Example of Plurality voting electing "lose to all" candidate

Let the four candidates be A, B, C, and D.

#voterstheir vote
28 A>B>C>D
25 B>C>D>A
24 C>D>B>A
23 D>C>B>A

In this situation, A would lose to any opponent in a head-to-head election by a huge 72-to-28 margin, far larger than the hugest "landslide" in US presidential election history. And A is ranked dead last by 72% of the voters.

But thanks to the insanely idiotic plurality, aka "first past the post" voting system, A is elected with 28% of the vote, beating out everybody else (each with ≤25%).

In the 3-candidate random elections model this happens in approximately one in six plurality 3-candidate elections. It is plausible that it happened in the Nicaraguan 2006 presidential election, and it definitely happened in the 2009 Burlington (VT) mayor election among the top 3 candidates.

In this example, B beats each opponent pairwise by at least a 53-47 margin and hence presumably "should" have been the easy winner; and indeed B would have won with both Condorcet and Borda voting. On the other hand C would have won IRV voting, using these ballots. (B or C also would usually have won with range or approval voting, but we cannot which tell with certainty because these ballots have not stated the voters' scores or approval-decisions on the candidates.)

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