[EM] Manipulation Proofing Approval

[Forest Simmons]

Approval's weakness is that it is vulnerable to media manipulation.

To counteract this we could look at all of the approval winners under all 
possible media manipulations, and then choose by random ballot from these.

Less ambitious, but feasible and adequate:

Choose by random ballot from among all of the Strategy A winners.

An alternative X is a strategy A winner iff there exist alternatives Y and 
Z such that X is the approval winner when all voters place their approval 
cutoff on the Z side of Y.


The media tends to encourage the use of strategy A by playing up two 
candidates, and giving one of them a slight edge over the other.

Under pure Approval, the media could pick a strategy A winner X by playing 
up the Y and Z candidates, slightly favoring Y.

How do we find the strategy A winners?

For N alternatives, we need to sum an N by N by N dimensional array.

The (i,j,k) entry is a one or a zero depending on whether the ballot in 
question would approve candidate k given candidate i is the most likely to 
win, and candidate j has the rest of the probability.

Candidate k is a strategy A winner iff for some i and j, the (i,j,k) entry 
in the array sum is larger than the (i,j,m) entry for all m not equal to 
k.

Basically, we are manipulating in favor of each candidate to remove the 
advantage of the ones that are favored by the media.

That's all I have time for now, but what do you think of this idea?

Forest