On Dec 17, 2004, at 3:35 PM, Forest Simmons wrote:
Forest wrote ...Suppose that there are only three candidates, and you think that your
compromise C has a significantly better chance than your favorite F of
winning against the candidate D that you dislike the most, and that
there is a good chance that D will be one of the finalists. Suppose
further, that F and C both have decent chances of getting into the
final round.
In this situation, you have an incentive to "bury" your favorite F, i.e. to try and make F lose in the first round.
Brian replied ...
I don't think this can happen with IRNR.
If I truly prefer F>C>D, if I'm right about IRNR then it should be
impossible to find a configuration of votes for which it's better for
me to vote C>D>F (or C>F>D ?). In this hypothetical vote configuration,
if I vote honestly F>C>D, then D will be elected, but if I vote C
first, C will be elected. But this is not possible with IRNR because of
the re-normalization process that happens on each round.
If I vote F=1.0, C=0.8, D=0.0 and F is disqualified, then my second round re-normalized vote is C=1.0, D=0.0 . In fact, no matter what my rating of F and C (holding D constant at 0.0), if either of them is eliminated in the first round, my second round vote will be {the remaining of F or C}=1.0, D=0.0 . And if that doesn't elect someone I want, nothing will.
Nothing will only because by then it is too late:
Suppose that F is the one that makes it to the final round and that F loses to D, but that C is preferred above D by more voters than not.
Then it would have been to your advantage to rate C at the top and F at the bottom, but now it's too late.
"Hindsight is 20/20, buy low, sell high, etc."
But if you were led to believe or strongly suspect (before voting) that C could beat D, while F could not, and that one of C or F would be eliminated in the first round, then you would be tempted to bury F before it was too late.
It took me a while to think of an example, but I did wind up finding a case where if I vote honestly for F>C>D, D wins, but if I vote C first, C wins. Part of my problem in finding the example is that it requires me to be some kind of oddball voter. I prefer F>C>D, where most F supporters like both D and C. D supporters are not so generous and strongly dislike F.
Ok, here's the case:
[ F , C , D ]
1.0, 0.5, 0.0
*2 0.0, 0.5, 1.0
*2 1.0, 0.5, 0.5
IRNR winner is "D"
http://bolson.org/v/et?vrr=-r&if=- f&cand=3&seats=1&data=1.0%2C+0.5%2C+0.0%0D%0A*2+0.0%2C+0.5%2C+1.0%0D%0A* 2+1.0%2C+0.5%2C+0.5&irnr=1
vs.
[ F , C , D ]
0.0, 1.0, 0.0
*2 0.0, 0.5, 1.0
*2 1.0, 0.5, 0.5
IRNR winner is "C"
http://bolson.org/v/et?vrr=-r&if=- f&cand=3&seats=1&data=0.0%2C+1.0%2C+0.0%0D%0A*2+0.0%2C+0.5%2C+1.0%0D%0A* 2+1.0%2C+0.5%2C+0.5&irnr=1
But, based on this setup, what _should_ happen? In the first case there is wide spread support or approval for "D", so "D" _should_ win. In the second case, "C" has the broadest support and _should_ win. Is it really so bad that a faction representing 1/5th of the vote is able to veto its least favorite candidate? Or is the philosophical objection to the fact this this veto comes at the cost of a dishonest, strategic vote?
Oh well, back to the drawing board in search of a social utility maximizing, singularity free, strategy free election method. I'm going to implement Gradual Approval and add it to my Election Calculator soon. Then we'll see what kind of puzzles we can dream up for it.
Brian Olson http://bolson.org/
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