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. 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.
| |||