Condorcet voting
Create this voteA Condorcet winner is an option that would beat every alternative in a head-to-head vote. Each voter submits a ranking, which tells the count which option they prefer in any pair.
For each comparison, a ballot counts for whichever of the two options it ranks higher. The option does not have to be that voter’s first choice overall.
| Voters | First choice | Second choice | Third choice |
|---|---|---|---|
| 4 | Park | Cinema | Museum |
| 3 | Museum | Cinema | Park |
| 2 | Cinema | Museum | Park |
The three Museum voters and two Cinema voters prefer Cinema to Park.
The four Park voters and two Cinema voters prefer Cinema to Museum.
The three Museum voters and two Cinema voters prefer Museum to Park.
Cinema is the Condorcet winner. It wins against both alternatives.
A different set of rankings can produce a cycle
Three voters rank A → B → C, B → C → A, and C → A → B. Each option then wins one comparison and loses another.
No Condorcet winner: no option beats both alternatives.
Majority preference
A Condorcet winner does not need the same supporters in every comparison. Some voters may prefer it to one rival and others may prefer it to another. What matters is that it wins each comparison across the whole group.
An option ranked first by a majority will always pass this test. But a Condorcet winner need not have a majority of first choices, as the example shows.
When no option wins every comparison
Every voter can have a consistent ranking while the group’s majorities form a cycle: A beats B, B beats C, and C beats A. The people making up the majority change from one pair to the next. No option beats all the others. A tied comparison can also prevent a Condorcet winner.
Methods such as Ranked Pairs and Schulze add rules for choosing a winner in these cases. This site shows the comparisons and reports when no Condorcet winner exists.
Host this vote
Voters rank every option. The result includes every pairwise count. If no option beats every alternative, the group can discuss the result or choose another counting rule.