[EM] SARC answers, continued

[MIKE OSSIPOFF]

Dear Markus--

I'm sorry--when I replied to this letter yesterday, I assumed that
everything you said was in regard to the SARC example, and that
you were reading those other issues into the purpose of SARC,
which I of course denied. What I missed was that you were actually
speaking more generally, about how well SARC agrees with
larger or more general issues. I'll answer better this time,
but I believe that it isn't reasonable to judge SARC by
those other issues. The undesirability of defeating your favorite
or electing your last choice is surely enough to justify SARC,
without recourse to larger issues.

Anyway, I'd like to answer your questions again, differently.

First, though, I realize now that Nader/Gore won't be a SARC
badexample, because the number of people voting insincerely for
Gore is so great that if they stayed home that wouldn't leave
enough Nader voters to make Nader win. SARC still measures something
meaningful. And, with people reversing preferences in order to
get a better result, FBC will be violated for sure, as it always
is in our elections. And the reversal of preferences by members
of the Gore>Bush majority, in order to defeat Bush makes it
a demonstration of WDSC failure too. But it would be nice to
have a criterion about election-giveaway, but whose failure is
demonstrated in our U.S. partisan elections, like Nader/Gore/Bush.

Well, it's obvious that an election can be given away when you
vote someone over your favorite, and that when you do that
you're also voting a less-liked candidate over a more-liked one,
and so maybe FBC & WDSC are enough to show that problem in U.S.
elections.

Also, in my example, I didn't say anything about why, for people
whose sincere ranking is ABC, voting BAC in Borda is undominated.
It's undominated because there's a configuration of the other
voters for which that is the best way of voting. Here's such
a configuration of the other voters:

100: CBA
98: BCA

C wins. If 2 voters arrive and vote BCA, B wins. For those 2
voters, no other way of voting gives as good a result as BCA,
and so, for them (whose sincere ranking is ABC), BCA isn't
dominated by any other way of voting.

I forgot to say that there are 2 new voters, who vote the same
and share the same preferences.

It's reasonable that the meaning of a dominated strategy is the
same for a group of same-voting voters as for one voter.

Now, my answers:


    > Your sincere ranking is ABC
    >
    > 100 voters: ABC
    > 99 voters: BAC
    >
    > Without you, A wins.
    >
    > Then you show up, and, believing that B needs your vote against C,
    > you vote BAC. Now B wins. You've defeated your favorite by voting
    > an undefeated strategy.

    How do you interpret this example showing Borda violates SARC?

To that question my answer is the same: Whenever a same-voting
group of voters who share the same preferences vote an
undominated strategy, and thereby make their favorite lose or
their last choice win, when that wouldn't have happened had they
not showed up & voted, that violates SARC, because that's what
SARC says shouldn't happen.


    Do you say "It is a problem that this additional voter is punished
    for showing up and using an offensive strategy. An election method

Though I don't believe that pair of voters (I meant to say that
it's a pair of voters) voted an offensive strategy, no I don't
consider it a problem if offensive strategy is punished. That's
one thing that I like about Condorcet & Schulze, for instance,
the way they punish offensive strategy.





[Do I believe that an election method...]

    should guarantee that a given voter never worsens the result of
    the elections (due to his sincere preferences) by showing up
    independently on whether this voter votes sincerely or uses a
    defensive strategy or uses an offensive strategy."? Or do you

First of all, you know that goal is unattainable. Would I want
it if it were attainable? I don't know. Obviously new-voter
criteria don't tell the whole story about defensive strategy
hurting the voter's own interest, and I wouldn't want that
goal you describe if it would help offensive strategizers more
than people who are considering or using defensive strategy.
Fortunately it's a moot point, since it's an unattainable goal.

Of course, with the 1 method that meets SARC, offensive strategy
is impossible anyway. Do you know of any method whose only SARC
violation happens to offensive strategizers only?

[Do I...]


    say "It is not a problem that this additional voter is punished
    for showing up and using an offensive strategy. The fact that a

Though I don't agree that that pair of voters used offensive
strategy, it would not be a problem if offensive strategy is
punished. As I said, that's something that I like about Condorcet,
as compared to other pairwise-count methods, such as Tideman(m).

[The fact that a...]

    given voter can worsen the result of the elections (due to his
    sincere preferences) by showing up and using an offensive strategy
    deters this voter from using an offensive strategy."?

I agree that when a voter can worsen the outcome for himself by
using an offensive strategy, that deters offensive strategy.
But, as I said, with Approval, the only method that meets SARC,
there's no offensive strategy to deter, since offensive strategy
is impossible and has no meaning in Approval.

Can you show me a method whose only SARC violation is one which
punishes offensive strategy?

Mike Ossipoff



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