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

[Jameson Quinn]

2011/7/24 Andy Jennings <elections at jenningsstory.com>

> On Thu, Jul 21, 2011 at 9:45 AM, Jameson Quinn <jameson.quinn at gmail.com>wrote:
>
>> So, here's the simpler procedure:
>>
>> While there are more uneliminated candidates than empty seats:
>>
>> Divide each ballot by the number of uneliminated candidates it approves
>> If there are any candidates with more than a Droop quota:
>>
>> Elect the one with the highest score (previously "unique ballots")
>> Discard a Droop quota of randomly-chosen ballots which approve the elected
>> candidate, starting with the ones delegated to that candidate
>> Assign that candidates pre-declared approvals on any undiscarded delegated
>> ballots for that candidate
>>
>> Otherwise:
>>
>> Eliminate the candidate with the lowest score
>> Assign that candidates pre-declared approvals on any delegated ballots for
>> that candidate
>>
>> Elect all remaining candidates to fill the seats.
>
>
>
> Okay, I really love how simple this is.  From the description, it sounds
> like it would be explainable and would work well.  I wonder how it does in
> simulations and if we can find any problematic scenarios.
>
> Questions:
> - Is there a "bullet vote but don't delegate" option like normal SODA?
>

Yes, but it's pretty useless. In general, your vote will be more likely to
be decisive in some context, the closer to half of the candidates you
approve. Voting for just one candidate is pretty unlikely to have any effect
on results.


>
> - 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. And in the single-winner case it amounts to a supermajority
requirement; and these don't have an illustrious history in my view.

(I suppose that you could have an explicit "tiebreaker representative", with
only half a vote. But that amounts to "same voting power as everyone else,
unless an odd number of people abstain", which is just silly.)

>
> - Without the delegation, is it the same as any other
> PR-with-approval-ballots method in existence?
>

I expect that non-delegated votes will be rarer than in plain SODA, for the
reasons I mentioned above relating to bullet votes. So it's not too
important. But without delegation, this method reduces to the same
approval-based method as two-rating-level AT-TV. This system is to me an
obvious case - it's the simplest form of sequential representative approval
voting - and so I would not be surprised to learn that someone has already
named it, but if so, I'm not aware of that. I guess I'd call it SRAV if it
needs a name, see previous sentence.


>
> 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.

JQ
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