[EM] Tweaks to Asset Voting for multiwinner elections

[Michael Rouse]

Kicking around a few ideas here, but assuming you have a number of 
candidates running for a fixed but limited number of seats in a 
legislature, how about:


1. Require each candidate to publicly rank all other candidates in the 
race before the election.

2. Allow voters to rank *one or more *candidates in order of preference 
on their ballot (if you bother ranking someone it's assumed you are okay 
with electing them -- if you don't want someone elected, you don't rank 
them, kind of like in Approval).

3. Pick the group of candidates (equal to the number of open positions) 
appearing on the largest number of *unique* ballots. This is the most 
interesting step to me, since it seems like it would be the most 
computationally-intensive step. In the (probably) unusual case that more 
than one group has the same number of unique ballots, there are several 
easy tie-breakers, so I'll ignore it as a distraction for now.

4. Looking at each ballot, if one or more candidates ranked on it are in 
the winning group in step 3, the highest ranked winning candidate gets 
the asset.

5. If a ballot does not contain a candidate that is part of the winning 
group, look at the rank order of the top candidate on the ballot, and 
transfer the asset (votes) to the highest ranked person who is in the 
winning group.


As a brief explanation of each step,

1. Allows a complete ranking so no ballot is completely wasted. Plus, 
this information is useful in itself -- if a candidate ranks highly 
someone I detest, I can either not vote for them, or rank enough 
candidates so it's unlikely my vote will be transferred.

2. Allows voters to pick however many candidates without splitting their 
vote (some edge cases are possible, where a lower rank on a ballot could 
knock out a preferred candidate, which is why you don't rank someone 
unless you approve of them).

3. Maximizes the number of people whose vote goes to good candidate 
(good in the sense that the voter is content with the result).

4. Minimizes votes "wasted" by padding someone's victory -- a person 
with twice as many votes has twice the assets to wield.

5. Gives votes that would otherwise be wasted to the least offensive 
candidate in the winning group.


One nice aspect is the lower bound -- where the number of winning 
candidates equals just one -- is just the Approval winner.


Like I mentioned, just musing about things, though I would be interested 
in other's thoughts.

Mike

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