Re: [EM] Winners or representation?
On 11/04/2022 09:22, Richard Lung wrote:
Kristofer,
“election criteria” are to be found in the four scales of measurement,
which I have been discussing. They are the criteria not just of
“electics” but of the sciences in general. STV has essentially
satisfied the main four scales, for nearly one and a half centuries.
Commencing with the philosophes, of the eighteenth-century
Enlightenment, continuing with the philosophical radicals,
pre-eminently John Stuart Mill. Mill advocated universal male and
female suffrage, amounting to a nominal scale of one person one vote.
The philosophes provided the ordinal scale, in preference voting.
Borda provided an assumed interval scale. In the 1850s, Carl Andrae ,
also Thomas Hare, provided an ordinal scale and a ratio scale, with
Personal Representation by STV (preference voting and proportional
counting). JB Gregory provided a real interval scale for STV, in 1880.
Before the twentieth-century, in North America, Personal
Representation was already being advocated, for instance in New York,
as part of the Progressive Era. In the early twentieth century,
Clarence Hoag and George Hallett picked up on HG Wells, a direct
intellectual descendant of Hare and Mill, advocating at-large STV/PR.
I was surprised to find a predominance of mathematicians (or to a
lesser extent, those of a scientific background) in the development
and promotion of the Andrae/Hare system.
Judged by their adherence to scientific measurement, mathematicians
played a positive role in realising democratic voting method.
Since the mid-twentieth century, mathematicians have played a negative
role, towards election method, epitomised by the so-called
Impossibility theorem. That school has failed to develop a "standard
model" of election method, which was previously developed from the
Andrae/Hare system.
Regards,
Richard Lung.
On 08/04/2022 23:14, Kristofer Munsterhjelm wrote:
On 05.04.2022 19:56, Richard Lung wrote:
On 05/04/2022 10:22, Richard Lung wrote:
Thru-out the world of academe, from the American Mathematical Society
to innumerable social choice classes, can or could be found examples
of how about five different single-member voting systems all produce
different results. This is held to demonstrate a theorem of the
Impossibility of determining a winner.
That doesn't seem to be related to either single- vs multi-winner or the
nonexistence/coherence of voting method criteria. It's more related to
IIA and rock-paper-scissors elections.
Would you say that my estimator analogy makes sense and shows that
election criteria can exist and be coherent?
-km
On 11.04.2022 20:48, Richard Lung wrote:
On 11/04/2022 09:22, Richard Lung wrote:
Kristofer,
“election criteria” are to be found in the four scales of measurement,
which I have been discussing. They are the criteria not just of
“electics” but of the sciences in general. STV has essentially
satisfied the main four scales, for nearly one and a half centuries.
I think we're talking about very different things in that case.
My definition of an election (method) criterion, and I think one shared
by the EM list, is that an election criterion is a statement about the
behavior of a method.
With the exception of the summability criterion, a criterion is either a
statement about outcomes for particular elections (e.g. the majority
criterion or Droop proportionality criterion) or about how the outcome
changes or doesn't change when something about the election changes
(e.g. the monotonicity criterion).
A method is then said to pass the criterion if the statement is true
when referring to that method (otherwise false if it doesn't, or
inapplicable).
(I could provide a more rigorous mathematical definition if required.)
Since this concept is very general about the behavior of election
methods (it can be used for rated methods, ranked ones, etc.), it
doesn't seem like different scales come into play.
As an example, let's choose Range voting as a typical cardinal method,
and IRV as a typical ordinal one, and reweighted range and STV as their
multi-winner versions.
Then it seems to me that we can just as easily ask if Range satisfies
the majority criterion (it does not) as we can ask whether IRV does (it
does). And similarly, we can just as easily ask if Reweighted Range
Voting satisfies Droop proportionality (it doesn't) as whether STV does
(it does).
It might be the case that proving that a particular method passes a
particular criterion requires considerations into just how the algorithm
works. But whether it's meaningful to speak of a criterion in isolation
does not seem to.
Properties like universal suffrage are more about voting in general than
about election methods.
-km