[EM] Rejecting fairness without a spec of reasoning

[Craig Carey]

At 2004-01-08 20:21 +0000 Thursday, Diana Galletly wrote:
>On Fri, 9 Jan 2004, Craig Carey wrote:
>
>> Simulated annealing is using random numbers to get around multiple
>> minima.
>
>Why on earth does one need to "get around" multiple minima (I assume
>you are talking local minima here ...) ?  What is the problem with
>multiple local minima?  And why can't one use analytical methods to
>deal with such?
>

The design of preferential voting methods has functions that are
partly logical, i.e. would have barriers lacking slopes allowing the
typical non-linear optimizer to estimate its boundary.

By 'dumb/stupid ' optimizer I meant one that performs better when
there are bigger discontinuities on the 1st derivative.

Researchers into the design of preferential voting methods might have
to write their own optimizer since there is nothing to copy. The
EM List is running in C.V.D. mode most of the time and it can't
create complex programs  that are suspected to be essential if man's
knowledge is to be advanced.

---

On the topic of the automated computation of electoral boundaries, 
an official could be faster (counting man-hours and not months)
than an EM List numerical analyst. Anyway, who cares: the
construction of advanced numerical computer programs does not seem
to happen here. The list's best members seem to be flopping after
50 lines of 'for loops' or some presumbably very simple Monte Carlo
random number program.

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


I have been unsubscribed. However I scavanged through my archives
for a recent unimportant message by Mr Schulze of Berlin.


At 2003-12-25 00:28 +0100 Thursday, Markus Schulze wrote:
>Dear Craig,
>
>you wrote (25 Dec 2003):
>> This can be named the Alternative Vote Twin Towers example: a support
...
>> http://groups.yahoo.com/group/single-transferable-vote/message/244
>>
>> +-----------------------------------+
>> |Winner: · ·A· · ·|Winner: · ·B· · ·|  Alternative Vote winners
>> +-----------------------------------+
>> | Tot: · 513000· ·| Tot: ·1024001· ·|
>> +-----------------------------------+
>> |· ·A· · · 1001· ·|· ·A· · 512000· ·| Change = +510999
>> | * BA · · ·999· ·|· ·BA · · 1001· ·| Change = +2
>> |· ·CBA· · 1000· ·| * CBA· · 1000· ·|
>> |· ·DBA· · 2000· ·|· ·DBA· · 2000· ·|
>> |· ·EBA· · 4000· ·|· ·EBA· · 4000· ·|
>> |· ·FBA· · 8000· ·|· ·FBA· · 8000· ·|
>> |· ·GBA· ·16000· ·|· ·GBA· ·16000· ·|
...
>> |· ·KBA· 256000· ·|· ·KBA· 256000· ·|
>> +-----------------------------------+
>
>This is neither an example showing Alternative Voting violates
>monotonicity nor an example showing Alternative Voting violates
>participation. This is an example showing Alternative Voting
>violates consistency. However, it has been demonstrated by
>HP Young that only positional methods (e.g. FPP, Borda,
>Approval Voting) satisfy consistency.
>

A pass under monotonicity removes the problem of the cascading
of votes and power loss. Monotonicity itself imposes smoothness
requirements by putting hard constraints on the angles by which
faces can tilt and differ from FPTP's.

An example very near to the above example will show a violation
of monotonicity. Monotonicity can be merged in with truncation
resistance or not. Persons can't simply get rid of monotonicity
by stating that they have done so. Instead they must get a full
list of the axioms and make sure that every axiom containing
monotonicity is worded against. Maybe some of the other
formulations appear to be more obviously best for a national
election.

Monotonicity can stop that type of example that is above so that
a search does not find any. In multiwinner elections it would
need to be accompanied by other multiwinner monotonicity rules
that don't allow a preference to jump onto the end of the paper
or off the end. That is a core mistake of Mr Schulze's
"Only 5 category" pairwise comparing followers, i.e. some foul-up
with bumping the last preference off the end. 

--

Suppose Young considered all (known and unknown) methods receiving
STV ballot papers. Then the wording of Mr Schulze has 3 holes in
it:
[1] Mr Schulze has an unknown  purpose that can can go well
   beyond stripping off original details and good references to
   accessible source allowing me to check. In fact the claim could
   be wrong and one that Mr Young would consider to be wrong.

[2] Mr Young got it wrong. Surely that is to be suspected of
   university academics who don't use the word "polytope" and
   who have not derived fair 3 candidate methods. Economists
   are especially prone to having faulty and unimportant results
   plainly stating beliefs are certainly approximately wrong.

[3] Another obvious thing is that the "Consistency" is somewhere
  stronger than monotonicity. So rejection of Consistency does
  imply anything about Monotonicity. The error perhaps gets in
  with the words "this is an example showing...". It could be
  matched up four hundreds of rules, only 40 of which can be
  shown to lack power. At best it was a desire to mislead or a
  blunder, or an instance of exercising a capacity to refer to
  other cellulose polymer based artefacts, and hopefully not
  a result of getting the implications wrong when trying to
  construct an argument built over some irrelevancy.


Politicians-and-Polytopes: the first voting method.