# [EM] élection de trois élection de trois

Kristofer Munsterhjelm km_elmet at lavabit.com
Fri Feb 24 13:44:07 PST 2012

```On 02/24/2012 02:15 AM, Kevin Venzke wrote:
> Hi,
>
> De : Kristofer Munsterhjelm<km_elmet at lavabit.com>
>> As a consequence, among ranked methods, some really bad methods (like Plurality)
>> gets it wrong when there are two candidates plus no-hopes; some slightly better
>> methods (like IRV, and perhaps I'd also put DAC/DSC here since it uses the same
>> logic) can identify and remove the no-hopes but then gives bad results when the
>> going gets tough; while yet other methods (such as Condorcet) use more consistent
>> logic and, though not perfect, handle three-way (and n>3 n-way) races much better.
>
> I guess I might measure this as the need to compromise or compress, since this is
> what you probably do when the method won't handle the third candidate well. One
> figure I like to compute is the % of voters compromising plus half the % that
> compress. If I do that I get this for 1D scenarios:
>
> 17.1% FPP
> 16.3% Approval
> 9.2% DSC
> 7.9% TACC (the worst-scoring Condorcet method)
> 6.5% IRV
> 3.9% DAC
> 0.1% AWP explicit (the best-scoring Condorcet method)

That seems quite unintuitive. Is Approval really worse on third parties
than IRV is? In Approval, at least you have the chance to get it right
if polls are correct, but IRV just forges on ahead and eliminates the
Plurality loser anyway.

Let's consider it from first principles. When a method does badly on
more than a certain number of viable candidates, that means that the
extra candidates disturb the picture so that the wrong candidate wins
unless the voters make use of widespread strategy to fix the method's
problems.

I suppose that is, in a sense, what's going on with Approval. The voters
need poll data to determine whether to vote {Nader, Gore} rather than
just {Nader} depending on Gore's viability vs. Bush. If Bush or Nader
hadn't been present, there wouldn't have been a problem.

So why does IRV seem to be worse than Approval? In the n > 3 case,
Approval defensive strategy is probably easier than IRV defensive
strategy. But what about when you have three viable candidates?

In both systems you have a compromise incentive. In a viable 3-candidate
scenario, say Burlington, in Approval, Wright voters have to decide
whether to vote {Wright, Montroll} or just {Wright}. In IRV, Wright
voters have to decide whether to vote Montroll > Wright or Wright >
Montroll. The difference might be that in IRV, the strategy gives the
appearance that Wright has no chance -- so people don't vote for him, so
he keeps on having no chance. On the other hand, in Approval, voters can
look at the polls and say "Wright's approaching Montroll so now I can
vote for Wright alone unless I'm risk-averse". It's a dangerous game,
but by no means is it foregone that Wright will lose.

But how to quantify that, I don't know; and perhaps that is all
tangential to whether a system can handle three candidates without
strategy being needed in the first place.

```