[EM] Interesting use of Borda count

[Bart Ingles]

I don't recall using the term "average ranking".  My focus was on
average (or total) point counts (i.e. Borda scores), as a way of showing
the practical and strategic equivalence among the Borda variations
mentioned.



Steve Barney wrote:
> 
> Bart:
> 
> OK, I get it now. When I see the term "average ranking" I think of something
> other than what you describe. I think you get a more intuitive, and perhaps
> more descriptive sense of "average ranking" if you do as follows. You average
> the RANKINGS for each candidate by dividing the sum of the rankings of each
> candidate by the number of voters. For example, if there are three candidates
> and two voters, one voting for A>B>C and the other voting for A>C>B, it goes
> like this:
> 
>            1 1
>            A A 1st
>            B C 2nd
>            C B 3rd
> 
>            A: (1+1)/2=1
>            B: (2+3)/2=2.5
>            C: (3+2)/2=2.5
> 
> That makes more sense to me, on an intuitive level, than averaging the total
> point scores. Don't you agree?
> 
> Steve Barney
> 
> PS: Thanks for the reference. That will help my education along.
> 
> --- In election-methods-list at y..., Bart Ingles <bartman at n...> wrote:
> >
> > Steve:
> >
> > I agree with your Saari results, if the two voters are ignorant enough
> > to actually bullet vote (even though this may accurately represent their
> > preferences).
> >
> > One of the ways to defeat Saari's variation is for the two voters to
> > collaborate:  One voter agrees to rank A, B, and C in order, while the
> > other ranks A, C, B.  So the individual ballots are worth (2, 1, 0) and
> > (2, 0, 1).  The combined total is (4, 1, 1), hence the per-ballot
> > average (2, .5, .5) I claimed below.
> >
> > Thus the suggestion that Saari's variation could function as a sort of
> > voter intelligence screen, since a potential bullet voter who doesn't
> > understand the above strategy has his voting power reduced by one-third.
> >
> > Samuel Merrill III (Making Multicandidate Elections More Democratic,
> > 1988) includes the following citation:
> >   Black, D. (1958) *The Theory of Committees and Elections*, Cambridge
> > University Press.
> >
> > I haven't read Black's work.  But the issue seems moot to me, since with
> > the voter strategy above (or the equivalent coin-toss strategy), the
> > three variations we have discussed (Borda, Black, and Saari) are all
> > equivalent.
> >
> > Bart
> 
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