[EM] "Power Truncation"?

Chris Benham chrisjbenham at optusnet.com.au
Tue Mar 6 07:26:47 PST 2007

Michael Ossipoff wrote:

>The Condorcet version that I propose is SSD, Schwartz Sequential Dropping. 
>It's defined at:
>     Schwartz Sequential Dropping (SSD):
> The "current Schwartz set is the Schwartz set based only on defeats 
> that haven't yet been dropped.
> Drop the weakest defeat among the members of the current Schwartz set. 
> Repeat till there's an unbeaten candidate.
> (The strength of B's defeat by A is measured by how many people have 
> voted A over B).
> ***

>Power truncation:
>If a voter power truncates candidates below a particular rank position, 
>then, the count scores each one of those candidates as if that voter had 
>ranked all the other candidates over him/her.
>[end of power truncation definition]


"Power truncation" strikes me as not one of your better ideas.

49: A "power truncates"
03: B>C
48: C>B

The "power truncation" appears to give A the win in defiance of  
Condorcet, Majority for Solid Coalitions
and Majority Loser.

B>C 52-48,  C>B 97-3
B>A 51-49
C>A 51-49

All candidates are pairwise beaten so are in the initial Schwartz set. 
A's defeats are the weakest so we drop
one at random and nothing changes so we drop the other one.  Then A is 
the only candidate with no (undropped)
defeat so A wins.

45: A  "power truncates" (sincere is A>C)
35: B>C
20: C "power truncates"

This is supposed to be a  "Nash equilibrium" situation in WV where the 
sincere CW wins.

B>C 80-20,  C>B 65-35
A>B 65-35,  B>A 55-45
C>A 55-45

Again, A's defeats are the weakest so they are dropped and A wins 
(defying Minimal Defense).

Chris Benham

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