[EM] (no subject)

[Russ Paielli]

MIKE OSSIPOFF nkklrp-at-hotmail.com |EMlist| wrote:
> 
> Forest was the first to mention the Better-Than-Expectation strategy for 
> Approval--the strategy whereby a voter votes for the candidates who are 
> better than his/her expectation for the election, better than the value 
> of the election. So the voter using that strategy votes for a candidate 
> if that candidate is so good that s/he would rather have that candidate 
> in office than hold the election.

You never answered my question about what it would mean to not "hold the 
election." Does that mean the incumbent stays in office, or does it mean 
that the government ends and anarchy begins?

> One can come up with situations in which that isn´t optimal. But it 
> maximizes one´s utility expectation if certain approximations or 
> assumptions are made. One usual assumption is that there are so many 
> voters that one´s own ballot won´t change the probabilities 
> significantly. By one approach, it´s also necessary to assume that the 
> voters are so numerous that ties & near-ties will have only 2 members, 
> and that Weber´s Pij = Wi*Wj, the product of the win-probabilities of i 
> & j.

That's called dropping second-order terms, the product of two small 
quantities.

> But, instead of the last 2 assumptions named in the previous paragraph, 
> it would also be enough to assume that when your vote for a candidate 
> increases his win-probability, it decreases everyone else´s 
> win-probability by a uniform factor.
> 
> That´s the approach that Russ used, except that he didn´t state that 
> assumption.

Yes I did. I said that the other winning probability ratios should 
remain unchanged.

> Russ, don´t take any of this as criticism--I´m just telling you so that 
> you´ll know.
> In your derivation-description, you stated the goal "to keep the sum of 
> all probabilities at unity without changing the probability ratios." But 
> keeping the other candidates win-probabilities in the same ratios isn´t 
> a goal of the derivation; it´s an  assumption by which 
> Better-Than-Expectation maximizes the voter´s utility expectation. It´s 
> important to state assumptions, and that particular assumption is really 
> key to the derivation.

Agreed. That *is* an assumption, and it could be stated more explicitly.

And thanks for the alternative derivation. Both derivations really just 
corroborate common sense.