[EM] Winning-votes intuitive?

[Forest Simmons]

On Wed, 20 Feb 2002, Rob LeGrand wrote:

> Adam wrote:
> > 49: Bush
> > 24: Gore
> > 27: Nader,Gore
> >
> > Bush beats Nader 49-27
> > Nader beats Gore 27-24
> > Gore beats Bush 51-49
> >
> > With ranked pairs, the Gore-Bush defeat is overturned, and Bush wins,
> > despite a true majority preferring Gore to Bush.  In SSD the Nader-Gore
> > defeat gets overturned, and Gore wins, which seems more intuitive to me.
> 
> I think the reason the winning-votes method seems more intuitive in this case
> is that, looking at the votes, there seem to be 49 Bush voters and 51
> Gore/Nader voters, so a Bush result seems wrong.  But that's misleading.  The
> 24 Gore voters don't prefer Nader to Bush.  If they had voted Gore>Nader>Bush,
> then I'd agree that Bush should lose.  But, if you ask me, the above election
> is more accurately expressed as
> 
> 49:Bush>Gore=Nader
> 24:Gore>Bush=Nader
> 27:Nader>Gore>Bush
> 
> which should be equivalent to
> 
> 49:Bush>Gore>Nader
> 49:Bush>Nader>Gore
> 24:Gore>Bush>Nader
> 24:Gore>Nader>Bush
> 54:Nader>Gore>Bush
> 

But suppose the truncation is interpreted as an Approval cutoff, then it
would be equivalent to

49:Bush>NOTB>Gore>Nader
49:Bush>NOTB>Nader>Gore
24:Gore>NOTB>Bush>Nader
24:Gore>NOTB>Nader>Bush
54:Nader>Gore>NOTB>Bush   

and the circular tie should be broken by Approval.

Given that interpretation the Approval winner is Gore.

Of course, the interpretation depends on the original contract with
the voters.  If the method is SSD, then the approval interpretation makes
sense.  If the method is Ranked Pairs, then the other interpretation makes
more sense.

Forest