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

Adam Tarr ahtarr at gmail.com
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 
> your compromise does beat your favorite, then you can still help your 
> compromise by strengthening that defeat. In order to do this, you have to 
> rank your compromise strictly ahead of your favorite.

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 

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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