[EM] Quick elimination of useless rules: my Meta-rules

[Craig Carey]

What are the seeming comments against the Electoral College for?.
It provides proportionality by providing a weighted summing of the
votes. A page here shows the weights. The pages allows a conclusion
that Demorep's wee comments adverse to the Electoral College would
be opposed California and Texas and other states.

The list probab



At 01:52 02.10.00 -0400 Monday, DEMOREP1 at aol.com wrote:
 >CVD is more than a little unhappy with Plurality (FPP) (i.e. minority rule
 >for single winner offices).
 >
 >U.S.A. voters are rather simple minded regarding math due to the massively
 >rotten public schools.
 >
 >Thus, Condorcet (head to head) math is somewhat difficult for lots of
 >ex-public school folks (notwithstanding the listings of various head to head
 >matches of sports teams).
 >
 >40 of the 50 U.S. States use plurality in primary elections. 10 have top 2
 >runoff primary elections (to get some attempt at majority rule at least in
 >primary nominees).  Many local governments have nonpartisan top 2N primary
 >elections (N to be elected).
 >
 >Few, if any, governments in the U.S. have runoff general elections if no
 >candidate gets a majority (happening more often with more minor parties in
 >more local elections).
 >
 >The above is why I suggest a simple YES/NO vote for single winner offices
 >(i.e. a variant of simple Approval) as the first (and only) step (until 
there
 >is widespread usage of Number Voting (1, 2, etc.) for proportional
 >representation elections) (to produce my suggested YES/NO, Number voting for
 >head to head, and summing of place votes if there is no head to head winner).
 >
 >The very dangerous and evil machinations of the 12th Amendment of the U.S.
 >Constitution on 7 Nov 2000 may easily produce a U.S. President who gets
 >elected in the infamous so-called *Electoral College* (538 partisan robot
 >Electors, 270 majority) with a minority of the popular votes (by the real
 >voters) AND gets less popular votes than the other major party candidate.
 >
 >The resulting uproar may produce some immediate and very serious movement 
for
 >election method reforms for such office (and thus other offices such as 
state
 >governor, city mayors, etc.)-- i.e. the EM list should try and get its act
 >together as an semi-emergency matter.

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The list ought set for itself an aim that no new rule is added without it
threatening another rule. Here is Mr Schulze: is he adding one rule or two,
in this next comment?:


At 02:35 02.10.00 +0200 Monday, Markus Schulze wrote:
...
 >I consider the independence from clones criterion to be more
 >important than the participation criterion. Therefore I prefer
 >IRV to FPP.
 >
 >Markus Schulze

Which rules are displaced?. It seems to not interest Mr Schulze.
I fancy it doesn't interest me. The smorgasboard of EM rule theory: tried
and proven to produce no results over 3 years. How long has it actually
been Markus?.

There is probability near 1 that these simple questions over incompatibility
can be answered using 3 or 4 papers in a 3 candidate election examples. The
'clones criteria' is rather difficult to understand. Mr Schulze should have
a mathematical formula (in my opinion) and not try to use English to
explain it. I had trouble with the explanation. Do try to define it say
using a formula that has a variable representing the number 7, when it is
making a Boolean statement about the 7th preference.

I dispute the "participation criteria" because it is very weak.
I seem to recall that Mr Schulze never defined it for cases when there is
more than 1 winner. I'd reject Markus Schulze's participation axiom with
unaltering finality on these two grounds:
(1) It is not defined for all numbers of candidates, nc=1,2,3,4,...,
     and numbers of winners, nw, where 0<=nw<=nc.
(2) It is too weak compared to P1. I suppose that P1 implies it. It has
     every appearance of being a useless idea [permitted paths have to lines
     through vertices.

Since there is such a bad tendency of writers to become secretive when
their own very bad ideas are questioned, maybe the list [for the moments
while I am still subscribed] could test all the rules against these
next meta-rules. The leave carnage of the list's rules ideas, and in
my opinion, they don't seem to get rid of a single rule that should be
retained

The Carey Meta-rules:

(I) The relative power of the rule does not decline too rapidly as the
     numbers of winners approaches being infinite. If there is  a violation
     of this, then the number of candidates when the rule has 1/100-th of
     the influence a good rule would have, can be calculated. We can
     devise definitions that return the sequence that has element NC[k]
     equal to the number of candidates when the rule has a constraining
     power equal to ((1/1000)**k)*(a power it ought have).

(2) The rule is well defined for all numbers of candidates nc, and all
     numbers of winners, where nc,nw=0,1,2,3,4,..., 0<=nw<=nc.

(3) Rules that seem to do something in a simplex of possible elections
     should be of the fullest power. For example, if they prohibit 10
     different papers alterations, then the rule must be investigated to
     see why it can't restrict all linear combinations (with non-negative
     weights) of those 10 types of alterations of papers. Another example
     is making a statement about one paper being rewritten as another,
     when the rule can be fixed into a statement that is of the form of
     constraining alterations of the full set of winners [not 1 winner
     since 2 meta-rules that out] into ANY other paper. Monotonicity can
     be strengthened into P1 [if truncation resistance is held, and
     meta-rule 3 therefore rules out use of monotonicity when truncation
     resistance is held.

(4) Rules must be defined and they must be of use mathematically.
     This seems a little suspect. I intend to rule out rules that alter
     one paper into two. While such a rule can be written down, i.e.
     defined, it is not a rule that would be used. When Mike Ossipoff
     explains rules to the list and explains corollaries (if ever) then
     that is "not a use of the rule". Most of the time Mike Ossipoff is
     using a copy and that and the original are not free of the use of
     undefined variables. A rule that is in the axioms and that is not
     ever used in the derivations can't be doing much more than
     threatening the consistency of the axioms.


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

Regarding meta-rule (2) I comment:  There are documents
     around penned by Mr Rob Lanphier (one a www.dmoz.org?) saying
     that this list discussed 1-winner elections. It is discouraged by old
     documents, to discuss modern voting theory at the Election Methods
     list. The EM list is founded upon a 1-winner vision that should make
     it useless to all that is alive or dead. In an anology with free
     societies, there are not hidden beliefs that the number of winners
     is equal to 1. Rob Lanphier probably should make a public statement.
     His original intent might have been to keep the list limited to
     discussing the idealism reducing Condorcet method, but the same rule
     is now ruling against discussions of the hardly more useful repaired
     Condorcet variants. I know what the subscribers want to tell me:
     these rules are just there for the tiny minority of mathematically
     minded morons and the real experts in voting theory can have upto
     6-10 different definitions of the same rules and shift and slur
     between them without noting or understanding that. It is adverse to
     progress.

Mr Commissar Spitzin Terrog, Mr Blinker Kretney and Bart Approval
Lossy Junior. (unsubscribed), and Mr Marijuana Bristle Floating Pea, and
Mr Renewed Moderator of the Reformed Single Holy Cross (fell from the
Internet), and the CVD Retardation and Mathematics Secretions Protection
Council (a reformed Board) and Bathyclese -- they all could have some of
these rules ruled out. By the time you read down to here, some of them
have already rejected all of the meta rules. My P1 is perhaps one of
the most significant discoveries in preferential voting theory in recent
time and so far none of these messages posters have warmed to the task
of thinking about it sufficiently to reject it or say it is...a bad
rule. Let's see what Demorep makes of Meta-rules.