[email protected] 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: [email protected]
Cc: Jameson Quinn , [email protected]
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.
----
Election-Methods mailing list - see http://electorama.com/em for list info
