[EM] "FBC vs Condorcet's Criterion"

[Kevin Venzke]

Hi Kristofer,


De : Kristofer Munsterhjelm <km_elmet at lavabit.com>
>À : Michael Ossipoff <email9648742 at gmail.com> 
>Cc : election-methods at electorama.com 
>Envoyé le : Mercredi 9 mai 2012 9h54
>Objet : Re: [EM] "FBC vs Condorcet's Criterion"
>
>
>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.
>
Did you cover the scenario where both Favorite and Compromise are in the Smith set? If not, is there some reason
for u/a FBC (whose definition I don't actually know) why this scenario doesn't matter?

In general the way C//A methods fail FBC is by creating incentive to make Compromise beat Favorite because "Worst"
will win the approval tiebreaker.

Thanks.

Kevin
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