[EM] Two Paramount Criteria

Craig Carey research at ijs.co.nz
Fri Dec 19 23:56:01 PST 2003

At 2003-12-18 13:29 -0800 Thursday, Forest Simmons wrote:
>For me two paramount criteria are
>(1) simplicity of optimal or near optimal strategy, and
>(2) as much voting power as possible consistent with (1).

That is not based on evidence, Mr Simmons.
The so called Schulze method (that recently appeared in a prestigious
English publication, namely Voting Matters (PDF files are around),
had the appearance of failing these strict rules:

(1) The number of winners should be correct.
   indicates that the Schulze method found the wrong number of winners.
   As might be expected, Mr Schulze has not commented on that or produced
   a defence against the allegation. In fact, so very complex is the method
   in its polytope form (and a optimal method would be much simpler), that
   the assumption should be that the method is guilty until cleared.

(2) The method should not have some bias. This fails methods that ignrore
   the votes and pick the first (not best) candidate on a list the method

   Shulze's believed the count of the papers could be ignored and the number
   of voters could be counted. That is stupid and some people don't seem to
   be able to stop or explain themselves without pointing invalid assumptions.

(3) When the papers are like STV' the winners ought be insensitive to the
  presence or absence of the very last preference in one or more papers.
  That Schulze method seemed to fail this test.


Outside of here the methods are simpler and the passes are found using 
arguments instead of with testing.

>There are various possible definitions of "voting power," but it should
>have something to do with the probability of one ballot or set of ballots
>being pivotal to the outcome in an election chosen at random from some
>family of elections.

That is dumb since it is vaguely stated and it makes use of probalities
that do not exist. I have already considered and partly solved the problem.

The only solution I found is to start off by never defining "the power of
a ballot paper.

Approximately, the fairness of an equal suffrage rule is written down in its
 2 parts:

[1] multiwinner monotonicity requiring 0 <= power
[2] multiwinner one man one vote requiring power <= 1

Here I write on the power of a single ballot paper.

Both those rules are infinitesimal (since fair). It would be suspect to
have power consider big changes in the votes.

A rule can only consider the facts, i.e. the changes in the votes and the
changes in the winners.

So the power number is only defined on ties.

It would not take account of Mr Simmons' probability since it was a lie
to say that they existed. Mr Simmons' apparently can write to me privately
but never actually sends out to me even one of these probability numbers.

It takes quite a few lines to write down a QE formula testing whether
a method passes the power<=1 rule. I was writing on power when writing
on P4 over a year ago, at politicians and polytopes.

Suppose the ballot paper being tested is x*(ABC), with its weight, x,
being a positive Real. Then the method can be failed by the 'as defined'
power<=1 part of the equal suffrage rule when it (ABC)-desirableness of
the winners can't be sustained|reproduced when its weight is positively
shifted onto only these shorter papers.  Each line provides a different

|  . .· {A,BC}
|  . .· {B,AC}
|  . .· {C,AB}
|  . .· {AB,AC}
|  . .· {AB,BC}
|  . .· {AC,BC}
|  . .· {A,B,C}
|  . .· {A,B,AC}
|  . .· {A,B,BC}
|  . .· {A,C,AB}
|  . .· {A,C,BC}
|  . .· {B,C,AB}
|  . .· {B,C,AC}
|  . .· {A,AB,AC}
|  . .· {B,AB,BC}
|  . .· {C,AC,BC}

Note only does the number of lines increase rapidly as candidates are
added, but the desirableness value takes 2**nw values where nw is the number
of winners.

Nowthat it is known that the algebra can get simpler when rules are combined
with dual polytopes. it could save time to merge all rules (except the
Approvalishy proportionality aim) into a single rule. That would get the
word power matching up better with the words "equal suffrage".

To get the power, e.g. q, (which is a real numbe), it can be inserted into an
appropriate place in the QE formula.

Mr Simmons is still implying that probability exists which appears to be
a lie. I did ask for the probability numbers. This mailing list has seen
this precise problem of untrue claims that numbers exist, when I asked
Mr Ossipoff for some probability numbers,

>Here's a method that comes close to satisfying these criteria:
>The method takes ranked ballots with equal rankings allowed, as input.
>The method first applies Rob LeGrand's "ballot-by-ballot" version of
>"strategy A" to all possible permutations of the ballot. [Yes, this method
>is computationally intractable.]
>If the same candidate wins for all permutations, then that candidate is
>declared winner.

Maybe that creates a new method instead of passing or failing an
existing method. So the previous topic of power has left.

>Else, Joe Weinstein's weighted median method is applied to determine the
>winner.  A candidate's weight is the number of permutations that it won
>(according to Rob) plus one (so that each candidate has non-zero weight).
>Although this method is computationally intractable,the method winner can
>be calculated with 99.9 percent accuracy without inordinate computational
>burden, by use of montecarlo methods, for example.

Oh, THE random number generating algorithms are in the future.

E.g. in a computer existing in the year 2973 (in 23 April).

Is that why you can't ever seem to get a probability number out after
being asked for that ?.

>The residual doubt is small compared to other sources of doubt in other
>voting methods, especially the doubt that the votes were sincere, or the
>doubt that the the voters were using their best strategy for maximizing
>their voting power.

"votes" are sincere and it is not voters. Voters can be absent is some
elections trialling a method, and so can probability numbers be absent.

>Note that the method is completely deterministic,

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