On 02/03/2012 02:26 PM, Jameson Quinn wrote:
Of course, in most real-world elections I've ever heard of, 4 candidates are plenty. So is there a way to fix SODA to make those pesky 5-candidate scenarios go away? Analogously, Condorcet's paradox arises for 3 or more candidates, but you can make 3 candidates paradox-free if you require a 2/3 supermajority, and continue to etcetera with an arbitrarily high supermajority.
I thought 2/3 supermajorities always were transitive. How would you make a supermajority cycle with many candidates?
(Warren says, on his singlepeakedness theorem page, that any N-way Condorcet cycle with N > 3 can be reduced to a 3-cycle; just draw a chord to create a 3-cycle.)
One possibility would be for predeclared candidate preferences to be a single approval ballot, rather than a preference ordering. That way, in the scenario described above the delegator candidates could not disagree on the order of preference of the target candidates. This would actually simplify SODA rather than complicating it.
Could you use a rated method instead of a ranked one for the candidate delegation orders?
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