[EM] SARC definition improvement

[Markus Schulze]

Dear Mike,

you wrote (2 Sep 2000):
> In my preliminary reply I agreed that that strategy is "offensive"
> in another sense--aesthetically offensive, or offensively
> ill-advised, and something that tends to elect an offensive
> person.
>
> But I don't agree that it's offensive strategy in the sense that
> you were using the term in your letter, and in the sense that
> we here use the term "offensive strategy".
>
> You say that strategy is offensive if it tries to get a different
> result than the all-sincere result. I can't tell you how you
> should define "offensive" & "defensive". But "offensive" implies
> that someone is being offended against, someone with a rightful
> win. Or some rightful result is being offended against. Do you
> believe that Plurality's result is rightful when everyone votes
> sincerely and a sincere CW loses? Because if that isn't a
> rightful result, it doesn't sound convincing to say that
> strategy to elect the sincere CW is "offensive strategy".
>
> I claim that my definition of defensive strategy is more in
> keeping with what we'd agree is a rightful or wrongful result.
>
> Strategy intended to gain a result that a majority wants, or
> to protect the win of a sincere CW is what I mean by defensive
> strategy.
>
> Strategy intended to change the victory from a not-majority-defeated
> candidate to a majority defeated candidate, or to take the
> win away from a sincere CW is what I'd call offensive strategy.
>
> As for what I mean by "...that a majority wants":
>
> A majority has the power to gain any result it wants. It has
> the power to elect someone if a majority wants to elect him.
> It has the power to prevent the election of someone whom a
> majority want to prevent the election of.
>
> If a majority all want a certain candidate to win, they don't
> need strategy with any of the methods being proposed here.
> Probably not with any method other than Borda. They merely all
> vote him as favorite.
>
> The problem is when all that a certain majority agrees on is that
> there's someone whom they don't want to elect. In that case,
> with most methods, some sort of strategy is needed to ensure that
> that person won't win. The majority defensive strategy criteria
> are explicitly about that.
>
> Now, I realize that the only time you're sure you want someone
> to win is if they're your favorite, and the only time you're
> sure you don't want someone to win is if they're your last choice
> (because if it were him or someone you like even less, you'd rather
> he win). But still, the voting of LO2E voters is intended to make
> someone lose. The LO2E voter is more interested in making a certain
> candidate lose than he is in electing the one whom he would mose
> like to elect. So I feel that it's important to deal with what
> people have to do to make someone lose, which is what the LO2E
> voter insists on doing.
>
> So I feel that majority will, or sincere CW status, is more
> justifiably something for defining "offensive" & "defensive" by
> than what some bad method would do if everyone voted sincerely.
>
> Does the will of the majority or the sincere CW's right to win
> count for less to you than what Plurality would do under sincere
> voting?

A FPP supporter will claim that the FPP winner is the best guess for
best candidate. A Borda supporter will claim that the Borda winner
is the best guess for best candidate. A IRV supporter will claim
that the IRV winner is the best guess for best candidate.

When you now say that a sincere Condorcet winner is a rightful
winner and that therefore a strategy to elect a sincere Condorcet
winner is defensive (even if the used election method doesn't meet
the Condorcet criterion) and should never be punished, then you
judge the heuristic of one election method by demonstrating that
if you use the heuristic of another election method then this
election method behaves wrongfully.

It is clear that you must not criticize election method X for not
being election method Y. When the supporters of a given election
method don't consider the Condorcet criterion to be important, then
it doesn't make any sense to say that it is a problem when some
voters are punished for voting insincerely to elect a sincere
Condorcet winner.

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de