[EM] above/below line voting

Forest Simmons fsimmons at pcc.edu
Fri Mar 22 13:33:50 PST 2002

Recently someone mentioned the above/below line options for voting in
Australian elections. It was mentioned that most voters just choose to
vote above the line, i.e. trust their favorite party to take care of the
details.  In a way this is just designating their party as proxy to use
their vote as the party sees fit.

[It also reminded me of filing Federal Income Tax here in the states; some
people use the short form and others itemize.]

It seems to me that we could adapt the above/below line idea so that it
would work for single winner elections as well as PR elections in a way
that would make it both simpler and more responsive than the Australian

For now I will stick to the single winner case:

Instead of each party having a ranking of its candidates, each candidate
would rate each of the candidates (including self at the max) on a scale
of zero to 100.

Voters would have two options, of which the first would be like voting
above the line or filling out a short form, and the second would be like
voting below the line or itemizing.

In the first option you would simply designate one of the candidates
(instead of a party) as your proxy. Presumably you would choose the
candidate whose rating of the candidates most closely reflected your own
opinion, or if you didn't feel qualified to rate all of the candidates, it
would be the candidate that you respected and trusted the most.

This would give you a better chance of feeling good about your "above line
vote" than the Australian system, because (1) you trust your favorite more
than her party, and (2) greater choice increases your chances of finding a
rating schedule that you like.

To "itemize," you simply submit your ballot as an Approval ballot; you
don't need as much resolution as the candidates, because you are voting
only one ballot, while they vote many as proxies.  Too much resolution
would make it an arduous task, anyway.  [The candidates have more time,
interest, and resources for devoting to that task, so they mustn't

The candidates' CR ballots reveal something about them; birds of a feather
flock together.  Would have Bush and Gore rated each other above Nader,
reflecting their common fundamental allegiance to Corporate America?  Or
would they have considered Nader to be a compromise?  We'll never know for
sure (though we have strong suspicions), but it would have been revealed
by this system I'm talking about, and BEFORE you voted.

Here's how the ballots are tallied:

Each ballot is converted into a pairwise matrix; the ones that indicate a
candidate as proxy are converted into a copy of the pairwise matrix of
that candidate, while the Approval ballots are converted in the natural

[By the "natural way" I mean considering approved candidates as equally
ranked in first position, and unapproved candidates as equally ranked as
low as possible.]

The sum of these pairwise matrices is checked for a Condorcet winner.

If there is no CW, then there are several possible ways to complete the

(1) complete according to some well established Condorcet method.

(2) complete by total approval, where 50 is the approval cutoff on the CR
ballots, and the approval ballots are counted as usual. This would require
keeping an approval tally on all of the ballots as they are converted to
pairwise form. [easily done]

(3) complete by total approval, but let allow the candidates to adjust
their approval cutoffs to any level between 40 and 60, say, based on
information gleaned from the pairwise totals.

Note that only this third option would require the proxy to actually act
as proxy.  Neither of the other options even requires keeping track of how
many voters each candidate was proxy for.  Of course that tally is easy to
keep, and should be kept for public information in any case.

That completes the description of the method.

Here are some possible variations:

A voter may designate her ballot to be counted as proxy or approval.  Now
suppose the voter marks three candidates under the proxy option. Then each
of those candidates acts as one third proxy for her, i.e. each of those
candidates' pairwise matrices gets divided by three before being added
into the tally.

The below line option could actually be a different ballot, just as the
tax form for itemization is different from the short form. In that case
the "long form" ballot could be a CR ballot of greater resolution than
two. For that matter, why not let the voter choose between two or three
resolution options depending on how much time and energy she wanted to
devote to preparation for voting?

[All CR ballots (no matter the resolution) are easily transformed into
pairwise comparison matrices.]

What do you think?


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