[EM] truncation dilemma

[fsimmons at pcc.edu]

>1a. Probabilistic dilemma. If truncation causes a cycle, then there is some
probabilistic tiebreaker which always includes some chance of C winning.
This can act as a goad to A and B voters to cooperate. I suspect that some
system like this might be the theoretical optimum response if voters were
pure rational agents; however, real people tend not to like probabilistic
election systems.

Sports fans don't object to the use of a certain amount of randomization in deciding the order of contests 
in a tournament.

A single elimination tournament, for example, needs a "seed" order.  If a random order is not used, then 
(if I remember correctly) the contestants with the better records are seeded near the end of the 
tournament, to avoid anticlimatic contests at the end of the tournament.

I suggest the following way of picking a seed order SO for an election:  use the order of a random ballot 
refined by the orders of additional ballots until the order is complete.

One way to use the seed order SO is by single elimination, starting at the bottom of the list and working 
up.

Another (distinct!) way is to elect the lowest alternative on the list that pairwise beats every alternative 
listed above it.

Here's my favorite: initialize X as the highest alternative in the SO.  While X is covered, replace X with the 
highest alternative on the SO that covers X.  Then elect the final value of X.

When the seed order SO is the refined random ballot order as given above or any other social order that 
is monotone and clone free, these methods will pick from the Smith set, while preserving the clone 
independence and monotonicity.  Furthermore, the last of these (my favorite), satisfies Independence 
from both Smith and Pareto Dominated Alternatives, and will elect from the uncovered set.

Do these methods solve the truncation dilemma?