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[note 2] 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 ...
The classic example of a positional voting electoral system is the Borda count. [1] Typically, for a single-winner election with N candidates, a first preference is worth N points, a second preference N – 1 points, a third preference N – 2 points and so on until the last ( N th) preference that is worth just 1 point.
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.
k-Borda: each voter gives, to each committee member, his Borda count. Each voter ranks the candidates and the rankings are scored together. The k candidates with the highest total Borda score are elected. Borda-Chamberlin-Courant (BCC): each voter gives, to each committee, the Borda count of his most preferred candidate in the committee. [12]
Some systems, and the Borda count in particular, are vulnerable when the distribution of candidates is displaced relative to the distribution of voters. The attached table shows the accuracy of the Borda count (as a percentage) when an infinite population of voters satisfies a univariate Gaussian distribution and m candidates are drawn from a ...
Instant-runoff voting, the Kemeny-Young method, Minimax Condorcet, Ranked Pairs, top-two runoff, First-past-the-post, and the Schulze method all elect B in the scenario above, and thus fail IIA after C is removed. The Borda count and Bucklin voting both elect C in the scenario above, and thus fail IIA after A is removed.
The Borda count is an example of a clone-positive method; in fact, the method is so clone-positive that any candidate can simply "clone their way to victory", and the winner being the coalition that runs the most clones. A method can also fail the independence of clones criterion without being clone-positive or clone-negative.
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 ...