## [Computational Complexity] Randomness in Voting

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• Every voting scheme has the property that in some scenario a change of a single vote can change the outcome. When a major election has a very close result,
Message 1 of 1 , Jan 2 7:05 AM
Every voting scheme has the property that in some scenario a change of a single vote can change the outcome. When a major election has a very close result, like the current senate race in Minnesota or the 2000 presidential race in Florida, every vote gets scrutinized very carefully and the process can drag out for months.

This scrutinization ignores the randomness factor. Some people got stuck in traffic or maybe had some emergency that prevented them from voting. Some people went to the wrong voting area or their registration got lost. Some people just plain filled in the wrong oval, voting for the wrong candidate. These problems are rare and roughly cancel themselves out but in a very close election like Minnesota the randomness greatly outweighs the disputed ballots. Yet because of the hard cut-off the scrutinized ballots get the most attention.

I suggest we eliminate the hard-cut off by adding our own randomness. For simplicity suppose we had two candidates, Al and Norm, who received x and y votes respectively. We flip z=x+y uniform random coins. If the number of heads is at most x we declare Al the winner and Norm the winner otherwise. If x > z/2+ 10 z1/2 then this process would make Al the winner almost all the time. But as x and y get very close the probability that Al wins approaches 1/2. Since a change of a few disputed votes won't affect the probability dramatically, we won't have so many battles over so little.

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Posted By Lance to Computational Complexity at 1/02/2009 09:03:00 AM

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