[EM] 3-valued Booleans inside rules, passing Condorcet (Re: [EM] "More often" (was: IRV and Condorcet operating identically)

[Craig Carey]

At 03\03\01 09:49 -0500 Saturday, Stephane Rouillon wrote:
...
 >what is the participation criterion?
 >
 >Steph
 >
 >Markus Schulze a écrit :
 >
 >> > FBC is the only criteria that favors Approval
 >> > over Condorcet.
 >>
 >> Condorcet violates the participation criterion.
 >> Approval Voting meets the participation criterion.
 >>

And the missing third sentence is: both statements are so
unimportant as to be best ignored.

There is no clue there on the weightiness of the claims. I am
sure that they are not important. Certainly that view can locked
down if the definition of the "criterion" is not available.

To the extent possible, please regard the following comments being
about an election having only the papers (AB), (B), and (C). For
that election, the Condorcet method has an undefined region of
quite a big size.

It is controversial to create a weak rule and see that it passes
some methods and not others. Instead a plausible rule that fails
all the methods that need to pass can be used, but it is length
(or bigness) of the worst failure is measured. It looked
interesting when 2 winner 4 candidate STV was proven at the STV
mailing list to be not monotonic with the support rise harmed
being about 17%.

Quite so. Shulze can tell us why he missed out using enough words.
Whether or not the participation axiom is a good friend of IRV or
not, it not figured out by me yet. However it is certainly a rule
that can be not used during design for being too weak. It could
be of interest when failing methods. Questions on its goodness can
be ignored while the details are not here. I really can't be bothered
considering whether Mr Schulze was correct in saying that the rule
failed one of those two methods. There can be two cases: the
participation axiom or whatever, is implied by a better rule or it
isn't. Then it can be rejected as a rule to not use, in both cases.
The idea that faulty methods can have their credibility raised by
getting a pass under a weaker rule, is fragile since the weaker
rule or strong (in this pro-monotonicity style) is susceptible to
being sabotaged by impurities in the support rise that should not
harm.

Also people that say that FBC is this and that, all of which are
untrue (while the comments are groper fish and the direction of the
groping is not too obvious, and maybe Ossipoff can post up some
equations), all seems to have more readily trusted and quoted by
some of the EM List new members, than what the stuff that Mr Schulze
writes.

Is this the same as the Participation Axiom ?. Is the person who
is the authority on rewording the definition of the
"participation criterion", Mr B Cretney?.

Problem 1. The rule says that when votes for a candidate disappear
then it does not change from a loser into a winner. Maybe only
FPTP papers were thought of. But this seems to be a example where
it should be possible to say that if A loses the first then it
should lose the second. The possible problem is that the rule
either rules out this alteration or it is incomplete/vague:

.1000 A
. . 2 B
. . 3 C
. 400 BCA
. . x S

.1000 A
. . 2 B
. . 3 C
. 400 BC  <-- so A has to stay losing, (participation axiom)
. . x S

There might very easily be a problem: this is OK for the
"participation criterion" but whoever defined it, didn't get the
definition to allow this.

In a past message, Mr Schulze initially didn't see that the
preceding preferences would need to be kept constant. (In this
example the "BC" papers).

I can only complain about the "criteron"-ization of rules.
Literature is hardly better if calling it an "axiom" when it is
not used in a theory.

So Condorcet meets the partipation criterion, and hence the
rule ("criterion") excuses the method every time it can't find
any winners in one of the two cases.

Suppose the method returns whatever, and the rule handles the
result by converting it into a scalar value using this?:

    Term := {} /= (L . Winners)

There "." is an operator to intersect sets. The rule then
processes that term using OR, AND, Exists, and For_All.

Does Condorcet return and undefined value (a third value of the
2 valued Boolean scheme) ?, or does it just make the set of
Winners be an empty set.


CASE 1:
If Condorcet (etc) returns an undefined value, then the rule does
not fail it and it does not pass it, but instead it returns an
undefined result. To fix that, the undefined value has to be
explicitly converted into either true or false.

CASE 2
A fairly natural thing for a method that gets the wrong number of
winners, is to return whatever it could return. For that case
the rule is very likely to unforgiving over a failure to get the
number of winners correct. Extra text/symbols may have to be
added before Condorcet can be passed.

There is no problem with multivalued methods: the result of the
rule is multivalued. Also the rules can easily handle all ties
correctly. It is up to the method to hide all internal ties, i.e.
flats of undefined "outcomes" where the winner sets on both sides
are the same. The simplest thing to do is to fail the method and
force the method design and fill up the cuts that have the same
winners on both sides.

A question is: is there a rarely seen philosophy that likes to
rename rules as criterion and thinks that when that is done,
then methods that can't always get the number of winners right,
are passed, and WITHOUT the extra code making it forgive the
lapse, being added to the quantifier logic of the rule.

I guess we sould see the classic Shulze brevity in respose to
this. The target here is the http://www.condorcet.org/ group.

At 03\03\01 09:49 -0500 Saturday, Stephane Rouillon wrote:
...
 >what is the participation criterion?
 >

With me having the rules down to about 3:
  * Right number of winners (no undefined values)
  * P2 ( 2(AB) = (ABC)+(ABD) if all candidates = {A,B,C,D}, etc.)
  * Interim Equal suffrage (defined with 2 statements about
    preference shifting)

Maybe the 1st two could be merged into the 3rd. To impose a
right number of winners rule, can be done by making the touching
rigid (snap-rotatable) polytope that defines the acceptable
normal vectors, be empty.

With P2, the touching polytope of Equal Suffrage is cut up into
a subspace and the quite possibly the definition of Equal Suffrage
is changed.

______________

G. A. Craig Carey

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