[Election-Methods] Spearman-unbiased apportionment

[Steve Eppley]

Peter Barath wrote:
-snip-
> ...      I am reminded of a conversation
> many years ago. I don't remember who mentioned, without any
> practical reference, only as a mathemathical curiosity, that
> if we are to elect numbers of representatives in differently
> populated districts, the "true" method is when the number of
> the representatives is proportional to the square root of
> the population.
>
> As far as I can remember, it was something about the
> probability of being a pivotal voter. (Which also gets
> a big role in the theorization of the Clarke-tax.)
>
> I'm not sure if I would be able to check it, but somehow
> my feeling is that it can easily be well grounded.
>
> At least if we think of the representatives as clones who
> always vote the same way. If there are parties and the
> representatives are party-proportional, this remark seems
> invalid to me.
>
> Peter Barath
>
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>   

If my recollection is correct, there is a related argument in Judith 
Best's book "In Defense Of The Electoral College."  One of her 
conclusions was that, even though small states are represented more than 
proportionally in the Electoral College, contrary to appearances large 
states are not underrepresented in it.

Salvador Barbera and Matt Jackson wrote a paper published in 2006 titled 
"On the Weights of Nations: Assigning Voting Weights in a Heterogeneous 
Union" (abstract at <http://ideas.repec.org/p/clt/sswopa/1196.html>) 
that I haven't read but which might also be relevant.

--Steve