New Condorcet-ish method: "weak & strong preferences"

[Steve Eppley]

Here's a variation of ranked ballots (which purists will rightly
consider to be something other than ranked ballots).  The method 
might be named "BeatsAll//WeakMeansIndifferent//Condorcet".

The voters would be able to express two strengths of relative
preference (plus indifference), not just a preference order. 

   Example ballot:
   A > B >> C > D=E >> F

The symbol '>' can be read as "is SOMEWHAT preferred to".
The symbol '>>' can be read as "is STRONGLY preferred to".

Choices left unranked would be treated as if the voter had ranked
them last and had used the stronger preference '>>' to separate them
from those explicitly ranked.

In the pairwise tallying, '>' is initially treated the same as '>>',
a full strength preference.  If there's a choice which beats all
other choices pairwise, it wins.  (In other words, exaggeration of
preference intensities won't defeat a choice which beats all others
pairwise.)

If there's no choice which beats all others pairwise, the first
(circular) tie-breaker treats the weak preference '>' the same as
indifference '=' in a re-tally.  

   Example:
   23:  A >> B >> C
   23:  A >> C >> B
   10:  B >> A >> C
   10:  B >> C >> A
   34:  C  > B >> A          <--- these use the "weaker" preference

               prefer A more      prefer B more     prefer C more
   A vs B            46                 54W
   A vs C            56W                                  44
   B vs C                               43                57W

   No choice beat all others.  
   Then the ballots are treated as:
   23:  A >> B >> C
   23:  A >> C >> B
   10:  B >> A >> C
   10:  B >> C >> A
   34:  C  = B >> A          <--- the '>' becomes a '='

   and re-tallied:
               prefer A more      prefer B more     prefer C more
   A vs B            46                 54W
   A vs C            56W                                  44
   B vs C                               43W               23
   B beats all others and is elected.

Though I've expressed the pairwise matrix in the reverse sense as 
"preferences for" instead of "preferences against", I'd suggest using 
Condorcet(EM)'s "against" to resolve a continued circular tie.

By expressing a "weaker" preference for the favorite over the
"lesser evil", the 34 voters have chosen to protect (elect) their
compromise choice.

The method seems very similar to the "fancy" iterative methods we
discussed months ago, where the algorithm iteratively translates
preferences to indifference when necessary to make a voter's
compromise choice less beaten than the voter's greater evil.

It appears at first glance that the weaker preference '>' can't be
used in offensive voter strategy.  The voter who uses it instead of
the full strength '>>' would be making some less preferred choice
less beaten than otherwise, with no reduction in the "beatenness" of
a more preferred choice.  So the '>' appears to be useful only for
defensive strategy.  It might be used unnecessarily, but its use
wouldn't entail a misrepresentation of preference order.

I haven't had time to examine this method much.  At first glance, 
it appears to perform reasonably well on some of the standards and
criteria some of us have been advocating.  And the distinction
between the "weaker" and "stronger" preferences may be a reasonably
compelling way to break circular ties.  

On the other hand, it would be harder for the voters to vote than
simple rankings, and the tally algorithm appears more complex to
understand than Condorcet since there's an extra step.  And I
haven't really looked for possible strategy problems and mandate
interpretation problems. 

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