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[note 1] The Borda count was the sole method used for membership election to the Academy from 1795 until 1800, when it was supplemented by other methods at the urging of Napoleon. Charles L. Dodgson (Lewis Carroll, 1832–1898) proposed a version of the Borda count in "A discussion of the various methods of procedure in conducting elections ...
This method is more favourable to candidates with many first preferences than the conventional Borda count. It has been described as a system "somewhere between plurality and the Borda count, but as veering more towards plurality". [5] Simulations show that 30% of Nauru elections would produce different outcomes if counted using standard Borda ...
The Borda count is a weighted-rank system that assigns scores to each candidate based on their position in each ballot. If m is the total number of candidates, the candidate ranked first on a ballot receives m − 1 points, the second receives m − 2 , and so on, until the last-ranked candidate who receives zero.
The Borda count does not comply with the Condorcet criterion in the following case. Consider an election consisting of five voters and three alternatives (candidates A, B, and C), with the following votes: A > B > C: 3; B > C > A: 2; In this election, the Borda count awards 2 points for 1st choice, 1 point for second and 0 points for third.
Instant runoff (IRV), minimax and the Borda count are natural tie-breaks. The first two are not frequently advocated for this use but are sometimes discussed in connection with Smith's method where similar considerations apply. Dasgupta and Maskin proposed the Borda count as a Copeland tie-break: this is known as the Dasgupta-Maskin method. [11]
The Borda count, minimax, Kemeny–Young, Copeland's method, plurality, and the two-round system all fail the independence of clones criterion. Voting methods that limit the number of allowed ranks also fail the criterion, because the addition of clones can leave voters with insufficient space to express their preferences about other candidates.
The Borda count and Bucklin voting both elect in the scenario above, and thus fail IIA after is removed. Copeland's method returns a three-way tie, but can be shown to fail IIA by going in the opposite direction.
For example, the Black method chooses the Condorcet winner if it exists, but uses the Borda count instead if there is a cycle (the method is named for Duncan Black). A more sophisticated two-stage process is, in the event of a cycle, to use a separate voting system to find the winner but to restrict this second stage to a certain subset of ...