On May 22, 2004, at 5:00 PM, Adam H Tarr wrote:
Some rated systems behave differently if signed numbers are used or if positive-only numbers are used.
when?
Combinations of normalization and shifting can alter a vote such that you can't reverse the process and get the original vote back again.
Shift, then normalize, and if you try to shift back the vote will be different.
So, this is why it's important to decide whether one has a signed range or a positive-only range. Shifting between them isn't necessarily a lossless operation.
Also, stretching a vote, so that it's minimum rating is the acceptable minimum AND it's maximum rating is the acceptable maximum, an operation which involves a shift, subtly changes the vote.
Maximizing a vote, a pure multiplication so that it's minimum rating is the acceptable minimum OR it's maximum rating is the acceptable maximum, is perhaps a 'safer' or 'more pure' operation on the vote.
Normalizing, setting the total voting power to a standard amount is also a multiplication only operation, and thus 'safe'.
It may yet be that "stretching" the ratings of a vote is the right strategy, and it would be "fair" to put a stretching filter on the input to a Cardinal Ratings variation so that each voter gets their vote changed "for their own good" to follow an optimal strategy.
But, I'm not here talking about any specific ratings based election method or its strategy.
My simulator has a mode where the population is split up into equal sized chunks and each uses a different strategy to modify their votes. I count an Election Method as good when the group that votes honestly has the highest average happiness (over several thousand simulated elections).
Brian Olson http://bolson.org/
---- Election-methods mailing list - see http://electorama.com/em for list info
