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

[Toby Pereira]

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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