Condorcet paradox: Difference between revisions
no edit summary
No edit summary |
No edit summary |
||
Line 1:
{{Wikipedia|Condorcet paradox}}[[Image:Condorcetparadox.png|thumb|right|A majority of the dots are closer to B than A, C than B, and A than C.]]
[[File:Condorcet cycle simple example.png|thumb|1417x1417px|A Condorcet cycle example with ice cream flavors, with reference to the [[Smith set]].]]
The '''voting paradox''', '''Condorcet paradox''', or '''Condorcet cycle''' is when within a set of candidates, no one candidate is preferred by at least as many voters as all the other candidates in the set when looking at their [[Pairwise counting|pairwise matchups]]. It essentially means that within that set of candidates, no matter which candidate you pick, more voters always prefer some other candidate in the set. If there is a Condorcet cycle for 1st place (the winner), then all candidates in the cycle will be in the [[Smith set|Smith Set]] (the fewest candidates preferred by more voters than all others). It is a situation noted by the [[Marquis de Condorcet]] in the late 18th century,
in which collective preferences can be cyclic (i.e. not transitive), even if the preferences of individual voters are not i.e. between three candidates, the first can be preferred by a majority over the second, and the second by a majority over the third, yet the first candidate isn't preferred by a majority over the third (in fact, the third candidate can even be preferred by a majority over the first candidate).
This is paradoxical, because it means that majority wishes can be in conflict with each other. When this occurs, it is because the conflicting majorities are each made up of different groups of individuals.
| |||