[EM] Juho--Why Largest-Remainder/Hamilton is unbiased

[MIKE OSSIPOFF]

I'll speak of it in terms of PR, because that's where LR is used. A party's 
remainder can be from 0 to almost 1, and, on average, it's .5  That means .5 
quotas of remainder for each party. That means .5 remainder seats per party. 
So, since remainders, in the long run, are randomly ordered, a party's 
expectation is half of a remainder seat  So, for instance, the party with 
4.5 quotas has an expectation of 4.5 seats. So, on average, seats per quota 
is the same for all the parties.

No doubt that isn't really a solid demonstration, but it's plausible.

Because I'm used to single-winner methods, where merit differences are 
drastic, maybe I'm a bit over-dramatic in my criticism of apportionment and 
PR methods, none of which are really bad. In particular, LR, being unbiased, 
would be fine, in spite of its game-of-chance component. I've enjoyed 
betting small amounts at the craps table. But never bet what you can't 
afford to lose. So, Juho, say your favorite party is proportionally 
qualified for one seat. LR might give it one, two, or zero seats. Do you 
really want to play double-or-nothing with your representation?

Mike Ossipoff

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