[EM] How would you fix California's top two primary?

[C.Benham]

On 1/12/2017 4:19 PM, Rob Lanphier wrote:
> That goes a bit too far in the other direction. Consider a profile like
> this:
>
> 99: A B
>   1: C
>
> It seems pretty clear that the candidates to go to the second round
> should be A and B, but Approval-and-removal will pick either {A, C} or
> {B, C}. Of course, the real world probably won't have this kind of
> pathological election situation, but the bias is still there to a lesser
> degree: it disproportionately picks "extremists" for the second seat
> (i.e. candidates whose voters wouldn't vote for the first winner).

Presumably just as in normal (vote for one candidate) Top Two Runoff, 
there doesn't
have to be a second round.

If the most approved candidate A is approved on more than half the 
ballots then just
elect A.

Or you could reweight the ballots that supported A to something above 
zero, so that
a faction with a big enough majority is able to fill both runoff spots.

Chris


On 1/12/2017 4:19 PM, Rob Lanphier wrote:
> On Tue, Jan 10, 2017 at 3:56 PM, Kristofer Munsterhjelm
> <km_elmet at t-online.de> wrote:
>> On 01/10/2017 09:13 PM, Monkey Puzzle wrote:
>>> If Top Two is required, I would prefer Approval voting, then include the
>>> Approval winner (AW1), plus the approval winner after all AW1-approving
>>> ballots are removed.  This would be clone independent and would
>>> generally tend to include candidates from two different parties.  It is
>>> basically a 2-person multiwinner election using Approval reweighted voting.
>> That goes a bit too far in the other direction. Consider a profile like
>> this:
>>
>> 99: A B
>>   1: C
>>
>> It seems pretty clear that the candidates to go to the second round
>> should be A and B, but Approval-and-removal will pick either {A, C} or
>> {B, C}. Of course, the real world probably won't have this kind of
>> pathological election situation, but the bias is still there to a lesser
>> degree: it disproportionately picks "extremists" for the second seat
>> (i.e. candidates whose voters wouldn't vote for the first winner).
> This is an intriguing corner case.  Let's define a goal, and see if we
> can find a system that meets it.
>
> Possible constraints:
> *  An open primary that allows for two viable candidates to emerge
> *  A general election where the largest percentage possible has
> expressed approval of at least one candidate in the primary
>
> Approve-and-removal seems to result in the outcome you suggest.
> Worse, the lack of summability makes the method uncomfortably complex.
>
> It seems that it's worth exploring the full range:
> #1:
> 51: A B
> 49: C
>
> #2
> 70: A B
> 30: C
>
> #3:
> 99: A B
> 1: C
>
> Scenario #1 seems to clearly call for some form of
> approval-and-removal to ensure proportionality.  A vs C would be
> respectable choices for the general.
> Scenario #3 is an extreme case where a crackpot is able to gain the
> approval of a tiny slice of the electorate, and the general election
> seems a waste of time.  A vs B seems the best choice for the general.
>
> However, what about scenario #2?  Allowing A & B to move the general
> seems to marginalize the views of C in a way that seems like a
> disadvantage when considered against old-school, closed-primary FPTP.
>
> The percentage chosen in my scenario #2 was somewhat arbitrary, and
> was one that involved working within the two candidate general
> election constraint.  Perhaps that number is worth playing with.  Or,
> perhaps "number of candidates in the general election" is instead a
> number worth playing with.
>
>
>
>> If your complexity budget is so that you can't do anything more complex
>> than approval-and-remove, go with approval-and-remove because it's
>> better than just picking two Approval winners right out. But if you can,
>> the following might be better:
>>
>> A little bit more complex: First pick the Approval winner. Then randomly
>> remove ballots that approved of this winner until you've either removed
>> every ballot that approves of the winner, or 1/3 of the total number of
>> ballots. Then pick the Approval winner by the remaining ballots (ignore
>> the first winner if he's still number one).
>>
>> This is closer to Droop-proportional, but has a vote management
>> incentive. The following mitigates the vote management incentive, but is
>> more complex still:
>>
>> First pick the Approval winner W.
>> For each other candidate X:
>> Until you have removed 1/3 of the total number of ballots or every
>> ballot that approves W, first remove ballots that approve W but not X,
>> then ballots that approve both W and X. Count X's approval according to
>> the remaining ballots after removal, then put the ballots you removed
>> back in the pile so you can repeat for the next candidate.
>>
>> The candidate with the greatest thus counted approval score gets the
>> second seat in the runoff. (This is essentially the constraint method
>> with two seats and Approval.)
> This deserves more thought than I can give it right now.  It seems
> worth examining further.
>
> Rob
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