[EM] Covering Embarrassment

[Forest Simmons]

For the benefit of people new to the concept of covering, I should point
out that not being covered by A is equivalent to having a beatpath to A of
two or fewer steps. So an "unqualifiedly" uncovered candidate has, for each
candidate X, a short beatpath (fewer than three steps) to X.

The beauty of a short beatpath is its immediacy compared to a longer one
... as the path gets longer it kind of leaks information like the telephone
game.

Note, for example, that a beatpath whose weakest step is a 100%n/(n+1)
defeat cannot cycle in fewer than (n +1) steps ... the stronger the
beatpath, the more steps necessary to lose transitivity. Conversely. the
shorter the beatpath, the more likely the defeats will survive the entire
length of the bestpath.

 Notice, in particular, that if B defeats both A and every candidate that A
defeats, then there is no beatpath of length one or two from A to B.

Note also that the covering relation (unlike the ordinary defeat relation)
is transitive:  if C covers B, and B covers A, then C also covers A.

-Forest



On Sun, Sep 11, 2022, 5:18 PM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

>
>
> On Sun, Sep 11, 2022, 4:05 PM robert bristow-johnson <
> rbj at audioimagination.com> wrote:
>
>>
>>
>> > On 09/11/2022 6:12 PM EDT Forest Simmons <forest.simmons21 at gmail.com>
>> wrote:
>> >
>> >
>> > Have you every had one of those dreams where you are out in public and
>> suddenly notice that you are unclothed?
>> >
>> of course.
>>
>> > 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.
>> >
>>
>> Well, now I need a definition of a what or who is "covered".
>>
>> > 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.
>> >
>>
>> okay, so A pairwise defeats a bunch of candidates that B also does, but B
>> defeats A.
>
>
> Not so fast.  B covers A only if B not only defeats  A, but also B defeats
> or ties abdolutely every (not just a "bunch of") candidate defeated by A.
>
> Could there be Candidate C that defeats them both, head to head?
>>
>
> Yes, and if C were the CW then every candidate except C would be covered.
>
> A Condorcet winner is always uncovered, and  when there is no Condorcet
> winner, at least one member of the Smith set will be uncovered. In general
> every non-Smith candidate is covered by every Smith candidate ... the
> uncovered set (the "Landau set") is always contained in (sometimes
> properly) the Smith set.
>
>>
>> > In other words, A wins, but A is covered (by B for example). Wouldn't
>> that embarrass A?
>> >
>>
>> well, obviously minority-elected candidates win and are not embarrassed
>> for winning an election.  Like both W and the evil T****.  They can deny
>> the problem (like this is too complicated) or they can make up and excuse
>> (Montroll or Begich didn't get enough base support)
>>
>> > 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.
>> >
>>
>> This being "covered" thing isn't a problem if the Condorcet winner is
>> elected, if a CW exists, is it?  Does it manifest when there is a CW?
>>
>
> No, only when there is no CW.
>
> So a simple way to ensure that the CW will always win when there is one,
> to apply the "afterburner" to every election as a matter of policy. This
> policy ensures more ... it ensures that a Smith candidate will win if there
> is one, and that that Smith member will also be a Landau member.
>
>>
>> How many elections do we expect to lack a Condorcet winner?  So far,
>> FairVote has looked at, they used to say, 440 U.S. RCV elections, all had a
>> CW, and only one failed to elect the CW.  Now there are two anomalous
>> elections, Alaska 2022 and Bulington 2009.  So far 100% having CW and 99.6%
>> electing the CW using Hare RCV.
>>
>
>
> Not every ballot CW is a sincere CW.
>
> In fact, because IRV is so defacto vulnerable to compromise, as well as to
> Duverger's Law,  voters tend to make up for IRV''s lack of sincere
> Condorcet efficiency by both nominating and voting for compromise
> candidates ... ballot CW's that are not necessarily sincere CW's.
>
>
>> Must we use Copeland if there are easier ways to get the CW elected?
>>
>
> As I mentioned, Copeland is not a good option, because it is neither
> decisive, nor clone free.
>
> That's why a much more practical option is to add a simple, zero cost
> "afterburner" that protects any method against Covering Embarrassment.
>
> That said, we now have clean, short beatpath versions of RP that can serve
> as stand-alone Landau efficient methods ... the ones mentioned above that
> we introduced a few weeks ago ... "without fanfare" ... maybe we should
> have hired a brass band:-)
>
> -Forest
>
>>
>> --
>>
>> r b-j . _ . _ . _ . _ rbj at audioimagination.com
>>
>> "Imagination is more important than knowledge."
>>
>> .
>> .
>> .
>>
>
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