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

[Rob Lanphier]

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