[EM] Gervase Lam, ratings reply

[Brian Olson]

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/