[EM] Doesn't everybody see that IRV=BORDA?

James Gilmour jgilmour at globalnet.co.uk
Mon Jan 26 13:05:30 PST 2004

> >Paul wrote (here converted to plain text):
> >> It is fairly easy to prove that IRV always selects the 
> Borda winner.

I asked:
> >Surely this statement is wrong?
> >Consider 3 candidates and 7 voters:
> > A>B>C: 4
> > B>C>A: 2
> > C>B>A: 1

Paul replied: 
> In this case, there's a majority winner and no need to invoke 
> IRV or Borda or Condorcet. A wins 4>3 period.

But that doesn't answer the question.  In any case, you cannot change the counting rules part way
through the count just because you've seen the first preferences.  A Borda election is a Borda
election: points are allocated to every preference and the result depends on the summation of all
those points.  In the example above Borda gives a different "winner" from IRV, Condorcet and
Plurality.  So, to go back to the question that was prompted by your statement, how can you prove
"that IRV always selects the Borda winner"?

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