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Nonmonotonicity? - Peter Hentges

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March 20th, 2008


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09:37 am - 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?

(5 comments | Leave a comment)

Comments:


[User Picture]
From:minnehaha
Date:March 20th, 2008 04:04 pm (UTC)
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I don't, but I can give you the email address of the woman who ran the petition drive, and who knows more about this than anyone else I can think of.

K.
[User Picture]
From:jbru
Date:March 20th, 2008 04:14 pm (UTC)
(Link)
Am mostly just curious because this guy sounds like a crank but is planning on doing dumb things like filing for court injunctions to stop Minneapolis from implementing IRV. (Never mind that he lives in Apple Valley, apparently.) I'd like to be able to speak about it intelligently to my councilperson if necessary.

So, yeah, shoot me that email. I'll share whatever I learn.
From:progressnerd
Date:March 20th, 2008 05:03 pm (UTC)

Not likely

(Link)
First, no voting system is perfect. If non-monotonicity is a "nightmare", there is no word to explain the scenarios that arise under alternative systems. In practice, IRV's non-monotonicity is extremely difficult to exploit. Exploiting it requires knowing detailed knowledge about how everyone will rank prior to the election. It simply does not occur as a problem in any of the places IRV has been used for years, like Australia. If the author of the criticism can provide any proof of it being exploited to any consequence in history, I'd be amazed.

For every alternative voting system (and there are many), you will find some die-hard advocate of it somewhere. But what they more or less agree on is that the one we have no is by far the worst. Fortunately, nearly the entire electoral reform community, and every major electoral reform organization, has considered all the alternatives and deemed IRV to be the single-winner method we should all be working towards.
[User Picture]
From:jbru
Date:March 20th, 2008 06:05 pm (UTC)

Re: Not likely

(Link)
In my searching I found a reference to "range" voting, where instead of ranking you indicate a preference for each candidate across a range (1-100, say). The candidate with the highest average score wins. Like you say, no system is perfect and this alternative to IRV sounded vastly more complex even if it would prevent the (rare) non-monotonicity of IRV.

I also doubted that this purported flaw of IRV ever turned up in actual practice. I'm guessing the guy is just some nut-job that's got a bee in his bonnet.
[User Picture]
From:davidschroth
Date:March 21st, 2008 03:01 am (UTC)
(Link)
A comparison of voting systems can be found at http://bcn.boulder.co.us/government/approvalvote/altvote.html

My impression is that the deficiencies the authors cite seem unlikely to appear in real situations.

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