# [EM] élection de trois élection de trois

Jameson Quinn jameson.quinn at gmail.com
Thu Feb 23 11:04:27 PST 2012

```2012/2/23 Kristofer Munsterhjelm <km_elmet at lavabit.com>

> On 02/20/2012 03:13 AM, robert bristow-johnson wrote:
>
>> On 2/19/12 8:53 PM, David L Wetzell wrote:
>>
>>> It seems quite a few election rules get quirky in one way or the other
>>> with a 3-way competitive election.
>>>
>>> That might be a point worth considering in the abstract in a paper or
>>> something.... why are 3-way single-winner elections quirky?
>>>
>>>
>> isn't it obvious?
>>
>> http://en.wikipedia.org/wiki/**Duverger%27s_law<http://en.wikipedia.org/wiki/Duverger%27s_law>
>>
>> to wit: Duverger suggests two reasons why single-member district
>> plurality voting systems favor a two party system. One is the result of
>> the "fusion" (or an alliance very like fusion) of the weak parties, and
>> the other is the "elimination" of weak parties by the voters, by which
>> he means that the voters gradually desert the weak parties on the
>> grounds that they have no chance of winning.
>>
>
> I'd call Duverger's law more an effect rather than a cause. The question
> in itself is why some methods seem to have a much harder time dealing with
> three-way (and n > 3 way) races than 2-candidate or 2.5 candidate races.
>
> I think the answer is simple enough:
>
> - When you have two candidates, there's one strategy-proof deterministic
> method, and its name is majority rule.
>
> - When you have two candidates and a bunch of tiny ones, it's usually
> pretty easy to know who the tiny ones are and remove them so they don't
> upset the outcome. (IRV does this)
>
> - But when you have three or more candidates, Arrow's impossibility
> theorem says that you can't have a ranked method that's independent of
> irrelevant alternatives. So no such method can be perfect. The concept of
> removing irrelevant candidates to reduce to majority rule no longer works,
> because you can't say "these candidates are obviously tiny and so should
> never win" when they're all strong contenders.
>
> 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.
>
> Rated method supporters, like Warren, would likely say that the rated
> methods are even better since they can pass IIA and so can scale to any
> number of candidates. They do pass IIA, but in exchange people have to be
> able to say how much they like a candidate rather than just
> better/worse-than, and it doesn't get around Gibbard-Satterthwaite.
>

Note that SODA avoids most pathologies up to 4 candidates. It does not, as
I've previously claimed, meet FBC even for three candidates*. But it is
monotonic, consistent, participation, IIA, and cloneproof up to 4
candidates, and it handles the chicken dilemma both honestly and
strategically. Of course, in order to accomplish this, you must give up
some freedom; in this case, the freedom to vote anything more expressive
than approval if you don't happen to agree with your favorite candidate's
preferences.

*There is an FBC fix for SODA which works for n candidates, is n^2
summable, and does not break the other properties given here; I'll write
more on that later, when I've had more time to think about it. Both the
problem and the fix are more theoretically than practically interesting; I
would never advise FBC strategy in SODA with anything less than perfect
polling.

>
> (Finally, just to preemptively head that off: just because no ranked
> method can meet IIA doesn't mean they are all equally bad. Just because
> there's no such thing as perpetual motion doesn't mean a modern steam
> turbine is just as inefficient as the aelopile. I don't think you think so,
> but certain others on the list might, so I'll make that clear.)

Agreed. In a similar sense, just because all rated methods ask for degrees
of preference and aren't 100% strategy-proof, doesn't mean that they are
all equally sensitive to strategies involving preference degrees. It's
clear that people on this list seem to have preferences for ranked or rated
ballot formats; but regardless of those preferences, I think both sides can
agree that a good method even of the "worse" ballot format is better than a
bad one with the "better" format.

Jameson
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20120223/09a0a16a/attachment-0004.htm>
```