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

Jobst Heitzig heitzig-j at web.de
Fri Sep 9 05:34:08 PDT 2005

Dear Adam!

You wrote:
> imagine many of the CBA voters have strategically upranked A (with some of them approving A as well) in order to create a cycle.  Here is the "concrete example":
>  10% C>>B>A  (the "honest" ones)
>  23% C>>A>B
>  18% C>A>>B
>  12% B>C>>A
>  12% B>>A>C
>  17% A>B>>C
>  10% A>>B>C

Hm. This adds up to 102%, but I guess from what you wrote next that the first 10% are meant to be just 8%. I will assume so here.

>  B>C  41% approval
I suppose this means the B>C defeat is considered to have strength 41% since this is B's approval.
>  C>A  61% approval
>  A>B 45% approval

OK. In DMC, C wins. That is, the C voters have sucessively buried B. But the last 10% A-voters can prevent this by approving of B also. This means that it seems wise to approve the Condorcet winner and all above her in order to assure a good compromise, right?

But you suggest not this easy countermeasure but a more difficult one:

>  Now, imagine you are in the 17% A>B>>C faction, and you are aware of the situation.  The only way you can prevent C from winning is by insincerely disapproving of A.
>  10% C>>B>A
>  23% C>>A>B
>  18% C>A>>B
>  12% B>C>>A
>  24% B>>A>C (including 12% insincerely disapproving of A)
>  5% A>B>>C  (the "honest" ones)
>  10% A>>B>C
>  Now A's approval (33%) is lower than B's (41%), which allows B to win the election.

It is true that they can perform this, but it is false that this is the only strategy for the A-voters to prevent the C-voters from manipulating the election by burying. In fact, it is far more natural for the A-voters to just approve B which effectively protects B from losing.

You could answer that this requires that some of the last 10% approve B but that they perhaps won't do so since they don't care which of their non-approved candidates B,C wins. But then you assume that the actual sincere preferences are rather like this:

49% C>>B>A
12% B>C>>A
12% B>>A>C
17% A>B>>C
10% A>>B=C

In this situation, C is the *sincere* Condorcet winner and no strategizing by the C voters is necessary.
>  There is a rather large set of situations where this can occur.  I constructed this one to be what I saw as a plausible situation where insincere order-reversal and disapproval was clearly a superior strategy.

Superior to just approving B as I suggest? Why do you think so?

>  In winning votes, the ABC faction can simply equal-rank.  

So you suggest winning votes was better since it provides for a counterstrategy which requires *insincere* rankings. But in DMC the counterstrategy I specifyed above involves only sincere rankings, so I guess this rather shows that DMC is better in this situation. 

Yours, Jobst

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