# [EM] RE: FBC comparison: WV, margins, MMPO, DMC

Fri Sep 9 19:18:01 PDT 2005

```On 9/9/05, Simmons, Forest <simmonfo at up.edu> wrote:

Adam and Kevin have argued that Winning Approval tends to encourage Favorite
> Betrayal more than Winning Votes does.
>
> But a thorough examination of the possibilities does not seem to support
> that view.

A "thorough examination" would really involve some sort of simulation or
aggregation of a whole host of reasonable scenarios; something neither you
nor I have done in any form. All we have are our gut instincts about the
likeliness of various scenarios, which disagree. Kevin has discussed running
a simulation to test this, which seems like a great idea.

When winning votes is used as a measure of defeat strength, you know that if
> compromise by strengthening that defeat. In order to do this, you have to

Let's examine the case you're hypothesizing here.

A priori, assume our sincere preference is A>C>B. You said that compromise
beats favorite, so C>A. Since compromise doesn't already win, we know B>C.
Since the case is trivial (and hopeless) if B is the Condorcet winner, we
assume the cycle A>B>C>A.

Since you state a need for favorite betrayal ("helping your compromise")
here, we can further assume that the weakest defeat is A>B, causing B to be
elected.

So strengthening C>A does nothing for our cause. What we actually need to do
is WEAKEN B>C or C>A, so that A>B is no longer the weakest defeat.

But a priori, C>B and A>C are our sincere preferences. We are already doing
everything in our power to weaken those defeats.

So order-reversal cannot help our case here. Winning votes is immune to this
particular favortie beytrayal scenario. Your scenario does not make sense,
as I understand it. Maybe I made a mistake in my analysis; if you believe
so, then please present an example.

Summary: This conversation shows that it would take a lot of confidence in a
> set of unlikely (but possible) conditions to entice a rational voter into
> Favorite Betrayal under DMC even if condition (3) is thought to be likely.
> Furthermore, if condition (3) is known to be false, then there is no
> Favorite Betrayal incentive at all.
>
> Does that help?

What would be more convincing to me would be to show a reasonable scenario
where wv has favorite betrayal incentive, but DMC does not. I believe I have
shown the opposite.
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