Arrow's impossibility theorem: Difference between revisions
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(Rephrased to make more clear that normalization is not necessarily strategic, by moving strategic voting to a separate paragraph.) |
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===Benefits=== |
===Benefits=== |
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{{See also|Independence of irrelevant alternatives}} |
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There are two main "benefits" that come from evading Arrow's theorem: when candidates enter or drop out of the race, this doesn't impact the choice between the remaining candidates, and when voters are trying to impact the race between a certain set of candidates, they need only alter the portions of their ballot that show their preferences among that set of candidates. |
There are two main "benefits" that come from evading Arrow's theorem: when candidates enter or drop out of the race, this doesn't impact the choice between the remaining candidates, and when voters are trying to impact the race between a certain set of candidates, they need only alter the portions of their ballot that show their preferences among that set of candidates. |
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However, note that to obtain the first benefit, one of the assumptions used in Arrow's Theorem is that voters do not change their preferences on a given set of candidates regardless of whether candidates not in the set are running or not running. If voters [[Normalization|normalize]] their rated ballots |
However, note that to obtain the first benefit, one of the assumptions used in Arrow's Theorem is that voters do not change their preferences on a given set of candidates regardless of whether candidates not in the set are running or not running. Suppose that an election is being conducted using a rated method that passes IIA. If the voters [[Normalization|normalize]] their rated ballots, the first benefit is lost. For example:<blockquote>1: A:10 B:6 C:0 |
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1: B:10 C:4 A:0 |
1: B:10 C:4 A:0 |
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1: B:10 A:0 |
1: B:10 A:0 |
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1: A:10 B:0</blockquote>Scores are A 20, B 10, and now A wins in Score voting. This example uses the standard [[Condorcet paradox]] but presented in rated form. |
1: A:10 B:0</blockquote>Scores are A 20, B 10, and now A wins in Score voting. This example uses the standard [[Condorcet paradox]], but presented in rated form. |
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In addition, if the voters [[Strategic voting|vote strategically]], the first benefit is also lost. |
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===Caveats=== |
===Caveats=== |
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