latest commentaries on this matter.) Some fables also run through the collective memory of science. Some authors have commented upon the near-coincidence of the two dates of publication and the physical proximity of the two academicians who were both at the Paris Academy of Sciences. Some have imagined a dialogue, if not a controversy. Studies published during the two last decades provide some insight into this seeming connection.
منابع مشابه
The Borda count in n-dimensional issue space
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...
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A conversation has been going on for over 200 years that is not concluded (nor will this paper conclude it). Is it normatively appropriate to impose a condition of independence of irrelevant alternatives on choice or ordering rules? This paper reviews the conversation since it began in 1784. It sides with Arrow against Saari. The transparency of the Borda rule is simultaneously its theoretical ...
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The Condorcet winner in an election is the candidate that would be able to defeat each of the other candidates in a series of pairwise elections. The Condorcet efficiency of a voting rule is the conditional probability that it would elect the Condorcet winner, given that a Condorcet winner exists. A closed form representation is obtained for the Condorcet efficiency of Borda Rule in three candi...
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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 ...
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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...
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