[EM] Fixing IRV

[Blake Cretney]

On Fri, 10 Aug 2001 13:46:08 -0700 (PDT)
Forest Simmons <fsimmons at pcc.edu> wrote:

> Here's another way to fix IRV:
> 
> At each stage of the runoff eliminate the candidate with the
greatest
> pairwise defeat.

I call this pairwise-elimination on my web site.  It is clone
independent, and meets the Smith criterion (which implies the
Condorcet criterion).  However it is non-monotonic, and fails reversal
symmetry.

> This method is very close to minmax, but not quite the same.

Minmax is monotonic at the expense of clone independence and Smith. 
It isn't reverse symmetric either.  Both methods pass the Condorcet
criterion.  They can be expected to be quite different when there is
no Condorcet winner.

Another method would be to eliminate the candidate with the fewest
first preferences among the non-eliminated candidate (like IRV) until
one candidate is the Condorcet winner.  This has similar properties to
pairwise-elimination.

Also, the method Roy Johnson mentions,
> Method: Compute the sum of each row. Eliminate the row and column
> corresponding to the lowest sum, repeat with remaining figures.

is Nanson's method.  It passes Smith, but fails clone independence,
monotonicity, and reversal symmetry.

---
Blake Cretney

See my Election Method Resource page at
http://www.fortunecity.com/meltingpot/harrow/124