[EM] UncAAO
Chris Benham
chrisjbenham at optusnet.com.au
Fri Mar 2 23:09:08 PST 2007
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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