[EM] "FBC vs Condorcet's Criterion"

[Kristofer Munsterhjelm]

On 05/08/2012 08:46 PM, Michael Ossipoff wrote:
> Since Richard wants to make a "which one wins" comparison between
> FBC and Condorcet's Criterion (CC), then I'll remind him that, when
> FBC failure sufficiently makes its problem, CC compiance becomes
> quite meaningless and valueless. And there is good reason to believe,
> as described in my previous post, that Condorcet's FBC failure _will_
> fully make its problem in our public elections.

I'll get to your larger post later, but it seems what need isn't FBC as 
such, but rather u/a FBC.

Here's a Condorcet method I think meets u/a FBC: Each voter submits a 
ranked ballot with an Approval cutoff. The most Approved candidate in 
the Smith set wins.

If everybody ranks Approval style, then this becomes Approval. So let's 
see if there's any reason to favorite betray instead of ranking Approval 
style.

If there is no cycle, then you can't make an acceptable have a greater 
chance of winning over an unacceptable by ranking Compromise over 
Favorite versus ranking Favorite over Compromise.

If there's a cycle and Favorite is in the Smith set, but Compromise is 
not, then the only reason for getting Compromise into the Smith set 
would be to defend against an unacceptable candidate winning. However, 
you can do that by just voting Approval style. Since Smith set members 
are "only beaten by other Smith set members", Favorite vs Compromise 
doesn't enter into it as long as you put both above the cutoff and all 
the unacceptables below it.

If there's a cycle and Compromise is in the Smith set, but Favorite is 
not, then because this is an u/a election, it doesn't matter. You'll 
still get an acceptable.

If there's a cycle and neither Compromise nor Favorite is in the Smith 
set, then voting Approval style will make Compromise and Favorite both 
maximally work to push the unacceptables out of the Smith set.

Hence it seems that the method above meets u/a FBC. By the time people 
get past u/a, they'll no longer be overcompromising and so "proper" FBC 
failure doesn't matter. So Condorcet can meet u/a FBC.

I'm not saying Smith,Approval is necessarily a good method, but I only 
have to show a single method to disprove that u/a FBC and Condorcet is 
incompatible.