Arrow's impossibility theorem: Difference between revisions

(→‎Notes: Linking directly to Pareto efficiency)
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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.
 
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 even a single votervoters [[Normalization|normalizesnormalize]] their rated ballotballots or otherwise[[Strategic deviates from thisvoting|vote assumptionstrategically]], it fails. ExampleFor example:<blockquote>1: A:10 B:6 C:0
 
1: B:10 C:4 A:0