[EM] Centrist vs. non-Centrists (was A distance based method)

[Kristofer Munsterhjelm]

fsimmons at pcc.edu wrote:
> 
> ----- Original Message -----
> From: Kristofer Munsterhjelm 
> Date: Wednesday, July 13, 2011 2:12 pm
> Subject: Re: [EM] Centrist vs. non-Centrists (was A distance based method)
> To: fsimmons at pcc.edu
> Cc: Jameson Quinn , election-methods at lists.electorama.com

>> I think you said that these are related, even: that PR methods and 
>> stochastic single-winner methods are similar, seeking 
>> proportionality (the former in seats, the latter in time).
>>
> 
> Precisely. Andy Jennings was the one who hit on the key idea for
> constructing a lottery directly from a PR method; just do an N-winner
> PR method for large N, and treat the candidates like we treat parties
> in a party list method; keep the candidates in the running after they
> have already won a seat. Then the number of seats won by the
> candidate divided by the total number of seats is the candidate's
> probability in the lottery.

How would that work with combinatorial methods like PAV -- would you 
just clone each candidate a very large number of times? (I guess the 
question is academic because running a combinatorial method with a very 
large number of candidates would take too much time anyway.)

Also, is there any way of going in the reverse direction? I can see how 
one could turn the lottery into a party list PR allocation: just give 
each party a number of seats proportional to the chance they have in the 
lottery, resolving rounding problems by apportionment algorithm of 
choice. That works when the number of seats is large. There might be too 
little information to go to individual member multiwinner methods from a 
lottery, though.
Perhaps something to the effect of, when picking n members, just spin a 
roulette wheel with zones of size proportional to the chances in the 
lottery. If the ball lands on a zone of an already elected candidate, 
spin again, otherwise elect the candidate in question. Repeat until n 
candidates have been elected. That is nondeterministic, however.