# [EM] Method Definition Considerations

Forest Simmons forest.simmons21 at gmail.com
Sat Jun 4 18:14:05 PDT 2022

```Traditional math exposition, whether text book, lecture, journal article,
or monograph,  tends to have a top down deductive logical structure that
belies all of the messy trial and error scratch work that accompanied the
creative process.

This was the style of Gauss ... unveil the finished work in all of its
polished, deductive logical glory, without any hint of the inductive
scaffolding or chisel marks that went into the finished work.

On the other hand, Euler led his reader through his discovery process ...
the  chronological sequence of insights that led to his results without all
of the tidying up that would conceal the nitty gritty details.

Pure mathematicians tend to admire Gauss's style, while most engineers and
other applied mathematicians have a greater affinity for the style of Euler.

I have learned from over 40 years of teaching mathematics at all levels
from basic arithmetic to linear algebra, and differential equations, as
well as probability & statistics, that about 80 percent of students want to
learn the "how" before the "why" .... about half of the rest have zero
interest in the "why" ... and the others are completely content with a
cursory understanding of the "why" before getting down to the nitty gritty
...which is the healthiest attitude, in my humble opinion.

What does this have to do with election methods?

Consider this example:

Elect the candidate that outranks any other given candidate on more ballots
than not, if there is such a candidate. Otherwise, elect the candidate that
on the most ballots outranks at least one other candidate. Resolve any
further ambiguity in favor of the tied candidate with the greatest number

To an election scientist this descripotion is a complete definition of what
has sometimes been called, "Implicit Approval Completed Condorcet."

It seems very concrete, down-to-earth, and nitty gritty. It specifies quite
precisely in plain English which candidate is to be elected on the basis of
a given set of voted ordinal ballots.

But we know from experience that the top FAQ will be, "How are we supposed
to find such a candidate?"

That question will never arise in connection with IRV.

Why not?

Because (1) the standard definition of IRV is entirely operational: step1,
step 2, etc. Furthermore (2) it is modeled on a well known run-off process.

My main point is that we need to keep this handicap in mind when broaching
any method for public consumption.

People expect an election method to consist of elimination steps described
in the language of vote transfers, in order to transparently preserve the
"one person, one vote" dictum.

Most people would not say that an election method "has" a counting
procedure ... rather they would consider the election method to "be"  a
counting procedure.

To them, two different counting procedures are two different election
methods, never mind the possibility that they could be equivalent methods
derived from a common characterization.

We ignore these considerations at our own peril!

I'm talking about public consumption. Of course ...  in technical discourse
(not intended for the lay public) it is a practical necessity to assume a
certain level of election science maturity.

The rule is to keep your intended readership in mind, and some kind of
"swim at your own risk" warning (explicit or implicit) for others.

Of course, some people want to read things for which they lack the
prerequisite knowledge. It might be good for them ... especially if it
contains words that excite the imagination!

-Forest
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