[EM] "Compliant SODA?": seeking a SODA version which may meet more criteria

[Kristofer Munsterhjelm]

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?