[EM] Why All the Fuss?

[Forest Simmons]

Why can't we just have majority rule? Why all the fiss?

Many a student of my "Math for Liberal Arts" class asked me that question
during the decades I taught the Community College course by that name.

 That's the reason Joe Malkovich's contribution to the textbook was so
important ... his examples of ballot profiles for which no two of several
different majority rule methods agreed on who should be elected.

Most if not all of these methods start out with the phrase..."Elect the
majority winner if there is one, otherwise cull out the weakest (meaning
democratically weakest) candidates one by one until there is a majority
winner among the remaining."

But there is no agreement on what constitutes "democratically weak' ... and
it makes a big difference!

So what can we do?

One thing we have tried without much success is to suggest that the next
best thing, lacking a first preference majority winner ... is to elect the
candidate unbeaten by any majority comparison with another candidate.

But just as there is no guaranteed outright majority winner ... neither is
there any guarantee of the existence of a pairwise unbeaten candidate.

It turns out that the best we can guarantee along these lines is the
existence of at least one candidate that can pairwise beat in two steps
every candidate that he cannot defeat in one step (by a majority of the
participating voters).

Such a candidate is said to be "uncovered."  We're going to need a better
word than that if we want to get anybody on board with this minimum
guaranteeable standard of "majority rule."

Let's say a candidate is "democratically strong" if it has a beatpath to
every other candidate ... and is "very strong majority pairwise" if it has
a beatpath of one or two steps to each of the other candidates ... each
step being a pairwise victory by a majority of the participating voters ...
meaning voters expressing a preference.

Then the "Strong Majority Pairwise Criterion" (SMPC) is satisfied only by
methods that always elect uncovered candidates.

Contrast that with the weaker, relatively impotent Condorcet Criterion
which is satisfied by any method that elects an unbeaten candidate "when
such a candidate exists" ... the copout escape clause in quotes letting the
method off the hook whenever things start to get interesting.

Another way to express compliance with this SMPC criterion is "Landau
Efficient."

Every method under the "Worst-Elimination" umbrella is seamlessly Landau
Efficient ... it effortlessly (and without fanfare) satisfies the SMPC ...
no matter what nominal standard of worst is instantiated into the umbrella
template.

Who can name even one commonly known election method that is Landau
efficient?

What's more ... no matter the nominal "worst" criterion, the method will be
more or less burial resistant ... as I will explain presently.

I suggest that proposals for any method under this umbrella, include
verbiage to the effect ...

"When there is no majority winner or any candidate that a majority of the
participating voters rank ahead of each of the other candidates ... cull
out one-by-one the nominally "worst" candidates as well as any
democratically weaker candidates (as determined by majority ballot
preferences) until there is a majority winner among the remaining
candidates."

This umbrella is so robust that the choice of nominal "worst" is not overly
critical.  The main thing is to keep it simple enough that (1) voters can
easily understand and relate to it, and (2) it can be efficiently and
transparently tallied by precinct without multiple passes through the
ballots.

Complicated "worst" criteria are the ones that tend to introduce crowding
and teaming distortions ... smallest Borda score is a example of this kind
of "worst" criterion ... pun intended.

Anti-vote splitting can be easily ensured (in general) by allowing
equal-top whole counting, and multiple truncations in large elections.

In the continuation I will explain why this method tends to backfire on
buriers.

At some point those who have power to advocate for one method over another
need to understand them beyond the surface heuristics that appeal to the
impatient public.

Among other things enlightened defenders of electoral democracy need to
understand the "squeeze effect" and "burial ploys" ...

To be continued ...

-Forest
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