[EM] math 103 website - Arrow & Saari

Forest Simmons fsimmons at pcc.edu
Mon Jan 7 18:16:06 PST 2002

On Mon, 7 Jan 2002, Steve Barney wrote:

> Bart:
> What is the definition of a "deterministic" voting system, as Saari apparently
> uses the term?

I think in this context it refers to how well you can predict the ballots
from the utilities.  As Bart says, given these extreme utilities it is
easier to predict the Approval ballots than to predict the Borda ballots. 

> 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).

Here are two distinct elections with the same number of ballots and the
same final Borda talleys for each candidate:

Election 1:


Election 2:



> 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
> =====
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