[EM] average over time proportionality election method

[Raphael Ryan]

Jobst Heitzig <heitzig-j at web.de> wrote:

>I would instead find the following variant natural:
>
>Start with "excess" 0 for all voters. In each election, add to each
>voter's excess the fraction of the vote she received in that election
>(that is, a number between 0 and 1) to get the new excess. Elect the
>candidate whose so-computed excess is largest and subtract 1 from this
>voter's excess.
>
>In this way, a candidate's "excess" is exactly the number of times that
>candidate should have won by the proportionality requirement, minus the
>number of times the candidate did actually win. Since it is easy to see
>that these excesses sum up to 0 and are always between -1 and the number
>of candidates, it follows directly that in the long run the quotient
>between wins deserved and wins received converges exactly to 1 for each
>candidate, with the order of convergence being 1/#elections. And: at no
>time is there a candidate who won more than one time more often than she
>deserved!
>
>So, what was the motivation for your version?
>
>Yours, Jobst

The two reasons were that I didn't want voter turnout for the election that you vote on to matter as much and that I didn't want candidates to be able to end up with negative excess.

If each candidate is given a number from 0 to 1 depending on voter turnout, then a voter's vote in a high turnout election is worth more than in a low turnout election.  This is probably not really a big issue.  However, I like the idea of putting in a system that encourages candidates to get people to vote.  

What about setting the threshold to the average turnout over the last 10 elections.  This gives a reasonably stable threshold but still allows votes counted in a high turnout election to count for just as much as a low turnout election.  It does have the problem of negative excesses though.

Also, I am not so sure I like the idea of negative excesses.  I suggested in my first post that on resignation or death a candidate would be allowed to pass his excess on to another person.  There would be no equivalent for excess debt.  I guess it could be good for representative churn.  However, if there were 2 similar candidates, and one had a negative excess, there would be little point in voting for the one with excess debt as the other candidate would be worth more.  Also, a strategy to maximise seats would be to run a different candidate each time so that you win but end up in debt.  This would push up that viewpoints number of seats above average.

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