[EM] Presidential debate ordering

[Gervase Lam]

> Date: Sat, 19 May 2007 16:38:03 -0700 (PDT)
> From: <mrouse1 at mrouse.com>
> Subject: [EM] Presidential debate ordering

> A few days ago, we had the Republican debates on TV, and I came to the
> conclusion that having ten people on the stage at once was an unmanageable
> mess.

> What I'd like to see is one-on-one, round-robin debates. Now, we could
> pair up the candidates randomly, but where is the fun in that? What I
> thought might be interesting is to have each candidate pick the order he
> wanted to debate every other candidate, and choose the order that best
> matches the aggregate preference.

> Anyone know the best way to do something like this?

My initial idea was to have a pairwise matrix ballot that contains all
the head-to-heads between each candidate.  Each candidate then votes
Approval style for the head-to-heads (including the head-to-heads
involving the voting candidate himself).

The voting is then tallied, with the head-to-heads that are Approved by
both the involved candidates listed first and then the head-to-heads
that are Approved by only one of the involved candidates.  Ties are
broken by the total number of Approval votes the head-to-heads (i.e. the
votes from candidates not involved in the head-to-head in question are
included).

However, James Green-Armytage mentioned Reciprocal Pairing on this list
in the past.  I rediscovered it in the following web page:

<http://fc.antioch.edu/~james_green-armytage/vm/reciprocal.htm>

I would do an initial Reciprocal Pairing.  This would get give the
'first pairings.'  I would then remove from each candidates' ballots the
candidates they have already debated with and then repeat the Reciprocal
Pairing.

As the candidates can't really be divided into 'stationary' and 'active'
groups, I would use something more like the 'Random-Order Method' that is
mentioned.  However, to lessen the effect of the paradoxes mentioned on
the web page, I would have the candidates enter the room in a pre-
determined order.  Maybe those who have already debated with the
candidates that they most preferred would enter the room first.

Wikipedia has also got an article on this that mentions further
variations, though not with any detail:

<http://en.wikipedia.org/wiki/Stable_marriage_problem>

There is one problem I have with allowing the candidates to determine
who they should debate with.

Suppose there are two front runners.  In a poll, the first front runner
is deemed to be the Condorcet winner.  The second front runner would be
the Condorcet winner but for the first front runner.

The first front runner realises that in a head-to-head debate, he would
do badly against the second front runner.  Therefore, the first front
runner does not rank the second front runner.  This means that the two
front runners will never debate with each other.

One way around the problem is to somehow only count the candidate's
ballot that favours the head-to-head the most.  However, you then may
get the situation that all of the other candidates rank the first front
runner top on their ballots.  That would mean that the first front
runner may never get the chance to debate with the second front runner.

Alternatively, may be James's Debate Inclusion method could be used
instead:

<http://fc.antioch.edu/~james_green-armytage/vm/debate.htm>

Thanks,
Gervase.