> Can anybody think of a Three Candidate example where this method
would give unreasonable results?
One could say that the Condorcet winner is always reasonable, and in
the case of a sincere loop all three candidates are reasonable since
they all have (max length 2) beatpath to all others. The first
complaints might come from the the random nature of the election. If
one has some criterion that tells which one of the candidates is best
then electing someone else than that candidate (maybe the worst one)
(assuming that the votes are sincere enough) could be considered
unreasonable.
> Can anybody think of a Three Candidate example where insincere
voting would not be too risky under this method?
Insincere voting might first emerge in the form of voters burying or
not ranking the worst competitor(s) of their favourite candidate. This
kind of insincere voting (that might target the next election, not
necessarily change the winner of this election) might not be too risky
in some situations, but this is of course not the kind of insincere/
strategic voting scenario that you asked for.
Insincere full ranking instead of a vote that includes sincere equal
rankings could be a good strategy (to create or not to create a loop).
In the example that you gave the fact that there are no C>B>A votes
means (as you say) that it is probable that C is close to A, and A
voters will not have incentive to vote insincerely. This is however
not the only reasonable scenario. It is also possible that A voters do
not like C although C voters do like A. This is not the most common
scenario but sometimes opinions may go also this way.
Juho
On Jul 5, 2010, at 9:11 PM, [email protected] wrote:
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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