[EM] Confirmed!: Condorcet efficiency of IRV > 2-stage runoff

[Forest Simmons]

On Fri, 20 Sep 2002, Rob LeGrand wrote in part:

> Sincere preferences:
>
> 45:Reagan>Anderson>Carter
> 35:Carter>Anderson>Reagan
> 20:Anderson>Carter>Reagan
>
> Plurality equilibrium:
>
> 45:Reagan
> 35:Carter
> 20:Carter   <--- insincere
>
> IRV equilibrium:
>
> 45:Anderson>Reagan>Carter   <--- insincere
> 35:Carter>Anderson>Reagan
> 20:Anderson>Carter>Reagan
>
> Note that there are two other plurality equilibria.  In fact, there's a
> plurality equilibrium for each sincere pairwise majority in an
> election, so there's always at least one that elects the Condorcet
> winner.  I believe the IRV equilibrium above is unique, so all of the
> plurality and IRV equilibria for this electorate entail insincerity.
>

Very informative examples, but the existence of different equilibria
doesn't quite answer the original question, which was formulated in terms
of near optimal strategy given near perfect information.

Given the sincere preferences of your example it seems more likely to me
that optimal (and near optimal) strategy for plurality would lead to the
other equilibrium that you mentioned:

45:Anderson  <--- insincere
35:Carter
20:Anderson

The Reagan faction knows that more than 50 percent of the voters rank
Reagan dead last so that he has no chance of winning, therefore they have
nothing to lose by voting for Anderson.

In the plurality equilibrium that you suggested the Anderson faction had
to defect even while they knew there was a good chance of winning if they
didn't defect.

Perhaps you were assuming that the plurality voters had only plurality
polling information, but I'm assuming that both had the same near perfect
information.

Forest

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