On Wed, Sep 16, 2009 at 11:45 AM, James Gilmour <[email protected]> wrote: >> In Meek, elected means that you have at least a Droop quota >> (and can have any "keep value" between zero and one) . > > This is confusingly expressed. It is impossible to be elected with a keep > value of zero.
The rule is that they can have a keep value in the range from zero to 1. Eliminated candidates have a keep value of zero and remaining/not elected/running candidates have a keep value of 1. For each ballot, a voting weight of 1 is given to the first choice. That candidate keeps a fraction of the voting weight received equal to his keep value and passes the rest on to the next choice and so on. What is nice is that if you multiply a candidate's keep value by a constant, then his vote total will also scale by the amount. This is because every piece of voting weight he receives is multiplied by his keep value. Thus if a candidate has more than a quota you can multiply his keep value by (Quota)/(His vote total) and he will automatically end up with exactly a quota, after that step. The vote weight that he lost is shared between all the other candidates. Thus the candidate's vote total drops to the quota, but all other candidates' totals increase or stay the same (if they were ranked higher on a ballot, their vote is not affected, and if they are lower on a ballot, they receive more vote weight from that ballot). Thus this operation will never move a candidate who has more than a quota to a total that is below the quota. If you do this over and over for all elected candidates, they will converge to a quota each (as each step decreases their keep value). There is a theorem that shows that this will always converge to the same final set of keep values. Once another candidate goes above the quota, he can also be designated as elected and have his keep value reduced too. If after the convergence completes, all the seats aren't filled, then the candidate with the fewest votes is eliminated and has his keep value set to zero. A more accurate rule is that if - the total surplus of all the elected candidates is -- greater than the difference between the 2 weakest candidates, and -- greater than the difference between the strongest unelected candidate and the quota then eliminate the lowest candidates Effectively, that means the surplus isn't enough to elect another candidate even if it all went to the strongest unelected candidate and it isn't enough to change the relative order of the bottom 2, then you can eliminate and there is no point in further convergence processing. The bottom 2 rule could also be changed so that the bottom N candidates can be eliminated if the sum of their votes and the surplus is less than that (N+1)th worst candidate (unless that would result in insufficient remaining candidates to fill all the seats). In New Zealand, convergence is consided to have happened when all elected candidates are within 10E-8 of a vote of the quota, rather than defining it in terms of it being impossible for any other candidate to be elected. ---- Election-Methods mailing list - see http://electorama.com/em for list info
