# [EM] Power of votes with approval

Elisabeth Varin/Stephane Rouillon stephane.rouillon at sympatico.ca
Sun Jan 5 20:40:58 PST 2003

```Bart --,

I do not know why but I had previously some kind
of engineer reflex: I was normalizing the sum of
utilities to 1. Even worse, I was equally spreading
candidates like .4 , .3 , .2 and .1 . So your explanation ended up to
my previous strategy for approval.

I was doing that because of the differential analysis
I usually do about any decision. what is common to both
case does not matter. So, if two candidates were great,
but only differ on a very small issue, I would place the one I
prefer with a utility of 1 and the other with 0.
This works very well with two candidates.
Now suppose we add a third candidate, the most stupid
person I ever listened to. Now the fair utility of the two good guys
could be 100 and 97 compared to mister 3. But my normalization
step would produce value of .5 , .485 and .015.

I realize now that the normalization is OK,
it is the equal spreading which is not. And it has consequences
only for three or more candidates.
Thanks, what follows is exactly what I would do now...

Bart Ingles a écrit :

> Stephane, you wrote:
> > For Approval, this is how I would do, I am not sure it is optimal.
> > 1) I would cut all candidates into two equal groups the ones I like, the
> > ones I do not.
> > Without poll information, I believe it is the vote that would optimize
> > my voting power...
>
> You seem to be equating 'voting power' with 'number of distinctions
> drawn between approved and unapproved candidates'.  This might be true
> when averaged across the universe of election possibilities, but not
> necessarily for a given election unless the mean utility for all
> candidates just happens to coincide with the median utility from your
> point of view.
>
> A better definition of voting power might be "the ability to influence
> the outcome of an election in a preferred direction."  Voting for
> exactly half of the candidates may not do this, even in the absence of
> polling information.
>
> cardinal ratings (as an approximation of utility) for these candidates
> are 100, 8, 6, 4, 2, and 0 respectively.  The average rating for these
> candidates is 20.  Since only candidate A is rated above the average,
> you should vote only for A.
>
> Using the strategy you proposed above would require you to vote ABC,
> which would merely increase the likelihood of electing someone you
> strongly dislike (B or C).  In other words, the expected outcome without
> your vote is 20.  Voting for candidates rated less than 20 can only
> worsen the outcome.
>
> Similarly, if your sincere cardinal ratings for A>B>C>D>E>F are 100, 98,
> 96, 94, 92, 0, you should vote for ABCDE, since only candidate F is
> worse than the average rating of 80.
>
> > 2) If I can get some poll information I judge reliable enough:
> > out of my desired candidates, I would vote for the one I prefer the most
> > and would approve too all my desired candidates that obtain a better
> > position
> > according to the poll.
> > Example: sincere preferences A>B>C>D | E>F>G>H
> > No poll: vote ABCD.
> > The poll: D>H>B>A>C>G>F>E. I would vote ABD.
>
> Again, optimal strategy would depend on your sincere ratings for the
> candidates, and would require more polling information than how the
> candidates were ranked in the poll.
>
> For example, suppose your ratings for the candidates are 100, 98, 12,
> 10, 8, 4, 2, 0, and the polls (in addition to the order shown above)
> also show that D, H, and B are in a fairly close 3-way contest, well
> ahead of the remaining candidates.  In that case, a vote for AB would be
> optimal.
>
> A simple, close-to-optimal strategy would be to first identify two or
> more frontrunners, if possible.  I would then determine the average
> rating of these frontrunners (36 being the average for D, H, and B in
> the above example) and vote only for candidates whom I rate higher than
> that average.
>
> Bart
>
> ----