<HTML><FONT FACE=arial,helvetica><HTML><FONT SIZE=2 PTSIZE=10 FAMILY="SANSSERIF" FACE="Arial" LANG="0">James Armytage-Green wrote:<BR>
<BR>
" However, I'm left with another question... What would happen in Meek if C<BR>
and D's votes were more evenly-distributed, so that no one had a surplus<BR>
right away... like this for example:<BR>
><BR>
<BR>
61: A<BR>
60: A>B<BR>
30: C>D<BR>
29: D>C<BR>
<BR>
After round one, if you recalculated the quota based on the amount of<BR>
exhausted (fractional) votes, then wouldn't you also recalculate the<BR>
retention fraction and the transfer fraction for A? That is, instead of<BR>
the retention fraction being 60 / 121, wouldn't it now be 49.752 / 121?<BR>
And if so, wouldn't that increase the amount of exhausted votes, which<BR>
would lower the quota, which would lower A's retention fraction, which<BR>
would increase the amount of exhausted votes, and so on? When would this<BR>
end? Does it just end when the quota drops below the amount of votes held<BR>
by one of the other candidates?"<BR>
<BR>
<BR>
The retention factor (or keep value) for A at the second stage of the count is 60/121=0.496 giving A 60.016 votes at stage 2 and 30.744 non-transferable votes ( 0.504 of the 61 A votes).<BR>
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The quota is then reduced to (180 - 30.744)/3 = 49.752 for the 3rd stage. A's keep value is then recalculated as 0.496 x (49.752/60.016) = 0.412 giving A 49.852 votes. The number of non-transferrable votes is now 0.588 x 61 = 35.868.<BR>
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For the 4th stage the quota is reduced to (180 - 35.868)/3 = 48.044. A's keep value is then recalculated as 0.412 x (48.044/49.852) = 0.398 giving A 48.158 votes.<BR>
<BR>
To cut a very long story (and set of calculations short) each time A's keep value and the quota are recalculated they reduce by a smaller amount ( A's keep value at the successive stages of the count is 1, 0.496, 0.412, 0.398, ...... the quota at successive stages of the count is 60, 49.852, 48.158, 47.76, ......). These number series finally converge and stabilise giving a fixed, stable value for the keep value and the quota. Keep values and the quota do not go on reducing forever.<BR>
<BR>
For all practical purposes as soon as the surplus to be transferred is less than the difference in votes between the candidate with lowest vote and the candidate with 2nd lowest vote the candidate with the lowest vote can be eliminated. <BR>
<BR>
David Gamble<BR>
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