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

[Andy Jennings]

Jameson Quinn wrote:
>
>   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.
>

You're still choosing randomly, right?  So the probability of surviving will
be proportional to the number of remaining hopeful candidates left on that
ballot.

I like it.  (I'm still kind of wary of non-deterministic methods, though.
 Not for myself, actually, but for selling them to the public.)

- Andy
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