[EM] Re Meek and Newland-Britton

[Dgamble997 at aol.com]

James Armytage-Green wrote:

" However, I'm left with another question... What would happen in Meek if C
and D's votes were more evenly-distributed, so that no one had a surplus
right away... like this for example:
>

61: A
60: A>B
30: C>D
29: D>C

    After round one, if you recalculated the quota based on the amount of
exhausted (fractional) votes, then wouldn't you also recalculate the
retention fraction and the transfer fraction for A? That is, instead of
the retention fraction being 60 / 121, wouldn't it now be 49.752 / 121?
And if so, wouldn't that increase the amount of exhausted votes, which
would lower the quota, which would lower A's retention fraction, which
would increase the amount of exhausted votes, and so on? When would this
end? Does it just end when the quota drops below the amount of votes held
by one of the other candidates?"


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).

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.

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.

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.

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. 

David Gamble




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