Peter Hentges (jbru) wrote,
Peter Hentges
jbru

Nonmonotonicity?

An article in the City Pages regarding the Instant Runoff Voting initiative that Minneapolis is scheduled to implement in 2009 has a paragraph with information from an IRV opponent.
In addition to insisting that IRV is needlessly complicated, he points out the flipside of the most common argument in favor of it: That it makes possible a scenario where a candidate wins a plurality but winds up losing after votes are redistributed. He also points to a nightmare scenario, known in academic circles as "nonmonotonicity," in which a voter could inadvertently harm her preferred candidate by ranking him higher than a less preferred alternative. "It's like putting a blindfold on the voter," he says.
Now, apart from not understanding how he could view it as "needlessly complicated" and thinking that a candidate with a plurality losing to a candidate with a majority after votes are distributed is a feature not a bug, I'm trying to figure out what this "nonmonotonicity" scenario is.

The one example I can find through our good friend Google runs something like this:
Say nearly everyone has voted, and they've voted like this:

35: ABC
33: BAC
32: CBA

C gets eliminated and the C votes transfer to B, who wins.

But, just before the polls are closed, 2 more voters decide that they should vote too, so that they can do their part to at least ensure that their last choice won't win. They vote CBA.

Because they showed up and voted, they changed the winner from B to C, their last choice.
But C isn't their last choice; they listed C first on their ballot. WTF? I think the author is trying to imagine a scenario where I know the results of the election before I vote and choose to rank a candidate first because I "know" they are going to be eliminated. But I can't fathom why I would choose to do that.

Does anyone have any other examples of what is, fairly obviously, an edge case? Or can otherwise explain the concept to me?
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