[EM] 'Strategies'

[Forest Simmons]

On Fri, 2 May 2003, [iso-8859-1] Kevin Venzke wrote:

> Forest,
>
> I didn't understand this.  Allow me to ask questions:
>
>  --- Forest Simmons <fsimmons at pcc.edu> a écrit : >
> > What if we changed this last step as follows?
> >
> > Elect THE CANDIDATE that is above the average rating (or ranking, if
> > ratings are not available) of the "finalists" on the greatest number of
> > ballots.
>
> Is "the candidate" one of the pair members?

No, that's why I say "provisional" below and put the word "finalist" in
quotes above.

>
> > In other words, consider the "PAIR" with greatest approval in the first
> > part as a pair of provisional finalists, and then in part two treat them
> > like equally ranked frontrunners in an approval election.
>
> I don't understand the circumstances resulting in the replacement of
> a provisional finalist.  Also, what do you mean by "treat them like
> equally ranked frontrunners in an approval election"?
>

Suppose that in an Approval election the two most popular candidates are
neck-to-neck in the polls. Which candidates would you approve?

If you don't vote at all then your expected utility is the average of
those two popular candidates. So if you do vote, and you want to raise
that expectation (however slightly), you should vote for all of the
candidates for whom your utility is above that expected utility.

This strategy doesn't necessarily increase the expected utility by the
greatest amount, but it comes close to maximizing the probability that the
winner utility with your vote will be higher than the winner utility
without your vote.

Now back to my suggested modification of the strong FBC method:

(1) Leave the first part unchanged: use approval of PAIRS to find a
candidate pair for use in the second part.

(2) In this part instead of doing a simple head-to-head comparison to see
which member of the PAIR is the winner, we make a different use of the
pair found in part (1) in which some other candidate might be the winner.

The pair of candidates is treated like the two neck-to-neck frontrunners
in an approval race discussed above, i.e. on each ballot their average
utility (Cardinal Rating) is calculated and used as an approval cutoff.

The Approval winner (based on these approval cutoffs) wins the election.

This modified method would satisfy the Pareto criterion, whereas the
original doesn't, since it is possible that both members of the approved
PAIR are beaten unanimously by some third candidate.


Forest