[EM] "More often" (was: IRV and Condorcet operating identically)

[Craig Carey]

At 03\03\02 00:19 +0100 Sunday, Markus Schulze wrote:
 >Dear Steph,
 >
 >you wrote (1 March 2003):
 >> I suppose you meant:
 >>
 >>   Suppose that candidate A is the winner. Suppose that
 >>   a set of voters, where each voter strictly prefers
 >>   candidate A to candidate B, is added to the original
 >>   profile. Then candidate B must not become the new winner.
 >
 >Yes. You're right.
 >

When Mr Schulze is brief then wrong too (maybe in general).

Firstly voters should be changed to papers.

The rule is one that is undesirable and it would not be an axiom.
So far Mr Sculze has not said that it is important. Complaining
about that would seem appropriate but the definition was not
available.

Now, we still have no definition.


This is to be allowed rather than prohibited (Mr Schulze appears
to be speaking against it):

    The "We" in the text described ballot papers grouped by their
    leading preferences.

   ----------------------------------------------------------------
   We'll take A and if not available then B, and we'll take C and
   if C's not available, then D.
   ----------------------------------------------------------------

Take is like desire. Mr Rouillon might otherwise write in and
suggest he could learn something when that is not likely to be
true: whatever that desire is, if it is not represented by an
equation that it can't be about rules uses in the design of
methods or for when they are rejected. I don't use rules to
reject (e.g. STV) that were not tested by having them axioms.
A bad option is to call a "rule" a "criterion". Presumably the
motive is that can reject methods. That fix seems to only
reduce the chance of the rules being rejected. But we need to
know who it was that came up with the idea of calling a rule
a criterion, before the non-monotonic topic of achieving the
opposite of the purpose becomes more interesting.

Here is an example:

Election 1: Papers = S1,          Winners = {A}
<-->
Election 2: Papers = S1 + (CDAB), Winners = {B}


Mr Schulze made just about the same mistake years ago, in this
mailing list, when replying to me. The mistake being to have the
preceding preference list not be the same in the two elections,
when commenting on candidate that didn't have the 1st preference.
to remind Mr Schulze, the topic was

     'should voters be punished for arriving at the election booths'.

The example below shows that they (i.e. papers) would be punished
with remarkable severity.


--------

Consider this (irv-wrong-winners, yet another wrong Mayor in office)
See that there is a large support rise for A and that causes
A to lose. This is nearly showing that the Alternative Vote
violates the Participation Axiom (unless I remember it incorrectly).


 >   ----------------------------
 >     A       19999      80004
 >     B           1          5
 >     BA      19997      19997
 >     CB      40002      40002
 >     DBA     20001      20001
 >   ----------------------------
 > Total:     100000     160009
 > AV Winner:      A          B
 >
 >1:1:elim B: 19997+19999=39996(A)
 >1:2:elim D: 39996+20001=59997(A)
 >1:3:test 40002(C)<59997(A)-->A wins
 >2:1:elim D: 20001+19997=39998(BA)
 >2:2:elim C: 40002+5+39998=80005
 >2:3:test 80004(A)<80005(B)-->B wins


Recapitulation: a huge 37% of the vote vanishes and they are all
  FPTP votes too.

--------------

That looks like a "classical participation axiom" problem (but it
is not since B got 4 votes).

Shulze wrote Yes but meant "No". A slip up of that sort is always
possible when the aim is to withhold the definition from
mathematicians while trying to lead others to believe that it
is indeed held.

Some things slip through the CVD cracks in wooden-floored building.

The META-RULE:

When that rule considers 2 or more election examples, then it will
impose that which is implied by the adding of the same preceding
preference list to all the papers that change in the examples.

A restriction of course is that the not-changing papers are
not considered by the rule but they could be considered by the
method being tested. Maybe the method has to be a fair method or
one that is all about restrictions on winners when altering papers.

This is about where the messages start to go downhill.

Shulze had a long military commander's stick and waved it and said
no factions shall form when over 50 million ballot papers. I
forget the name of the principle is and maybe Mr Schulze would
give it a name, for us.







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