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<p>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:</p>
<p><br>
</p>
<p>1. Require each candidate to publicly rank all other candidates
in the race before the election.</p>
<p>2. Allow voters to rank <b>one or more </b>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).</p>
<p>3. Pick the group of candidates (equal to the number of open
positions) appearing on the largest number of <b>unique</b>
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.<br>
</p>
<p>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. <br>
</p>
<p>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.<br>
</p>
<p><br>
</p>
<p>As a brief explanation of each step, <br>
</p>
<p>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.<br>
</p>
<p>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).</p>
<p>3. Maximizes the number of people whose vote goes to good
candidate (good in the sense that the voter is content with the
result).</p>
<p>4. Minimizes votes "wasted" by padding someone's victory -- a
person with twice as many votes has twice the assets to wield.</p>
<p>5. Gives votes that would otherwise be wasted to the least
offensive candidate in the winning group.</p>
<p><br>
</p>
<p>One nice aspect is the lower bound -- where the number of winning
candidates equals just one -- is just the Approval winner.</p>
<p><br>
</p>
<p>Like I mentioned, just musing about things, though I would be
interested in other's thoughts.</p>
<p>Mike<br>
</p>
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