[EM] Postscript: Bend it like Benham

[John B. Hodges]

(snip to this point)
I wrote:
New round. After counting first and second-place votes, B4 and B5 
exceed quota and tie for  first place, at 193 votes each. We give one 
seat to B4. Ballots of groups g, h, and i are marked as being worth 
0.1556886 of their previous value. That leaves group
f = 0.3041666   x 120 ballots = 36.5 votes total for the group
g = 0.0473552                 = 5.682624
h = 0.0473552                 = 5.682624
i = 0.1556886   x 120 ballots = 18.682632 votes total for the group
j = 0.0473552   x 120 ballots = 5.682624  votes total for the group

which totals to 72.230504 votes total remaining for the voters of 
party B. Add in the 400 of party A, ballots now total 472.23, new 
Droop quota is 158. (Odd. Perhaps multiplying fractions raises issues 
of precision? Or did I just make an error somewhere?)

At any rate, it's clear that the voters of party A will take the 
remaining two seats. So in this example at least, the algorithm gives 
the proper answer.
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Postscript: Yes, I made an error. Group j is still at 0.3041666 so it 
has 36.5 votes total for the group. Ballots now total 103.04788 for 
party B, 400 for party A, new Droop quota is 168. That much error I 
can accept from rounding.

The fact that party B has that many votes left after taking three 
seats makes me wonder if perhaps a larger quota should be used. 
Hare >= ideal quota >= Droop.
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John B. Hodges, jbhodges@  @usit.net
Do Justice, Love Mercy, and Be Irreverent.