Pairwise Vote Terminology (was Re: "Votes over")

[Norman Petry]

On March 20, Bart Ingles wrote (Re: Pairwise Vote Terminology (was Re:
"Votes over")):

>I kind of like:
>
>- Votes-Over (vo) in place of Winning-Votes
>- Weakest-Quorum (wq) in place of All-Votes (might be stretching the
>meaning of 'quorum', but at least this is more specific)
>
>I assume neither votes-under nor strongest-quorum would be useful
>concepts.  If necessary to make a further distinction:
>
>- Strongest-Votes-Over (svo) for a system that immediately picks the top
>pairing, and
>- Weakest-Votes-Over (wvo) for one that progressively eliminates the
>weakest pairing.
>
>You could probably use Strongest-Margin and Weakest-Margin in the same
>way.
>
>Do any of these correspond to previously-used terms (such as VA), or to
>particular methods or classes of methods?

What I was attempting to do by proposing the terms "winning-votes" (wv),
"losing-votes" (lv), "all-votes" (av) and "margins" (m) was distinguish
between the four different ways of addressing the problem of truncation
and/or pairwise abstention in *ANY* pairwise count rule.  The terms Blake
and I proposed were intended to convey in a value-neutral way the
distinctions between these four variants.  I was *NOT* attempting to rename
any existing methods.

For any pairwise method (that is, a method which uses only a matrix of pair
wins & losses to determine a winner), it is possible to pre-process the
pairwise matrix before applying the method to produce each particular
variant.  The first three of these approaches use "absolute votes", since
they use actual votes for counting purposes.  If "winning-votes" are used,
the pairwise minority totals are zeroed.  "Losing-votes" would zero the
pairwise majority totals, and "all-votes" (or "both-votes") just uses the
pairwise matrix directly (majorities and minorities).  Margins uses
majority-minority differences, if positive, or zero otherwise.

This terminology can potentially reduce the name confusion found on this
list, by allowing us to use a single term for the underlying method, and
added descriptors (where necessary) to distinguish between the variants.
For example, one simple method which has been discussed on many occasions
and named in many different ways is designed to minimise the number of
voters who would be *against* a particular candidate being elected.
Depending on the variant being discussed, it has been referred to as:

1. Condorcet(EM)
2. Plain Condorcet (PC)
3. Condorcet(VA)
4. Simpson-Kramer
5. Minimax
6. Maxmin (?)
...

It really doesn't matter which term is used to describe this method, but it
seems simpler to me if we pick *ONE* term (say, "Plain Condorcet") to
describe the basic procedure, with the designators I proposed (or something
better) to make the differences clear.  Here are some methods I've renamed
using this approach:

1. Condorcet(EM) --> Plain Condorcet(wv)
2. Plain Condorcet --> Plain Condorcet(wv)
3. Condorcet(VA) --> Plain Condorcet(wv)
4. Simpson-Kramer --> Plain Condorcet(av)
5. Minimax --> Plain Condorcet(m)
6. Maxmin --> Plain Condorcet(m? lv?)
7. Schulze --> Schulze(wv)
8. Path Voting --> Schulze(m)

Of course, each variant of a particular method is unique; some have merit
while others don't.  Still, one reason to classify the methods this way is
that it allows us to intelligently discuss the properties of either the
methods (schulze,tideman,...), or the variants (wv,lv,av,m) in an
intelligent way without getting bogged down in details about the other
issue.  For example, one thing I've observed while simulating these methods
& variants is that each basic method will have a particular performance
curve, with each variant modifying the basic response of the method in a
predictable way.  All-votes variants generally have higher accuracy;
marginal methods have better accuracy when truncation is minimal; All-votes
methods generally fail the Smith criterion; marginal methods always fail
GMC, BC, etc.

Therefore, I prefer to stick with the terminology I proposed.  It seems to
me that you are inventing terms which merely add to the confusion we have
already, since some of them appear to be rather vague descriptions of
existing voting *methods* (svo = Tideman? wvo = SD?), while the others (vo,
wq) describe *variants*.  Also, while it wouldn't really matter whether we
use 'va', 'wv' or 'vo' to refer to methods which only consider pairwise
majorities, I find the terminology you proposed to be *more* confusing than
my proposal.  For example, "votes-over" to me suggests margins, and "weakest
quorum" doesn't suggest any clear meaning (since quorums refer to the
minimum number of voters that must participate for an election to be valid,
and this is a consideration which is entirely irrelevant to the count rule
used).

I hope you will see the logic in this approach.


-- Norm Petry