[EM] Participation & SARC

[MIKE OSSIPOFF]

> > You said the voters were sophisticated, but you didn't say they
> > were perfectly informed. But if that's added then what you said
> > matches what I'd heard.
>
>By definition, a "sophisticated" voter
>(1) is perfectly informed about the sincere opinions of the other
>     voters and
>(2) takes the sincere opinions, the possible strategies and the
>     possible counterstrategies of the other voters into consideration
>     when he decides how to vote so that his own utility expectation
>     is maximized.

Ok, I didn't know that definition.

> > Of course SARC would be unmeetable too if it were about worsening
> > one's outcome, rather than just defeating one's favorite or
> > electing one's last choice.
>

>If you want to say that Approval Voting guarantees that if the
>voters are sophisticated then a like-minded group cannot change
>the winner from their favorite to a different candidate or from
>a different candidate to their least prefered candidate then I
>have to answer: I see no justification for this claim. Could
>you please give a heuristic or a proof of this claim?

Ok, in other words, demonstrate that Approval meets SARC.
First of all, though, SARC doesn't require that voters be
sophisticated, as you defined the term. All that's assumed is
that they vote in a way that could, with some configuration of
the other people's votes, produce an outcome that they like better
than every outcome they could get by any other way of voting.

In Approval, there's never a reason to not vote for your favorite.
And, in Approval, there's never a reason to vote for your last
choice. The only reason to not vote for someone is that you don't
want to help them beat someone whom you like more, agreed? Then
you could never have a reason to not vote for your favorite.
The only reason to vote for someone is to help them beat someone
whom you like less. Therefore there's never a reason to vote for
your last choice. So, whatever your strategy is, it's a sure thing
that, if you want to get your best result, you'll vote for your
favorite, but not for your last choice.

If you vote for your favorite, and you vote also for someone whom
you like less, then you aren't changing the order relation of their
vote-totals. If one of them would have gotten more votes than the
other without you voting, that same one will have more votes than
the other if you vote. So your participation can't make your
favorite lose.

If you don't vote for your last choice, and you also don't vote
for some candidate whom you like better than him, then you aren't
affecting the order relation of their vote totals. So, likewise,
when you don't vote for your last choice, there's no way that
your participation could cause your last choice to win if he
wouldn't have otherwise.

If you vote as SARC assumes, you'll vote for your favorite, because
not voting for your favorite could never give a better result
than voting for your favorite. Likewise, you wont' vote for your
last choice, because voting for your last choice could never give
a better result than not voting for him. So when you vote as SARC
assumes, you'll never make your favorite lose or make your last
choice win, if that wouldn't have happened without your
participation. But that's only true with Approval. No other method
meets SARC.

Mike Ossipoff

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