# [EM] élection de trois élection de trois

Kevin Venzke stepjak at yahoo.fr
Fri Feb 24 22:11:12 PST 2012

```Hi Kristofer,

De : Kristofer Munsterhjelm <km_elmet at lavabit.com>
>À : Kevin Venzke <stepjak at yahoo.fr>
>Cc : election-methods <election-methods at electorama.com>
>Envoyé le : Vendredi 24 février 2012 15h44
>Objet : Re: [EM] élection de trois élection de trois
>
>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.
>
Well, I have a few comments, though I can't do this topic as much justice as I'd like to be able to. I agree
that Approval ranking second-worst is unintuitive in this discussion.

For one thing, compression under Approval is forced more often than under other methods due to the
limited ballot. If you look at my second ranking, regarding perception of spoilers, you see Approval with
massive relative improvement (relative to FPP at least). So maybe one would rather look there.

However, incentive to compress is surely a problem, because bad things happen if the voter doesn't
deign to do it when he needs to. To the extent that candidates don't trust voters to use necessary strategy,
there is nomination disincentive, I expect.

It's possible we are seeing what I call Approval's "mittens problem." As in, it's wearing mittens. By election day
it can generally only elect two candidates (even if more than two might be CW). At the last minute, it can't
make a sudden change about who is a finalist. If I compare to MCA, which is quite similar to Approval in
general but with a simplistic majority check, my ad hoc stat drops from 16.3% to 10.0%. The perception of
spoiler stat drops from 2.2% to 1.2%. (1D spectrum assumption)

I am inclined to guess that Approval suffers more than it gains from not having even a rudimentary majority
check. When voters are strategic I don't think Approval gains anything at all, because the voters are simply
locked into what the polls are saying they can do. It's not as though a majority favorite is getting missed because
of strength of preference. He's missed because the method is inflexible.

But, suppose that compromise is the bigger problem, not compression. (I.e. FBC is what matters.) In that case
there is no contest: All of IRV's 6.5% is compromise and this is worse than every other method except FPP,
TTR, and DSC. (Again, assuming a 1D spectrum.)

(Fun fact: The fifth-worst for compromise is Condorcet//IRV.)

Also, we might be able to dismiss the "perception of spoiler" statistic, because this stat doesn't assume people
are voting sincerely. If I rig the sim to force everyone to vote sincerely, IRV's perception of spoilers leaps to
11.9% (in 1D that is). Strategic Approval was only 2.2%. Cutting that 11.9% down to <1% requires favorite
betrayal (i.e. IRV's only major strategy). To say it again, if you won't trust the voters to use necessary strategy,
I expect you don't nominate three candidates.

I hope something in this post sheds light on what might be going on...

Kevin
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