Sunday, September 13, 2015

truncated proportional representation

It's been a while since I've had a voting systems post.  I'm going to propose a voting system for a small panel of people that will attempt to give voice to a somewhat broad range of opinions, but also allows blocks of voters to exclude candidates whom they really dislike.  The original hope was that this would lead to something of a consensus panel, though that probably really depends a bit on what sort of electorate you have; in some of my generic frameworks it leads to representation that is somewhat uniform but with extremes cut off; the relative distribution is probably typically smoother than that, with centrists disproportionately elected but even somewhat extreme characters occasionally elected, but this seems like a useful concise name for the time being.  This will be a dynamic voting system, which is to say it is to be used in an environment in which it is practical to allow voters to vote, for results to be tabulated, and for voters to change their votes.  Unlike my previous such system, this one may actually invalidate some previously valid votes along the way, such that voters are to a greater degree "forced" to change their votes.

To begin, allow each voter to vote for, against, or neutral on each candidate; each candidate accrues +5 for each vote in favor and -4 for each vote against.  This is generically strategically identical to approval voting, where voters (with probability 1 for certain assumptions) will never be neutral on a candidate.  However, after some period of time, a maximum number of votes for/against is imposed; at each point in time the maximum number of votes in favor of candidates is equal to the maximum number of votes against candidates, and that maximum is gradually reduced from infinite to 1.  Votes for more than one candidate or against more than one candidate will be dropped at some point before the final vote, but may help voters to coordinate on preferred candidates in the meantime.  At the end the panel consists of the top net vote recipients.

Note that one could well jump to the final vote; if an environment makes dynamic systems impractical but has other means of disseminating information, especially strategic information, the earlier phases may be less useful than impractical.  The dynamic mechanism is intended to increase the likelihood of convergence to a good equilibrium.

For the models I tend to use, if there are a lot more candidates than positions, many of those candidates will converge toward zero in both votes for and votes against.  Some smaller number of candidates, still typically bigger than the size of the ultimate panel by at least one candidate, will remain "relevant".  These candidates will tend to include a number of centrists receiving relatively few votes in favor but even fewer votes against, with a disproportionately smaller number of candidates who are more polarizing, with more votes in favor and more votes opposed.

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