[EM] 2 oddities. Use for Borda(=<). Clarification.

[Michael Ossipoff]

I’ll start with the very brief clarification:

 I meant to say that Smith//Mid replaces Smith//Borda(=<) as an
autodeterent proposal of mine.

Use for Borda(=<):

First its definition again:

Your ranking gives to each candidate (of the Nc candidates) point for every
candidate that it doesn’t rank over hir.

Each of your equal top-ranked candidates receives the full maximum points.

But, the more candidates you bottom-rank, the more weakly they’re downrated.

Say you bottom-rank Worst. S/he gets 0 points.

Then say you also equal bottom-rank 2nd-Worst. Now Worst & 2nd-Worst each
get 1 point. You’ve weakened your downrating of Worst.

So you should instead rank 2nd-Worst at 2nd-from-bottom, directly above
Worst.

Now 2nd-Worst still gets only 1 point, & Worst still gets 0.

Likewise all the way up, among your disliked candidates.

This answers the often-expressed wish for a point-system to incentivize
varied-rating.

If that’s important, then Borda(=<) could also be used as a
Condorcet-completion method.

I wouldn’t. I prefer the Condorcet versions I’ve proposed for deterring or
thwarting offensive strategy.

Likewise I prefer Score to Borda(=<), because I want to fully bottom-rate
all of the Unacceptables.

I just mention Borda(=<) in case someone wants what it offers.

The oddities:

1.

An author, in an academic journal paper, proposed the following method:

Drop the weakest defeat in each cycle.

[end of definition]

As goes without saying,  there’s then always an unbeaten candidate.  …& as
goes without saying, s/he wins.

Speaking for myself, that sounds like a briefer wording of Ranked-Pairs
(RP).

But the author says it’s better than RP, & that it meets strong no-show
criteria that no other Condorcet method meets.

I don’t know how it differs from RP, other than briefer wording.

He also speaks of some ways that a (presumably) sincere circular-tie can
allow a spoiler, but not in his method, which he calls “Split-Cycles).

He defines a criterion, “Winner-Stability”:

If a wins, & another candidate b is added to the count, then a still wins
if a pairbeats b.

That combines guarantee about spoiling, & about someone taking away the win.

He says that Split-Cycles is the only Condorcet
method that meets Winner-Stability.

2.

Another author, also in an academic journal paper, called “The Myth of the
Condorcet Winner”, supports his claim that the CW (& the Condorcet
Criterion) isn’t the only valid standard for the best winner.

That isn’t news to many of us.

e.g. I prefer the Cardinal methods, except for in the current conditions
with so many lesser-evil voters.

 …& there’s no reason to say that the CW is better than the favorite of the
Mutual-Majority,  always chosen by Successive Topcount Elimination (STE)
(aka IRV or RCV), except for reassurance of lesser-evil voters, or people
who will be angry if a method elects someone to whom a majority prefer
someone else.

But what’s of interest is how he shows it. He speaks of
completely-symmetrical cycles, for which it must be a tie, because all
candidates have exactly the same status.

He calls such a cycle a “Condorcet complement, IIRC.

He points out that every cyclical contains 1 or more Condorcet complements.
  …& that when they’ve been removed, 1 at a time, there’s always an
unbeaten candidate, who could be meaningfully called the winner.

He gives an example to show that that winner can differ from the CW.
Because his winner has perfectly good validity as someone who arguably
should win, that’s how he shows that the CW isn’t the only
abstractly-arguably rightful winner (as many of us already knew).

I expected that his method, in the example, had chosen the STE winner.

But no; in his example, STE chooses the CW.  …& his method chooses
differently from both.

So he has a 3rd standard, different from the CW, & different from the
favorite of the Mutual-Majority.

He doesn’t propose Condorcet-Complement-Removal as a method, but it could
be one. I have no idea what its properties would be, what criteria it
meets, or whether it has a guarantee of interest.

But the CW is the winner with practical importance when needed (It’s needed
now).

…& the favorite of the Mutual-Majority has emotional appeal, which the
Condorcet-Complement-Removal winner doesn’t have.
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