Proposed SD Algorithm Defective

[David Catchpole]

If this is a Condorcet completion method, I might remind people that where
a paradox of voting occurs, exclusion of candidates who beat no-one cannot
break a paradoxical schedule of preferences. If the Simpson Set is the
set of candidates who do beat someone else, then any resolution of the
paradox leading from a candidate's exclusion must come from that set

On Tue, 25 Aug 1998, Norman Petry wrote:

> Blake,
> 
> You wrote:
> 
> >I think the best bet for an SD algorithm is
> >Repeat
> >    Eliminate everything not in the Simpson set
> >    Break lowest defeat
> >Until only one candidate is left
> 
> I'm not familiar with the Simpson Set.  Could you please post a definition?
> 
> TIA,
> 
> Norm Petry
> 
> 
> -----Original Message-----
> From: Blake Cretney <bcretney at my-dejanews.com>
> To: election-methods-list at eskimo.com <election-methods-list at eskimo.com>
> Date: August 24, 1998 7:19 PM
> Subject: Re: Proposed SD Algorithm Defective
> 
> 
> >
> >--
> >
> >On Wed, 19 Aug 1998 00:15:48   Norman Petry wrote:
> >>With a couple of slight changes, the algorithm idea I posted a few days
> ago
> >>is _close_ to being an accurate implementation of SD.  Here's how the
> steps
> >>should be listed:
> >>
> >>1) Check for any unbeaten candidates.  If 1 or more, then quit.
> >>2) Repeatedly eliminate beat-nothing candidates (E, then D in example).
> >>3) Break the weakest defeat(s).  Goto  step 1.
> >>
> >
> >I think the best bet for an SD algorithm is
> >Repeat
> >    Eliminate everything not in the Simpson set
> >    Break lowest defeat
> >Until only one candidate is left
> >
> >If anyone wants pseudo-code for doing this (including the Simpson set
> elimination step), I could provide it.
> >
> >I wouldn't describe this as simple, but it is possible, and it is more
> important that a method be simple to describe than to impliment.
> >
> >
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> >
> 
>