[EM] Complex Preferences [Was: A>B, B>A, A=B]

[wclark at xoom.org]

Many on this list have expressed a desire to represent complex voter
preferences over and above a simple ranking of candidates.  Typically this
is done in order to justify various strategy considerations.  Sometimes
even "non-linear" preferences are expressed, in which
Condorcet-cycle-style ambiguities are allowed for a *single* voter (such
as A>B>C>A).

No single ranking of candidates can express such relationships, not even
if equality and truncation are allowed.  Something more complex is
required, and I'd like to propose one such system.

Consider an election with three candidates: A, B, C.

There are 26 possible rankings, allowing equality and truncation:

(EMPTY)

A
B
C

A=B
B=C
C=A

A>B
B>C
C>A
A>C
C>B
B>A

A>B>C
B>C>A
C>A>B
A>C>B
C>B>A
B>A>C

A>B=C
B>C=A
C>A=B

A=C>B
B=C>A
B=A>C

A=B=C

Each such ranking can also be taken to represent a possible election
outcome, with equality indicating a tie and truncation indicating that a
candidate did not finish the race (either recieving 0 votes or dropping
out for some reason).  Determination of second (and additional) places can
be accomplished by re-tallying ballots with the previous winner
eliminated.

So, voter preferences can be thought of as expressing a desired outcome
for the election -- an outcome for *all* candidates, not just the first
place winner.  I believe this is justified by the fact that many voters
will care which candidate wins second place, since that so often
determines which party is deemed a "major" party in subsequent elections.

For instance, there are many current US voters who would prefer:

Kerry>Nader>Bush

or even:

Kerry=Nader>Bush

to:

Kerry>Bush>Nader

What's more, these same voters would likely prefer *any* of the above
outcomes to:

Bush>Kerry>Nader

So in order to fully express the preferences of these voters, a full
ranking of all 26 possible election outcomes would be in order.

Allowing for equality and truncation, there are far more than 26! rankings
of election outcomes, which is already more than 4x10^26.

I'd think *that* should allow for preferences as complex as you'd like to
make them, expressing any sort of strategy concerns or ambiguities you can
dream up.  It also strikes me as a straight-forward generalization of the
simpler preferences expressed by a single ranking.

-Bill Clark

-- 
Protest the 2-Party Duopoly:
http://vote.3rd.party.xoom.org/