[EM] Fwd: Introduction, brief definition, and arguments for RP

[Michael Ossipoff]

Though I still don't recommend RP, River, or Beatpath for current
(U.S.)conditions, but only for ideal majoritarian conditions, they're
probably good for most polling, except maybe leading up to an actual
official election.

With a Condorcet method, successful chicken-dilemma defection causes a
top-cycle. But it's known that top-cycles are very rare in polls.
Therefore, successful chicken dilemma defection isn't happening in
ranked polls.

When, at EM, we say RP, we aren't referring specifically to Tideman's
RP. We mean it in a more general sense. Here is how I define it:

Disregard each defeat that cycles with (only) stronger
not-disregarded, defeats.

[end of RP definition]

Not only is it one sentence, but it only requires one short line.

You could say it in terms of keeping (opposite of disregarding):

Keep every defeat that doesn't cycle with (only) stronger kept defeats.

[end of alternataive RP definition]

At least those are very brief definitions for when there are no
ties--Ties are vanishingly rare in public elections.

For River:

After "cycle with", add "or duplicate one or more".

Two defeats duplicate eachother if their defeated candidates are the
same candidate.

Of course, for anyone, like the general public, who isn't familiar
with those terms, they'd have to be defined. But that would happen by
itself, when rank-balloing and pairwise-count are introduced to
people:

Pairwise-Count & RP introduction:

Say you vote the ranking Z>X>Y.  Why did you rank X? Because you want
to defeat those you like less than X. In this case, that's Y.
Presumbly you're saying that you'd rather elect X than Y, and that if
you have to elect X or Y, you don't want to elect Y.


If more people rank X over Y, than Y over X, then that is a public
decision that X is better than Y. A public pairwise decision to that
effect. Such a decision is called a "defeat" of Y.

Those who ranked X over Y are saying that they don't want Y to win.
Those who ranked Y over X are saying that they don't want X to win. If
more people ranked X over Y than vice-versa, then the public decision
is that Y shouldn't win. And so Y shouldn't win.

Usually there's exactly one candidate who doesn't have that public
decision that s/he shouldn't win. S/he should win.

In that way, all of the public pairwise decisions can be honored.

With a small number of voters, there could be more than one such
candidate. They should all win (or be chosen-between with some
tiebreaking procedure).

But sometimes 3 or more candidates beat eachother (where "X beats Y"
means that there's a public pairwise decision for X over Y) cylically:
 X beats Y beats Z beats X.  That's called a 'cycle". Then, can be
impossible to honor all of the public pairwise decisions, because
everyone is beaten.

To elect anyone, 1 or more defeats must be disregarded, not honored.
"Kept" means not disregarded.

When defeats are in a cycle, they nullify eachother, because, in that
cycle, all of the cycle's candidates have the same beaten-status, and
the same "better-than" relation to eachother.

Keep each defeat that is in a cycle with (only) stronger kept defeats.

Here's the obvious procedure for that:

One at a time, in order of stronger first, consider each defeat as follows:

Keep it if it isn't in a cycle with some set of defeats that are aleady kept.

When all of the defeats have been so considered, a candidate wins if
s/he doen't have a kept defeat against hir.

[end of RP definition]

For RP:

After "isn't in a cycle with", add "and doesn't duplicate".

(In the case of duplicating, of course it could be a set of as few as
1 candidate).

Of course that 2nd definition, the procedure, is the usual definition
of RP. As for the first definition,the brief one, it may well have
already been posted here, or otherwise proposed before.

Michael Ossipoff