[EM] Re: Multiwinner Approval Strategy
MIKE OSSIPOFF
nkklrp at hotmail.com
Thu Feb 5 02:59:01 PST 2004
With 0-info it isn't as difficult to show that the 1-winner strategy is
good, in this case the above-mean strategy.
For 0-info, the slate approach isn't needed. The skates was just one way to
try to show that the better-than-expectation strategy is reasonable for
elections that are not 0-info.
If Pij is the probability that, if there are 2 candidates between whom my
vote for one and not the other can make or break a tie involving which will
beat the other out of being on the committee, then i & j will be those
candidates--then, just as in the 1-winner case, because it's 0-info, all the
Pij are the same and can be dropped.
Then the algebra is the same as in the 1-winner case, and leads to the
above-mean strategy of 0-info Approval
The only problem is that, as you mentioned, the actual outcomes in the
multilwinner are whole committees, and the utilitly of a whole committee
isn't just the sum of the utilities of its members, because, for instance,
if your faction has 5 of the 9 seats it has a majority, which is very
different from if it has only 4 of the 9 seats. But taking that into account
seems like it would be complicated. And if we ignore that problem, then the
above-mean strategy for 0-info is sound.
Perfect or not, the best strategy available is the one to use, and, at least
so far, for 0-info multiwinner Approval, the above-mean strategy is the best
strategy available.
Mike Ossipoff
_________________________________________________________________
High-speed users—be more efficient online with the new MSN Premium Internet
Software. http://join.msn.com/?pgmarket=en-us&page=byoa/prem&ST=1
More information about the Election-Methods
mailing list