[EM] Doesn't matter what preference means, Markus

[Markus Schulze]

Dear Mike,

you wrote (29 Jan 2002):
> Blake wrote to Mike (28 Jan 2002):
> > Having said all that, I'll get to how I interpret P&P. P&P talk about
> > ballots, and criteria and methods based on those ballots. By ballots
> > I could just as easily say preference orders.
>
> You could just as well say egg-salad sandwiches too. But when
> we say "I prefer chocolate to vanilla," we mean that I like chocolate
> better than vanilla. That's what preference means. If you want to
> call ballots preferences, than that must be stated, because that
> isn't what preference means, unless you say that that's what you're.

When I want to buy ice-cream for you and you say that you prefer
chocolate to vanilla, then I only know _that you say_ that you prefer
chocolate to vanilla. But I don't know whether your statement is sincere
or insincere. I will have to make the purchase without knowing whether
your statement is correct. However, when I make the decision without
knowing whether your statement is correct, then this doesn't mean
that I assume that your statement is correct. It simply means that
the question whether your statement is correct is of no concern for
me.

Similarily, an election method can only ask about your opinion.
And when you answer that you prefer candidate X to candidate Y,
then the election method has to make its decision without
knowing whether your statement is correct. Actually, whether
your statement is correct is of no concern for the election
method.

******

You wrote (29 Jan 2002):
> If they're talking about the candidate-orderings that are available
> to the count, then they're talking about ballots, unless the count
> is done by a psychic or that oracle that some here like to refer to
> sometimes. Thank you Blake for clarifying that they mean "ballot"
> when they say "preferences". It's sloppy, but at least we now know
> what they mean.

Due to Pattanaik and Peleg, the input of a decision scheme is a set of
linear orders. Of course, when you assume that the voters can rank the
candidates on the ballot, then you can simply say that the input of a
decision scheme is a set of ballots.

Markus Schulze