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

[Andy Jennings]

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...



>  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.

- Andy
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