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 
>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.

Chris Benham

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