[EM] CVD wants Alt.V to be fairer but it isn't: misleading website
Craig Carey
research at ijs.co.nz
Thu Dec 19 05:48:09 PST 2002
At 02\12\19 12:10 +0200 Thursday, Markus Schulze wrote:
...
More of this nonsensical notation that seems to be unthinkable unless
the author permanently lost in darkness. It is actually of interest since
it correlates a likelihood of many blunders in statement making.
However I shall try to clean up this definition:
A first thing to do is to delete the word voters. On the face of it, it
means that ballot papers are being grouped in an unspecified way (or as
more likely the case, the author can't can't access the meaning any
better than readers). Often that is no impediment to correcting it and
I have a go at doing that here.
>I wrote (28 Aug 1998):
>> Definition ("clones"):
>>
>> A[1],...,A[m] are a set of m clones if & only if the following
>> two statements are valid:
>>
>> (1) For every pair (A[i],A[j]) of two candidates of this set,
>>
>> for every voter V, and
>>
>> for every candidate C outside this set
>>
>> the following two statements are valid:
>>
>> (a) V strictly prefers A[i] to C,
>> if & only if V strictly prefers A[j] to C.
>> (b) V strictly prefers C to A[i],
>> if & only if V strictly prefers C to A[j].
>>
>> (2) For every candidate A[k] of this set and
>> for every candidate D outside this set
>> there is at least one voter W, who either
>> strictly prefers A[k] to D or strictly prefers D to A[k].
>
A is a list (the same as an array or vector). It shall be auto-converted
to a set as needed to get the correct input for the operators. The
"x precedes y in paper p" means both x and y are named by the paper and
the prerfence, x, is closer to the 1st preference.
Statment (1) is this:
(For all A, A is a list, all members of A are candidates, #A>=2)
(For all ai, aj)[ (ai in A, aj in A, not (ai=aj)) implies [
. . (For all p, p a ballot paper)
. . (For all t, t a real) % now the paper ("voter") V equals t.p
. . (For all C) [ (not (C in A)) implies [ % try having "this set" mean "A"
. . . . [ (both ai and C appear in p and ai precedes C) equals
. . . . . (both aj and C appear in p and aj precedes C)
. . . . ] and [
. . . . . (both C and ai appear in p and C precedes ai) equals
. . . . . (both C and aj appear in p and C precedes aj) ] ]] ]]
That looks a real rule since it is processing a method. Unfortunately
for the credibility of the rule, it never evaluates the method.
Two other little problems are:
(1) There is no use of a "(There Exists)". Thus the tiniest defect in the
rule allows it to be obvious that the whole rule has to be rejected.
(2) The variable "t" appears only one. The rule seems to consider only
kinds of ballot papers rather than kinds of ballot papers that had a
weight/count property.
That rule did not last long.
The instant collapse of theories that have entangled in them a notion
that it is best to use the word "voter" as if meaning "human" is not
actually advancing the cause of those that would assert that humans are
relevant.
The definition was last about 52 months ago.
----------------------------------------------------------------------
Let's get to the second. It does not seem to be linked up with the
first in any way, so we have 2 definitions. Hence easily neither is
the information sought ("independence from clones"). Or are they to be
AND-ed ?.
This definition also appears to not actually evaluate the winner findin
function that it is supposed to be checking.
>> (2) For every candidate A[k] of this set and
>> for every candidate D outside this set
>> there is at least one voter W, who either
>> strictly prefers A[k] to D or strictly prefers D to A[k].
>An election method violates "Independence from Clones" when there are
>situations where you can increase or decrease the probability that a
>given candidate is elected by introducing additional clones to a set
>of clones to which this candidate doesn't belong.
>
I remind Mr Schulze that polytopes do not have surfaces that get soft
or that start to vibrate when someone suggests that probability
exists. Until Mr Schulze fixes up the rule so that it does not completely
ignore the function that it is supposed to be checking, those that
believe that polytopes do not have probabilistic vibrating (or whatever)
surfaces, have an additional safeguard against having to absorb the
false suggestions that voting method have a relation to probability.
It is excessive to write out the rule in the style of logic, only to
later write that whether a candidate has a probability of winning.
The words
"candidate A is more likely to win the 2nd than to win the 1st"
maybe do or do not mean:
"it is never the case that candidate A loses the 2nd and wins the 1st"
>******
>
>You wrote (19 Dec 2002):
>> I suppose we have made some sort of progress since Mr Schulze has
>> now nearly eradicated the public possibility that he understands
>> what proportionality is.
>>
>> Lets have a look at that more closely: this was written:
>>
>> "proportionality is only defined for single-winner elections"
>
>Nope, I wrote (19 Dec 2002): "'Proportionality' has been defined
>only for multi-winner elections."
>
I define it for all numbers of winners. You comment is not relevant to
the topic which is attentive to the logical reasoning that was used
quite privately (provided that reasoning was used). There can be
an unlimited number of meanings for the word probability.
The comment "Nope" is not clarifying, but instead it is the first
appearance of a new limitation on offer. Also it is irrelevant to my
questioning on the presence or absence of a meta-axiom you personally
use that prevents a weighty respect for arbitrary rules. STV and IRV
eliminated at the first step by tests and don't seem to delete by
anti-arbitrariness rules. What other rule would be primarily used to
eliminate the PR-squared method of Wiseman. Instead of raising to
the power of 2.0, it could be a raising to the power of 2.01.
Indeed we want another meta-axiom that will extend other rules and
meta-axioms to their logical extents, and that other meta-axioms
would enlarge the power and applicability of the meta-axioms that
stop arbitrary rules like Tideman's rules, from being considered.
These meta-axioms are not needed to allow the deletion of your
"nope" comment since it is clarifying irrelevant information.
I will leave it 'not inquired into' on whether Mr Schulze believes
that the concept of proportionality provides guidance on whether
we can identify the winner of all 2+ candidate elections where
1 candidate has exactly 100% of the votes. Don't forget Mr Schulze
that every candidate can have more than 100% of the vote. Did Mr
Tideman make the same type of error or is the word "voter" a code
term implying that the weights are non-negative, or was there an
inaccuracy in the copying.
Craig Carey
Real facts for the Aquarian age:
http://groups.yahoo.com/group/politicians-and-polytopes
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