Condorcet Voting Paradox, explained.
The Condorcet voting paradox occurs when pairwise majority preferences cycle even though each voter has a consistent ranking.
Why it happens
Different pairs can be decided by different coalitions. Adding majority comparisons does not preserve the transitivity of the individual rankings, so a candidate who defeats every rival need not exist.
Individually consistent rankings can aggregate into a majority cycle: A defeats B, B defeats C, and C defeats A.
Read the result
At three voters in each group, compare all three vote counts. Increase the first group and notice when the cycle disappears. The bars show votes for the named side, not vote shares from three independent elections.
A worked example
A committee with three ranking groups
Three prefer A>B>C, three B>C>A and three C>A>B.
Six prefer A to B, six prefer B to C, and six prefer C to A.
Each majority is valid, but their cycle prevents a single candidate from beating both rivals.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Two groups contain three voters each; the first contains the chosen number. All pairwise votes are counted from strict rankings. A Condorcet winner must defeat both alternatives.
Where this idea is useful
A practical use
Meeting outcomes can depend on the order of pairwise votes when no option defeats every rival.
A common misconception
“A cycling majority means individual voters contradict themselves.”
Every individual ranking can remain consistent. The inconsistency arises in the aggregated pairwise relation.
What this explanation leaves out
- Only three ranking types are represented. The absence of a Condorcet winner does not mean voters themselves are inconsistent.
Why might agenda order matter?
A sequential pairwise process can eliminate an option before its favorable matchup occurs; a cycle makes the order consequential.
Does your group decision rule specify what happens when no option defeats every other one?
Further reading
Explore the original research or the teaching reference behind this experiment.