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

Adam Tarr ahtarr at gmail.com
Fri Sep 9 09:40:30 PDT 2005

On 9/9/05, Jobst Heitzig <heitzig-j at web.de> wrote:

 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.

Quite right, of course. Let me throw out a corrected example (although the 
strategy still works on the "102%" example):

9% C>>B>A
22% C>>A>B
18% C>A>>B
12% B>C>>A
12% B>>A>C
17% A>B>>C
10% A>>B>C

> 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?

Easy to make an example where that's not the case. Just imagine a slightly 
higher percentage of the CBA faction approve A:

9% C>>B>A
15% C>>A>B
25% C>A>>B
12% B>C>>A
12% B>>A>C
17% A>B>>C
10% A>>B>C

B>C 41% approval
C>A 61% approval
A>B 52% approval

Now at least some order-reversal is required. Or, if you like, let's move 
the "approval strategy" needle for the edge factions much farther over:

5% C>>B>A
5% C>>A>B
39% C>A>>B
12% B>C>>A
12% B>>A>C
25% A>B>>C
2% A>>B>C

B>C 49% approval
C>A 61% approval
A>B 66% approval

Now the only viable strategy for the 25% edge faction is for at least 18% of 
them to insincerely rank B>>A>C. Even if they can convince the "obstinate" 
2% to join them in strategic action, their only other option is for all 27% 
of them to completely order-reverse to B>A>>C, to make B the Condorcet 

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.

The point was that for the one faction I was talking about, the strategic 
vote involved order reversal and approval burial. The fact that other 
factions were not acting strategically is ultimately irrelevant. You could 
also have accused the 12% B>C>>A faction of nonstrategic approval strategy. 
Again, this is not the point. You asked for a situation where this was the 
optimal strategy, and I gave you one.

We could argue all day about how realistic the example is, and indeed that 
is an important question. My point is simply that the strategy applies over 
a much wider range of situations than it does in winning votes (although a 
narrower range than margins). I would trust Kevin's simulations to tell me 
how much often moreso than either of our intuitive instincts.

> 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?

Because the 17% A>B>>C voters do not have the power to coerce the 10% A>>B>C 
voters to vote how they want them to. They can try to convince them, and 
they will have a good argument on their side, but they may fail. This does 
not change the fact that their optimal strategy is B>>A>C. The question of 
what is the optimal strategy for that faction, alone, is not debateable. It 
is order-reversal and approval burial of their favorite.

I know see Kevin's response, where he stated this more succinctly.

> 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.

No, the 17% in the example I showed have no incentive to vote in a fashion 
other than A=B>C in winning votes. That is the point. The strategy of one 
faction is at question, not the strategy of every faction in the electorate.

Same election in winning votes:

9% C>B>A
40% C>A>B
12% B>C>A
12% B>A>C
27% A>B>C

B>C 51%
C>A 61%
A>B 67%

Now, if at least 17% of the A>B>C voters (that same 17% from before, of 
course) vote A=B>C, B wins. This is of course a less extreme strategy than 
B>A>C (or B>>A>C).
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