[EM] Paper By Ron Rivest

[fsimmons at pcc.edu]

This continues a thread that began last April with

http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2010-April/025841.htm

Rivest confessed in his paper his method is not monotone.  

Here's a closely related method that is monotone:

Voters submit ordinal ballots.

Two game theorists that have no interest in the outcome of the election, but are compulsive gamblers, are 
enlisted to help decide the outcome.

Without seeing any of the ballots, but after getting as much other information as they can amass by 
discreet indagations, both gamblers bet as to who will win the election.

If they bet on the same candidate, that candidate wins.  If they bet on different candidates, the winner is 
decided by random ballot between the two candidates, and the gambler who bet on the winner is declared 
winner of the bet.

The method satisfies the FBC, is monotone, clone proof, Independent from non-Smith alternatives, 
Independent from Pareto Dominated Alternatives, etc. 

This shows that it is possible to have a method with all of the compliances that you would ever want, 
including Condorcet efficient and zero incentive for insincere ballots, provided that you are not wed to 
determinism.

How does it accomplish this?

Exactly like Approval accomplishes all of its great compliances; it externalizes the strategic manipulation.

The manipulation can only happen when the two game theorist gamblers are inquiring around for 
information.  That is when it might be to your advantage to lie to them, i.e. to not answer their 
questionnaires truthfully.

The same thing happens in Approval.  If you are going to vote optimally on an approval ballot, you need to 
gather information ahead of time.  That is where all of the bluffing takes place.

Rivest's method is a DSV (Designated Strategy Voting) version of the game I have described.  No wonder it 
is non-monotone; we cannot even come up with a monotone DSV version of Approval.

In my next message I will propose a general method for making monotone DSV methods from base 
methods that are monotone only by virtue of their externalizing the strategic part of the election.

But for now, I would rather have you digest what I have presented so far.

Forest