Borda count: Difference between revisions
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(I've introduced the MBC, which is what Jean-Charles de Borda actually proposed.) |
(I'm talking about the MBC (as well as the BC).) |
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Voting systems are often compared using mathematically-defined criteria. See [[voting system criterion]] for a list of such criteria. |
Voting systems are often compared using mathematically-defined criteria. See [[voting system criterion]] for a list of such criteria. |
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The Borda count |
The Borda count BC and Modified Borda Count MBC satisfy the [[monotonicity criterion]], the [[summability criterion]], the [[consistency criterion]], the [[participation criterion]], the [[Plurality criterion]] (trivially), [[Reversal symmetry]], [[Intensity of Binary Independence]] and the [[Condorcet loser criterion]]. |
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It does not satisfy the [[Condorcet criterion]], the [[Independence of irrelevant alternatives]] criterion, or the [[Strategic nomination|Independence of Clones criterion]]. |
It does not satisfy the [[Condorcet criterion]], the [[Independence of irrelevant alternatives]] criterion, or the [[Strategic nomination|Independence of Clones criterion]]. |
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[[Donald G. Saari]] created a mathematical framework for evaluating positional methods in which he showed that Borda count has fewer opportunities for strategic voting than other positional methods, such as [[plurality voting]] or [[anti-plurality voting]], e.g.; "vote for two", "vote for three", etc. |
[[Donald G. Saari]] created a mathematical framework for evaluating positional methods in which he showed that Borda count has fewer opportunities for strategic voting than other positional methods, such as [[plurality voting]] or [[anti-plurality voting]], e.g.; "vote for two", "vote for three", etc. |
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The MBC and the Condorcet rules are the only voting procedures which count ''all'' the preferences cast by ''all'' voters ''always''; they are the most accurate. Given that the MBC is vulnerable to the independence criterion, while the Condorcet rule is prone to a paradox, but not vice versa, the best voting procedure of all could be a combined MBC/Condorcet analysis - a proposal first made by Charles Dodgson. |
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==Variants== |
==Variants== |