New pairwise tie-breaker (was Re: Various Condorcet Tie Breakers

[Steve Eppley]

DEMOREP1 wrote:
-snip-
>Any more ideas for tie breakers ?

I think most of the ones listed were quite flawed.  I also think it
would be better to call most of them pairwise tie-breakers, not
Condorcet tie-breakers, to avoid overuse of the term Condorcet.

But to answer your question, here's one I just invented, now ready
to be shot down.

It's similar to one of the methods (Young?) in Bruce's list.
The principle is to find the smallest modifications of the ballots
which would cause one of the candidates to beat all of the others 
pairwise, then call this candidate the winner.  

But I'll include the following constraint: Before modifying any '>'
or '<' rankings, see whether a beats-all winner can be made just by
modifying '=' rankings.  If so, then the winner is the one which can
be turned into a beats-all with the fewest number of changes from
'=' to '>' or '<'.  

Why modify the equal rankings first?  Because it's a much smaller
change from equal to *slightly* unequal than from *extremely* unequal
to equal.

Here are two familiar examples:

1. Dole and Clinton voters truncate.
   46: Dole > Clinton=Nader
   20: Clinton > Dole=Nader
   34: Nader > Clinton > Dole
   D<C 46 to 54
   C<N 20 to 34
   N<D 34 to 46
   Can a beats-all be made just by tweaking the Dole voters' C=N or
   the Clinton voters' D=N votes?  Yes, there are enough D=N votes 
   which can be changed to N>D votes so Nader beats all.  It takes
   13 of these.  It would take 15 C=N changes to C>N to make Clinton 
   beat all.  So Nader wins.

2. Dole voters order-reverse:
   46: Dole > Nader > Clinton
   20: Clinton > Dole=Nader
   34: Nader > Clinton > Dole
   D<C 46 to 54
   C<N 20 to 80
   N<D 34 to 46
   Can a beats-all be made just by tweaking the Clinton voters' D=N
   votes?  Yes, Nader can be made to beat Dole with 13 changes
   from D=N to N>D.

It appears from this superficial analysis that the Dole voters, if 
they sincerely prefer Clinton to Nader, would be better off ranking 
Clinton over Nader.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)