Re: Hybrid Theory

[Raul Miller <moth@debian.org>]

On Wed, Dec 11, 2002 at 03:52:13PM +1000, Anthony Towns wrote:
> > I don't think such cases exist (I'm working on how to show this).  On the
> > other hand, there are cases where "drop all failed supermajority before
> > CpSSD" gives results which are less like condorcet than "Hybrid Theory".
> 
> (Ah, assertions without examples. How helpful.)

A requires 2:1 majority; N is the default option
4 cAbN
1 cNAb
3 bcNA
3 AbcN

c defeats N 11:0
b defeats N 10:1
A defeats b 8:3
c defeats A 8:3
N superdefeats A 8:7
b defeats c 6:5

eliminate 6:5

c defeats N 11:0
b defeats N 10:1
A defeats b 8:3
c defeats A 8:3
N superdefeats A 8:7

c wins

This is the same outcome as you'd get without supermajority.  If A is
dropped before eliminating weakest defeats, b wins.

[Aside: I have already referred to Buddha's post, which proposes this
example, in this thread.  But, I apologize for not spelling it out in
more detail.]

> Define "like Condorcet".

Same outcome as Condorcet for the same votes.

Thanks,

-- 
Raul