[EM] To Bill Lewis Clark re: stepping-stone

Adam H Tarr atarr at ecn.purdue.edu
Sat Jan 24 16:13:01 PST 2004

>Incidentally, I've read claims in the past that there are potential
>scenarios in which IRV even does worse than Plurality, and I've conceded
>these as being true but describing extremely unrealistic situations. 
>People have asked me in private correspondence what these situations might
>be, and I can't construct any, so perhaps I conceded too much.
>So, when (if ever) does IRV perform worse than Plurality?

Mike Ossipoff has already pointed out some such scenarios, but I'll chime in 
with my favorite such example:

10% FarRight>Right>Centrist>Left>FarLeft
10% Right>FarRight>Centrist>Left>FarLeft
15% Right>Centrist>FarRight>Left>FarLeft
16% Centrist>Right>Left>FarRight>FarLeft
15% Centrist>Left>Right>FarLeft>FarRight
13% Left>Centrist>FarLeft>Right>FarRight
11% Left>FarLeft>Centrist>Right>FarRight
10% FarLeft>Left>Centrist>Right>FarRight

In this example, Plurality, Condorcet, Norda, Bucklin, MCA, Approval (under any 
reasonable strategy assumptions) all pick the centrist as the winner.  Only IRV 
picks someone else (Right).  As I have said before, I think it takes a good dose 
of cognitive dissonance to argue that the above example should result in someone 
other than Centrist being elected.

Here is another example - one where the eventual IRV winner has very weak 
first-preference support:

7%  FarRight>Right>LuckyRight>ModerateRight>ModerateLeft
2%  Right>FarRight>LuckyRight>ModerateRight>ModerateLeft
4%  Right>LuckyRight>FarRight>ModerateRight>ModerateLeft
7%  LuckyRight>ModerateRight>Right>ModerateLeft
15% ModerateRight>LuckyRight>ModerateLeft>Right
16% ModerateLeft>ModerateRight>LuckyRight>Left
15% ModerateLeft>Left>ModerateRight>FarLeft>LuckyRight
13% Left>ModerateLeft>FarLeft
11% Left>FarLeft>ModerateLeft
10% FarLeft>Left>ModerateLeft

Luckyright wins the election, despite the fact that ModerateLeft beats every 
other candidate in a two-way race by at least thirty points (i.e. a total 
landslide), and has the most first-place support by far.  Moreover, 
ModerateRight beats LuckyRight by an 80%-20% tally!  There's clearly at least 
two candidates that are more deserving than LuckyRight.


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