[EM] math 103 website - Arrow & Saari

Bart Ingles bartman at netgate.net
Tue Jan 8 23:47:25 PST 2002

```My impression was that he was talking about a given set of preference
orders always mapping to the same winner.  Saari seemed to find it
objectionable that individuals preferring A to B to C might not all vote
the same way -- i.e. that some would vote for A alone, while others
would vote for both A and B -- and that the outcome depends on such
factors as strategy and intensity.

As though it doesn't anyway, regardless of what system you use.

I don't know who would consider it important to find out preference
orders given the actual ballots, but to a certain extent this is
possible with approval voting.  For example, if an individual votes for
a frontrunner as well as a minor candidate, he probably preferred the
minor candidate first, and included the frontrunner as a backup choice.
If he had preferred the frontrunner, there would have been no incentive
to vote for a second candidate.

Bart

Steve Barney wrote:
>
> Bart:
>
> What is the definition of a "deterministic" voting system, as Saari apparently
> uses the term?
>
> I thought that it had something to do with being able to determine what the
> ballots said, from the final tally. I guess that the Borda Count is more
> "determinant" than the Plurality Vote that way, as you can't tell what the 2nd,
> 3rd, etc., preferences were at all. Perhaps the Approval Vote is similar to the
> Plurality Vote to the extent that voters choose to bullet vote, or because you
> cannot tell which approved candidates were more preferred than others. With the
> BC you can always tell (correct me if I'm wrong) how many first place votes,
> second place votes, etc., a candidate got, if you have the final tally and the
> number of ballots (assuming no truncated ballots).
>
> Steve Barney
>
> --- In election-methods-list at y..., Bart Ingles <bartman at n...> wrote:
> >
> [...]
> > Of course, how many voters would be willing to strategize in such a way
> > depends on the sophisication of the voters, and on the actual
> > intensities involved, so the actual outcome would be difficult to
> > predict.  So much for Borda being a deterministic voting system (one of
> > Saari's justifications for preferring Borda over approval voting).
> >
> > In this case, behavior under approval voting should be much more
> > predictable, since most or all of the voters could be expected to bullet
> > vote.
> >
> > Bart
>
> =====
> "Democracy"?: