[EM] My Favorite Majoritarian Ordinal Ballot Method
fsimmons at pcc.edu
fsimmons at pcc.edu
Mon Jul 5 11:11:51 PDT 2010
What if you could have a monotone, clone independent, that was not only Condorcet efficient, but
always picked from the uncovered set, independent from Smith and Pareto dominated alternatives, that
encouraged complete ranking, and was resistant to burial and truncation strategies?
The price you would have to pay would be a modicum of randomness for breaking "Condorcet Ties."
Here it is:
1. Construct a "tie breaking order" (TBO) by drawing a random ordinal ballot, and refinining its order with
additional such drawings if necessary, until the alternatives are completely ordered.
2. Initialize the variable X as the first alternative in the TBO.
3. While X is covered replace X with the first alternative in the TBO that covers X. EndWhile.
4. Elect the final value of X.
In the case of only three alternatives this method turns out to be the same as electing the CW when
there is one, else electing the favorite on a randomly drawn ballot.
To see why it resists burial, consider the following scenario:
40 A>B>C (sincere is A>C>B)
30 B>C>A
30 C>A>B
Alternative C is the sincere CW, but the A faction has buried C to create a cycle and thereby get some
positive probability of being elected. Is it worth it?
It is worth it only if the members of the A faction prefer a (4/7)A+(3/7)B lottery over a 100%C election.
How likely is this?
I contend that it is unlikely, because if C were almost as close to B as to A, then there would likely be
some voters with preference order C>B>A. The absence of ballots with these rankings suggests that C
is significantly closer to A than to B. In that case the 100%C election would be preferable to the
(4/7)A+(3/7)B lottery for the A faction, i.e. burial wouldn't pay.
Furthermore, if enough of these C>B>A rankings were thrown in to replace the 30 C>A>B with
14 C>A>B
16 C>B>A,
then the burial strategy would backfire causing B to be elected.
Can anybody think of a Three Candidate example where this method would give unreasonable results?
Can anybody think of a Three Candidate example where insincere voting would not be too risky under
this method?
Thanks,
Forest
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