[EM] Ken Johnson's Approval bad-example

[MIKE OSSIPOFF]

Ken Johnson said:

Here's an example of the kind of Bad Thing that can happen with
Approval. There are 3 candidates (A, B, C) and 10 voters. I am using
signed CR's in the range -1 to 1 (CR>0: approve, CR<0: disapprove).
Following are the sincere CR's:
9 voters: A(-1), B(0.1), C(1)
1 voter: A(-1), B(1), C(-0.1)
avg CR: A(-1), B(0.19), C(0.89)
approval: A(0), B(10), C(9)
plurality: A(0), B(1), C(9

I reply:

So you're saying that those 9 CBA voters believe that they need B to keep A 
from winning, even though A is everyone's last choice? That's a rather big 
mis-estimate on their part, wouldn't you say?

So they give the election to B, who wins even though 9 times as many people 
prefer C to B as prefer B to C.

You've shown that Approval can fail to elect the SU maximizer. Any method 
can do that. You've shown how big a mis-estimate it takes to do that in 
Approval.

Mike Ossipoff

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