[EM] PR-SODA? Try 2 (and 3)

[Jameson Quinn]

2011/7/25 Andy Jennings <elections at jenningsstory.com>

> Jameson Quinn wrote:
>
>> - Would it work just as well with the Hare quota?
>>>
>>
>> Yes, but see my other message about your median-based system. For
>> contentious elections, I prefer the Droop quota. With the Hare quota, the
>> last candidate elected is likely to have about half the support of all the
>> rest.
>>
>
> I don't think that's necessarily true.  It all depends how the voters are
> divided, how many candidates they approved, and the order in which they are
> eliminated.  If we're electing ten candidates, there's really no reason
> that, out of the last two-elevenths of the population, exactly 50% will be
> happy with the last candidate and 50% won't.  And I don't think we can
> decide beforehand that each candidate should represent one-eleventh of the
> population and one-eleventh of the population should be left unrepresented.
>
> Droop quota is natural in STV because it is the smallest number that can
> elect no more than the desired number of candidates.  With a cardinal method
> I think Droop is just arbitrary.  With one-winner approval voting, even 50%
> doesn't have any special significance.  We just take whoever is the
> candidate with the most approvals.
>
> I guess I prefer a method like Monroe, that tries to get as close to Hare
> as it can, and if not, it does the best it can.  Of course, it's not
> perfect...
>

I definitely like a method which, all else equal, maximizes the quota. That
is, it should generally have a quota of at least Droop, and up to Hare. But
the thing is that the more information there is on each ballot, the less
likely it is to be the case that all else really is equal. Pretty soon
maximizing the quota must balance against other concerns. In that case, I'd
be happy to give it some weight if possible, but I would be suspicious of a
method that reduces to a minority veto in the single-winner case.

>
>
>
>>  Suggestions:
>>> - When a candidate is elected and you need to discard ballots, you could
>>> specify a more detailed preference order:
>>> 1. Ballots which delegated to that candidate
>>> 2. Ballots which bullet voted that candidate and didn't delegate
>>> 3. Ballots which approved two candidates
>>> 4. Ballots which approved three candidates
>>> 5. Ballots which approved four candidates
>>> 6. And so on.
>>> This eliminates ballots first which approve fewer candidates.  You may
>>> still have to select randomly within these tiers, but it gives an incentive
>>> for people to approve more candidates, which helps the method work better.
>>>  Right?
>>>
>>
>> Well, up to a point. The problem would be if people approved a "no-hope"
>> candidate, just to puff up the number of approvals on their ballot. This is
>> a form of "Woodall free riding", and it could lead to DH3-type pathologies
>> in the worst case. I'd rather not go there.
>>
>
> Good point.  Although if there do happen to be any voters who bullet voted
> for that candidate but didn't delegate to him, then you should definitely
> eliminate those first (even before the delegated ones, I think).  Once that
> candidate is elected, ballots which don't approve any other candidates are
> pretty useless, so you might as well get rid of them.
>
> But after that, I can see why you would be reluctant to incentivize
> approving more candidates.
>
>
Here's an idea. When you have elected a candidate, choose which of their
ballots survive, not which are eliminated; and do so in proportion to the
number of remaining hopeful candidates approved per ballot. This naturally
eliminates bullet votes.

This would makes turkey-approval very dangerous; in the simplest analysis,
just as likely to backfire (which is very bad) as to serve (which is only a
little bit good). In fact, in a method like SODA-PR, which includes
elimination, that simplest-analysis/zero-information guess may be
(asymptotically close to) the best a strategic voter can do; so I would not
worry at all about this rule causing rational strategic over-approval in
such a method.

I wouldn't advocate this rule for SODA-PR, because I'm trying to keep that
system very simple. But it is a promising idea for systems which are not
prioritizing simplicity.

JQ
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