[EM] Truncation

[Forest Simmons]

On Thu, 19 Sep 2002, Dave Ketchum wrote:

> For the case I presented I care not about secrecy, and said nothing to
> suggest an interest in borderline decisions.  My goals were clear, and
> were presented.  The problem is in how to accomplish them since I can
> suspect others may be able to walk over me by understanding better how to
> take advantage of the flexibility offered by these rules.

I will let Rob LeGrand respond to the desirability of freely allowing
equal ranks elsewhere than the bottom (the usual convention for
truncation), and how much (if any) that would complicate or simplify
strategy in Condorcet methods.

It does seem to me that when the front runners are all bottom dwellers,
equal ranking near the top among more or less equally acceptable
candidates would make more sense than equal ranking at the bottom.

But correct me if I'm wrong; it seems to me that (up until now) your
biggest concern about ratings has been that it is relatively easy for you
to rank candidates, but relatively hard to rate or grade them. If so, how
can you say that borderline decisions don't interest you, when they pose
the only non-trivial challenge in the conversion from ranks to rates?

The simplest example of that is in filling out a two grade (pass/fail)
i.e. Approval ballot when there are three candidates which you have ranked
A>B>C.  You know that you should pass candidate A and fail Candidate C,
but how about candidate B?  Sometimes the answer to this question is
obvious.  When it isn't, then B is a borderline case, and a coin flip will
suffice nicely.

At resolution six or above these borderline decisions become less
excruciating.

Here are some other examples of conversions from rankings to Grade Ballots
showing the trivial nature of the non-borderline type decisions.

Suppose that the method is Ranked Pairs and that there are four candidates
which you want to fully rank on a Grade Ballot.  Then for instrumental
purposes it doesn't matter which four of the six grades you use for the
ranking, but you may gain psychological satisfaction from showing your
strongest preference by skipping a letter or two, or by not giving any
candidate a grade of A or B.

Suppose on the other hand that there are seventeen candidates and the
Grade Ballot (with plus/minus options) allows only sixteen distinct
grades.  Then you have to collapse at least one preference.

As long as at least one of the candidates in the collapse is not a front
runner it will make no difference in the election outcome.  Since it is
unlikely that all seventeen candidates are front runners the collapse can
be chosen at random among your minimally strong preferences which do not
involve two of the front runners.

A collapse made in this way will have no effect on the winner of the
election and no statistical effect on the grade point average of any
candidate.

It seems to me that the difficulty in a seventeen candidate election is
in ranking the candidates, not in converting a ranked ballot into a grade
ballot.

In any case you can do what they do in Australia, copy a sample ballot
recommended by your favorite party, union, or candidate.

If you feel strongly that the sample ballot gives too high or too low a
grade to some candidate, you can change it without having to explain your
reasons to anybody but God.

Another option recently suggested by Stephane is using grades A through Z.
By supplementing with plus/minus you could distinguish as many as seventy
levels even when leaving out the letters O and I that look too much like
zero and one.

A ballot might look like

Shade One Grade per Candidate as well as (optional) Plus or Minus Signs:

John Brown   A B C D E F G H J K L M N P Q R S T U V W X Y Z  +  -
Josie Rose   A B C D E F G H J K L M N P Q R S T U V W X Y Z  +  -
[etc.]

A reminder that A+ is the best possible and Z- the worst, would not be
totally redundant, like the warning label on steam irons, "Do not iron
garments while wearing them."

Although I prefer sticking to resolution six or lower, Stephane's
suggestion still beats numerical rankings and ratings, since it avoids the
main source of confusion.

Forest

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