IRV spoiler example – and also example of IRV eliminating a beats-all-winner

Let the three candidates be B, G, and N.

#voterstheir vote
35 B>G>N
32 G>B>N
23 N>G>B

Under IRV, G wins. But now the last ten voters show up (all saying N>G>B).

#voterstheir vote
35 B>G>N
32 G>B>N
33 N>G>B

Under IRV, now B wins, even though the ten new voters ranked B dead last and behind G.

Here N is a "spoiler" (despite any contention spoilers do not exist with IRV) because these voters' decision to honestly vote for their favorite (N, think of N as "Nader" if you want) caused their most-hated choice (B) to win. If they had dishonestly voted for their second-favorite, for example voting G>B>N or G>N>B, then G would have won. So Nader voters can, by the act of casting their honest vote, cause both Nader and their fallback option Gore to both lose. Nader still is a spoiler. IRV does not alter that fact.

But actually in this example, IRV features a worse kind of spoiler than normal. With normal plurality voting, if you vote honestly, you may not get as good a result as if you'd voted dishonestly – but at least you won't, by voting honestly, get a worse result than if you had refused to vote at all. With IRV, the Nader voters by voting honestly actually caused both Nader and their 2nd choice Gore to both lose, whereas if they'd refused to vote, Gore would have won.

Fact #1: Spoilers still exist with IRV, and indeed a worse kind of spoiler exists – in which voting honestly can actually be worse for you than refusing to vote at all.

But wait, there is more. In this example, the voters prefer G over B by 65-to-35 and prefer G over N by 67-to-33. Thus G is a huge majority winner (bigger landslide margin than any US presidential election in history!) versus either opponent head to head. But IRV, as we saw, refuses to elect G (indeed eliminating G in the first round) and elects B!

Fact #2: A winner with a huge supermajority of support versus every opponent can be eliminated by IRV in the very first round. Calling IRV winners "majority winners" is therefore untrue.


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