[EM] Covering Embarrassment

[Forest Simmons]

Have you every had one of those dreams where you are out in public and
suddenly notice that you are unclothed?

Well, nearly all election methods, Condorcet or not, that are either now in
use, or have been seriously proposed, suffer from the opposite problem:
they have no guarantee against electing covered candidates.

How (outside of a nudist colony) could that be a problem?

Well, suppose candidate A wins an RCV election of some kind, and the
ballots clearly show that candidate B outranks candidate A on a majority of
the ballots, but B is not head-head defeated by any candidate that A
defeats.

In other words, A wins, but A is covered (by B for example). Wouldn't that
embarrass A?

The B supporters would be more indignant, vociferous, and sarcastic than
even Trump, (unless B were like a spineless Gore, who capitulated without a
peep).

Why hasn't anybody addressed this elephant-in-the-room potential
embarrassment?

Answer: for the simple reason that up until very recently, the only known
monotonic RCV method immune to this embarrassment was Copeland, a clone
dependent method lacking a lot in decisiveness.

The first RCV method to decisively crack this barrier (earlier this year)
was Decloned KY Chain Climbing ... nice theoretically, but too esoteric for
public proposal.

More recently, and more practically, Kristofer and I have introduced
(without fanfare) a class of short beatpath methods that always elect
uncovered candidates monotonically and clone-free from RCV ballot sets.

Within that class, methods differ by different gauges of defeat strength,
in the same way that different versions of Ranked Pairs differ among
themselves.

My purpose in this post is not to propound any particular uncovered method,
but to give a general recipe for retro-fitting all currently used RCV
methods ... in order to confer upon them Covering Embarrassment Immunity.

Here is the Afterburner procedure for installing that retro-fit:

Initialize X as the (before retro-fit) method winner.

Then ...
While X is covered, replace it with the alternative (from among those that
cover it) with the one defeating it with the greatest defeat strength.
EndWhile

Elect the the final value of X, (i.e.the last candidate pointed at by the
variable X).

[Now you can see our main purpose for initiating our recent Defeat Strength
thread.]

Notice how naturally this "Afterburner" procedure confers Covering
Embarrassment protection onto Ranked Pairs!

It can do the same thing for IRV, Coombs, Borda, Bucklin, Kemeny Young,
DAC, DSC, etc, as well as for non-RCV methods that may admit inference of
ordinal preferences ... such as MJ, STAR, Approval Sorted Margins, DMC,
SPE, etc.

One of my favorites is Afterburner Fitted Usual Judgment (AFUJ), because UJ
by itself has only one serious technical defect ... potential covering
embarrassment.

In particular, the recent IRV embarrassments in Burlington and Alaska would
have harmlessly, and unceremoniously bounced off this shield.

Also, note that an afterburner shield protects against Burlington
embarrassments, but an upfront CW check does not guarantee protection
against covering embarrassment.  Afterburner protection is stronger than a
mere CW or Smith check up front ... even IRV restricted to Smith is not
immune to Covering Embarrassment.

So why would anybody resist zero-cost covering embarrassment protection?

Remember back in the 1970's ... the resistance against retro-fitting older
cars with seat belts?

"People will be trapped inside crashed cars!"

Doubtless we wil see the same reactionary attitudes about retro-fitting
current methods with "Covering Immunity Seatbelts."

Will a democracy ever arise on this planet progressive enough to make use
of it?

I'm optimistic about that possibility, but not optimistic enough to think
it will happen absent some kind of major revolution that saves our planet
from utter destruction.

-Forest
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