Forest W Simmons fsimmons at pcc.edu
Fri Mar 2 14:54:30 PST 2007

Here are the main advantages of UncAAO over other Condorcet methods:

1.  It is resistant to manipulation ... more so than Beatpath or Ranked 
Pairs, if I am not mistaken.

2.  It always chooses from the uncovered set.

3.  It is at least as easy as Ranked Pairs to describe. No mention of 
the possibility of cycles is needed, since the covering relation is 

4.  It is easier than Ranked Pairs or Beatpath to compute. One never 
has to check for cycles, since the covering relation is transitive.

5.  It takes into account strength of preference through appropriate 
use of Approval information.

With regards to point 1, consider the following example (sincere votes):

45 A>C>B
35 B>C>A
20 C>A>B

This is not a Nash Equilibrium for Margins, Ranked Pairs, PC, etc. 
because the A faction can improve its lot unilaterally by reversing C>B 
to B>C. 

Under winning votes the C faction can take defensive action and 
truncate to 20 C.  The resulting position is a Nash Equilibrium.

But under Unc, there is a Nash Equilibrium that involves no order 

45 A>>C>B
35 B>C>>A
20 C>>A>B


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