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.]]
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.
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.
Line 13:
If C is chosen as the winner, it can be argued that B should win instead, since two voters (1 and 2) prefer B to C and only one voter (3) prefers C to B. However, by the same argument A is preferred to B, and C is preferred to A, by a margin of two to one on each occasion.
When a [[Condorcet method]] is used to determine an election, a voting paradox among the ballots can mean that the election has no [[
Note that there is no fair and deterministic resolution based solely off of the ranked preferences to this trivial example because each candidate is in an exactly symmetrical situation.
It is believed to be uncommon for Condorcet cycles to occur, happening in about 9% of elections, depending on the scenario and makeup of the electorate. See [[W:Condorcet paradox#Likelihood%20of%20the%20paradox|w:Condorcet_paradox#Likelihood_of_the_paradox]]
| |||