Forest W Simmons wrote:
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
transitive.
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
Here C is the CW. Is this example right?
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.
Taking such "defensive action" causes B to win, so why would they want
to do that when they
prefer A to B? And I don't see why the resulting position is a "Nash
Equilibrium" (according to
the definition I googled up), because the sincere C>A faction can change
the winner from B to A
by changing their votes from C to C>A.
*
*DEFINITION: Nash Equilibrium* If there is a set of strategies with
the property that no player
can benefit by changing her strategy while the other players keep
their strategies unchanged, then
that set of strategies and the corresponding payoffs constitute the
Nash Equilibrium.
*http://william-king.www.drexel.edu/top/eco/game/nash.html
Chris Benham
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