## "Pocket size" IRV example refuting Richie's "Core support" theory

by Clay Shentrup

Here is a 4-candidate Instant Runoff Voting election (candidates named A,B,C,D):

#voters their vote
35% A > C > D > B
17% B > C > D > A
32% C > D > B > A
16% D > B > C > A

Instant Runoff Voting selects candidate B as the winner, beating A in the final round, 65% to 35%.

But wait!

A huge 67% majority of voters would rather have candidate C than candidate B. And candidate C received nearly twice as many first-place votes as candidate B, 32% to 17%. And an even larger 83% super-majority of voters would rather have candidate D than B (and D got just a little fewer first-place votes than B). So the claim that IRV "elects majority winners" is seriously misleading. Also...

• A is a spoiler (if he would drop out of the race, C would win instead of B).
• The first row of voters have an incentive to betray candidate A by pretending candidate C is their actual favorite - then they get their second choice instead of their last.
• The third row of voters have an incentive to betray candidate C by pretending candidate D is their favorite – then they get their second choice instead of their third.
• The first row of voters made a big mistake by voting honestly. Suppose of the 35 first-row voters, 20 had simply refused to vote. That move (not voting) would actually have been better for them than voting honestly because it would have caused C to win (whom they prefer over B). Their honest "B is worst" votes actually caused B to win!

Also, C is the Condorcet "beats-all" winner, but doesn't make it to the final round: 65% majority says C>A; 67% majority says C>B; 84% majority says C>D.

And A is the Condorcet "lose-to-all" loser, but makes it to the final round (65% majorities say others>A).

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