[EM] Top-two Approval Pairwise Runoff (TTAPR)

[Kristofer Munsterhjelm]

On 11/10/2016 09:19 PM, Monkey Puzzle wrote:
> Re-weighted Approval Voting would lose summability, but it might be
> worth considering.
> 
> To fill out your proposal, the Approval winner and the reweighted
> approval winner after reweighting are matched using the original ballot
> rank preferences.
> 
> This amounts to a two-seat multiwinner primary (satisfying some PR rule)
> with pairwise instant runoff.
> 
> I worry that introducing multiwinner strategy would still lead to
> two-party factionalism.
> 
> Would this still satisfy IIA?

It should be summable with order n^2. For each candidate C, keep a
"C-penalized Approval count" that is counted as usual except that where
every ballot that approves of C only counts 1/2 (or 1/3), instead of a
full point, towards the candidates that ballot approves.

Then you use the unpenalized Approval count to determine the ordinary
Approval Winner. Suppose the winner is x. Then you look up the winner in
x's penalized Approval count (say it's y). Finally, you determine the
pairwise winner between x and y based on non-penalized pairwise preferences.

You can't do better than O(n^2) since you'd presumably need the full
pairwise matrix anyway, so as far as asymptotics go, including the n
C-penalized Approval counts is essentially free.

Or am I missing something?