Arrow's impossibility theorem: Difference between revisions
Rephrased to make more clear that normalization is not necessarily strategic, by moving strategic voting to a separate paragraph.
(Rephrased to make more clear that normalization is not necessarily strategic, by moving strategic voting to a separate paragraph.) |
|||
Line 36:
===Benefits===
{{See also|Independence of irrelevant alternatives}}
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.
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,
1: B:10 C:4 A:0
Line 47 ⟶ 49:
1: B:10 A:0
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.
In addition, if the voters [[Strategic voting|vote strategically]], the first benefit is also lost.
===Caveats===
| |||