Re: Condorcet Voting and Supermajorities (Re: [CONSTITUTIONAL AMENDMENT] Disambiguation of 4.1.5)

[Buddha Buck <bmbuck@14850.com>]

> > On Fri, Dec 01, 2000 at 06:54:32AM -0500, Raul Miller wrote:
> > > However, with the 3:1 supermajority which affects A, you get:
> > > 10    : 0  B:C
> > >  3 1/3: 0  A:B
> > >  3 1/3: 0  A:C
> > > B wins.
> 
> On Fri, Dec 01, 2000 at 10:24:41PM +1000, Anthony Towns wrote:
> > This isn't correct: A wins by being preferred to all other options (A >
> > B, 3.3 to 0 and A > C, 3.3 to 0). The strengths of the victories don't
> > come into play unless you have a cycle.
> 
> I was talking about the smith/condorcet mechanism.

You may have been talking about it, but you didn't apply it properly.  
The SC method I described said "drop the weakest defeat from the Smith 
set until there is an undefeated option".

The Smith Set is defined as the smallest set of options that are not 
defeated by any option outside the Smith Set.

In your example, even after Supermajority scaling, you have A defeating 
B and C, so the Smith Set contains the sole option A.  

Option A is undefeated in the Smith set (trivially) so the SC method would declare 
A the victor, not B.

In fact, A would be the victor in any of the methods I mentioned, 
simply because it is an undefeated option.  Even after supermajority 
scaling. 


-- 
     Buddha Buck                             bmbuck@14850.com
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