Comments on David Marsay's Comments - Number 2

David Marsay djmarsay at
Fri Oct 9 04:31:18 PDT 1998

In response to:
>   ---------- Forwarded Letter ----------
> From:  Mike Allen
> Subject: Re: More comments on Lord Jenkin's proposals
> > >From: David Marsay
> >Subject: Re: UK - Lord Jenkin's Proposals
> >
> >     Any comment on this? (Mine below)  I claim.
> >1) Voters never have an incentive to vote other than for their true
> >preferences, since preferences count only when the higher choices have been
> >eliminated.
> Not so -- one can insincerely elevate a "pushover" that one's preferred
> candidate can easily beat, but who has the ability to eliminate a serious
> competitor.  For example, consider those Republicans who successfully aided
> David Duke to win the Democratic primary, knowing they could beat him in
> the general election.  To their advantage, they forced out a more viable
> Democrat.
Yes. I have some more to say, but I want to review it first. 
> >2) A candidate with > 50% of 1st place votes wins. So the method is
> >'majoritarian' in this sense.
> >     Like FPP and vote-ranking methods. Approval is not like this. (If a
> >'left' candidate has 51% support 2% of the supporters might rank a 'centre'
> >candidate 2nd, leading to a 'wrong' win for the centre candidate.)
> Only if the center candidate has more approval than the left candidate
> (e.g., support from 50% of the electorate plus the 2% of the electorate
> which support both the left and center candidates).  How is this win
> wrong??
It does not meet the majoritarian criterion at '2)' above. It may be 
that this criterion is wrong, but it is at the heart of UK thinking. 
> >3) A centre candidate will win unless it has the least support or some
> >other candidate has an absolute majority (as above).
> >    This violates the Smith criterion. But maybe that is a small price to
> >pay. In extremis, a centre candidate with 2 supporters could win using the
> >Smith criterion.  Do we really want to elect the candidate who has least
> >local support? Also note that methods that appear to
> >respect the Smith criterion do not encourage honest voting, so may not
> >'really' meet the criterion.
>         What is the Smith criterion?

Smith is a ranking criterion. A candidate is said to have an 
absolute majority over another if it is ranked higher on over half 
the ballots. The simplest application of the Smith criterion is that 
if one candidate has an absolute majority over every other, then it 
should win.

More generally, one can define a unique 'Smith set', which is the 
smallest non-empty set for which everything in the set (the sheep) 
has an absolute majority over everything outside the set (the goats). 
The criteria is that only sheep can win, or tie for a win.

This is the strongest non-controversial generalization of the 
majoritarian criterion. I think that any proposed 'majority voting' 
should meet it, but am not sure that majority voting is 'best' for 
all purposes.
Sorry folks, but apparently I have to do this. :-(
The views expressed above are entirely those of the writer
and do not represent the views, policy or understanding of
any other person or official body.

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