[EM] Condorcet Violates Strong FBC

[Forest Simmons]

Here's the instant version of CRAB:

Voters submit ranked preference ballots.

Suppose that there are N voters and K candidates.

Initialize a one by K array C by letting the j_th entry be the number of
first place votes of candidate j.

Then ...

While the maximum entry in C is less than N*K+1

   For each voted ballot b

     Form an approval ballot by approving down to the candidate with the
     greatest current entry in C, including approval for that
     "frontrunner" iff the ballot ranks the frontrunner above the
     current "runnerup" in C.

   Next b


   Add the approval votes to C


End While


The candidate with the greatest accumulated approval in the array C wins
the election.


[End of description of Instant Cumulative Approval Balloting]


Remark:  If the threshold of N*K+1 were replaced with a random number
between 1 and N^2+1 (not divulged until after all of the ballots are in),
then (I believe) the method would have the randomness that is necessary
for defeating the temptation to vote insincerely.

But for all practical purposes the number N*K+1 is large enough and
unpredictable enough (in public elections) to give the necessary illusion
of randomness to discourage insincere voting.

In the deterministic form the method is not monotone, but in the random
form (I believe) the method is monotone: if you move a candidate up the
ballot relative to other candidates, then her probability of winning
increases relative to the probabilities of the others.

Since the deterministic version is "pseudorandom" it is monotone for
practical purposes (if I am not mistaken about the monotonicity of the
random version).


Remark: The instant version of CRAB is summable in a data structure of
size K^3, so the method is computationally nice.

Forest


On Wed, 6 Nov 2002, Elisabeth Varin/Stephane Rouillon wrote:

> Please explain CRAB....

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