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

[Jameson Quinn]

2011/7/26 Jameson Quinn <jameson.quinn at gmail.com>

>
>
> 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.
>
>
I just realized that this method makes an interesting RRV-like method.
Instead of worrying about assigning ballots to candidates they approve, you
worry about keeping ballots that contain plenty of leftover approval for
later. I call it Remaining Ballot Weight. Dead-simple, two-step process:

Repeat:
1. Elect the highest range score
2. Reweight all ballots (from scratch) in proportion to their total range
score over remaining hopeful candidates.

On second thought, to prevent turkey-raising from being effective and safe,
you'd have to add a step 3, taken when necessary to maintain the proportion
(or, alternatively, the exponent?) between remaining seats and hopeful
candidates:

3. Eliminate the lowest range score.

Still, it's an unconventional system which I suspect could work very well
with either honest or rationally-strategic votes. I also suspect, though,
that humanly-irrational votes would tend to over-score/turkey-raise, so as
to "maintain their weights", and so it would in practice lead to DH3.

JQ
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