# [EM] thoughts on the pairwise matrix

Abd ul-Rahman Lomax abd at lomaxdesign.com
Tue Nov 29 12:27:27 PST 2005

```At 01:32 PM 11/29/2005, Paul Kislanko wrote:
>I actually have no method. But "Condorcet ballots" is an ambiguous term as
>used in the reply to me. I actualy suggested that there BE a well-defined CB
>such that for each pair of choices I vote "A, B, Either, or Neither". Then
>the matrix can be guaranteed to reflect the voters' pairwise preferences,
>instead of having to infer them (under different rules depending upon
>whether equal rankings and/or truncation is allowed).

Providing that overvoting is allowed, and also truncation (which is
generally a question of counting rules, not of ballot design, but
some machines may have interlocks which prevent overvoting), every
Condorcet ballot I've seen allows this. It is intrinsic to ranked
ballots. The only issue is the number of ranks; for practical
reasons, it may be limited.

The Australian ballot has the voter write in a rank number. Ballots
with a limited number of ranks allow determining "A, B, Either,
Neither," but not for every pair, just for the top pairs. Any pair
with a member with an expressed rank and the other with no rank is
explicit for the expressed rank. Any pair with equal ranks is Either.
And any pair with no rank for either candidate is Neither.

What is *not* shown in a Condorcet ballot is the strength of
preference. For that one needs Range. A Range ballot can be used to
infer pairwise preferences, and, again, Either is shown by rating
both candidates the same, and neither by rating both zero or
abstaining (depending on the rules).

Another additional feature not intrinsic to Condorcet is Approval
cutoff, which may be implemented on any ranked ballot by allowing a
dummy candidate representing the Approval cutoff rank. If this is
done, all candidate pairs with both members below that cutoff are
Neither. But Neither is really not informative or active in this
case. Neither is quite equivalent to ranking both candidates in last
expressed rank in a system requiring no truncation but allowing overvoting.

Condorcet methods use the matrix, essentially, to determine the
winner, if there is a Condorcet winner. If not, the details of the
particular method determine the winner.

Showing the election by overlaying the pairwise matrix with a win
marker (as cell color, for example), and sorting the rows and columns
in a manner relevant to the determination of the winner -- which
varies with the specific Condorcet method), can show the maximum
information possible without going into detailed ballot analysis
(which could require a *huge* amount of data, though truncated
versions of it might be manageable).

The raw ballot data should be available, *except* that some aspects
of it might be necessarily concealed, if secrecy of ballots is
important. This is because a ballot ranking *could* identify a
ballot. For example, in a 10-candidate election, one coercing a vote
could require the voter to rank the lower 9 candidates in a sequence
such as to make it extremely unlikely that a voter would
spontaneously rank them that way. This becomes even easier if
write-ins are allowed and are tabulated and reported.

However, a judicious choice of what data would be suppressed (by
being summarized in a way that conceals less-significant ballot data)
could leave the remainder of the data reasonable to open for public
access. In that 10-candidate election, perhaps only full data would
be available for the top N candidates, perhaps four or five. Or only
the data from ballots where there are N identical ballots, in the
topmost ranks.

This is the data that would be of significant interest.

Of course, with Asset Voting, the whole exercise becomes unnecessary.
Asset approaches the voting problem in an entirely different way. As
one way to vote Asset, pick the person who you would prefer for the
office, or, alternatively, whom you would prefer to choose who wins
the election. The latter is the most important, but this might
usually also be the former.

The skill for governing and the skill for choosing reliable governors
is essentially the same skill, because one who does not have the
latter would be unsuited for the former, since any governor must
essentially delegate a great deal of authority, or be overwhelmed and
dysfunctional.

```