Abstract
Forn candidates, a profile of voters defines a unique Borda election ranking for each of the 2n − (n + 1) subsets of two or more candidates. The Borda Dictionary is the set of all of these election listings that occur for any choice of a profile. As such, the dictionary contains all positive features, all flaws, and all paradoxes that can occur with single profile, sincere Borda elections. After the Borda Dictionary is characterized, it is used to show in what ways the Borda Count (BC) is an improvement over other positional voting methods and to derive several new BC properties. These properties include several new characterizations of the BC expressed in terms of axiomatic representations of social choice functions, as well as showing, for example, that the BC ranking ofn candidates can be uniquely determined by the BC rankings of all sets ofk <n candidates for any choice ofk between 2 andn.
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This research was supported, in part, by NSF grants IRI8415348, IRI-8803505 and a Fellowship from the Guggenheim Memorial Foundation.
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Saari, D.G. The Borda dictionary. Soc Choice Welfare 7, 279–317 (1990). https://doi.org/10.1007/BF01376279
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DOI: https://doi.org/10.1007/BF01376279