[EM] Is there any profile where IRV is worse than Plurality?

[Andy Jennings]

Very good example.  Thanks.



On Fri, Sep 23, 2011 at 4:32 PM, Toby Pereira <tdp201b at yahoo.co.uk> wrote:

> Andy
>
> Candidates can go up the rankings or down when a candidate is eliminated in
> IRV, and it's possible to do both in different rounds. A plurality winner
> could slip down and be eliminated in a case where they would have still gone
> up again and won had they not been eliminated. So:
>
>  30: A>B>C>D
> 26: B>A>C>D
> 24: C>A>B>D
> 10: D>B>A>C
> 10: D>C>A>B
>
>  Round 1:
> A: 30
> B: 26
> C: 24
> D: 20
>
>  D eliminated
>
>  Round 2:
> B: 36
> C: 34
> A: 30
>
>  A eliminated
>
>  Round 3:
> B: 66
> C: 34
>
>  B wins the IRV election whereas A would have been the plurality winner
> and the (quite strong) Condorcet winner.
>
>  A>B: 64-36
> A>C: 66-34
> A>D: 80-20
>
> Toby
>
>
>   *From:* Andy Jennings <elections at jenningsstory.com>
> *To:* EM <election-methods at lists.electorama.com>
> *Sent:* Saturday, 24 September 2011, 0:13
> *Subject:* [EM] Is there any profile where IRV is worse than Plurality?
>
> Since we're discussing IRV quite a bit lately, here's a question:
>
> - Is there any voter profile where IRV gives a worse result than plurality?
>
> I can't seem to think of one.  So is it true that, mathematically, IRV
> dominates Plurality, that is IRV is always at least as good as plurality and
> sometimes strictly better?
>
>
> Even if that is true, I still believe that IRV is harmful, socially.  By
> successfully avoiding the traditional spoiler problem (where spoilers are
> very weak), it leads people to believe that it is immune to the spoiler
> problem.  Then it leads them directly into the second-tier spoiler scenarios
> where a large group of voters will, by voting honestly, cause their least
> favorite candidate to win.
>
> ~ Andy
>
> ----
>
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