Didn't address Arrow's Paradox.
Arrow's paradox stems from the nature of transitivity - as the pointer
in the previous post shows. Numbers are transitive. Human values are
not. So, when we try to measure human values with numbers - something
is lost. Clever people can manipulate which information is lost to
determine outcomes against the will of people - even though the people
who are deciding against themselves make the decisions.
This is true whether you're voting in an election, or making decisions
in the closing room of your local car dealership. The decision making
process is organized to give those running the show the benefit of
your choices.
People intuitively feel this during elections which is why most refuse
to participate.
So, my solution to Arrow's Paradox is straightforward - as are all my
solutions. Basically numbers are more complicated than people
generally realize. Numbers occur in different varieties. There are
scalars - the numbers everyone thinks about when you talk about
numbers. There are vectors - these are ordered lists of scalars.
These are important in structuring information - and can be used to
draw pictures for example since ordered lists of numbers can be
represented by a directed line segment. The interesting thing about
vectors, is that they are in certain ways non-transitive. You can
reduce them to transitive values by doing things to them. Like
figuring out their length or their orientation and measuring them.
But vectors of themselves are non-transitive too. Then, there are
tensors -ordered tables of scalars (or ordered lists of vectors.)
Since Arrow's Paradox is generally introduced by examining a table of
values - we should keep this idea in mind. Tensors are non-transitive
too!
Now, there is a new field of study called emergent systems
http://www.it.swin.edu.au/centres/ciamas/tiki-index.php?page=Introduction
Might is be possible to create an emergent system involving vectors or
tensors that allow for rational collective choices to be made?
I think so.
my idea is two-fold;
(1) Create personal electronic wealth symbols that are used to
transact business. Individuals create their own money when they buy
something and redeem their own money when someone buys something from
them. This is the way nations work. Each person's spending and
redeeming habits are encoded in a table, very similar to the way a
credit report is used today.
(2) The electronic wealth symbols are vectors that encode a wide
variety of information useful to the people who use it. Wassily
Leontieff created the input-output method of econometric analysis. An
economy can be represented by a table of numbers. Each table can be
broken down into rows and columns. The columns represent all the
needs of each consuming activity in the economy. The rows represent
all the benefits of each productive activity in the economy.
Individual transactions can be encoded in this way as well. In any
event, the wealth symbols each person creates have a certain structure
that reflects that person's values and desires.
SYNTHESIS
So, the electronic currency is used to transact business and encode in
each transaction the reason for the transaction and the value of the
transaction to both parties - recording at least as well as a written
contract enforced by a court and attorneys.
The value of the currency automatically adjusts as it flows through
the electronic exchanges.
The structure each person gives to their currency reflects their
personal values. Collectively these structures combine to provide for
the emergence of cultural and social features rationally desired by
the population.
For example, if someone wanted to support cancer research with each
transaction - invoking it like a tax each time their currency was used
- this would reduce the value of the currency to others, but cause
money to flow to cancer research. If sufficient numbers of people
chose to support this activity - large quantities of money would flow.
Those qualified to receive it and under what terms, could be encoded
in the transaction matrix as well.
So, the issue in this new economy wouldn't be to find someone to work
for to get money. People would be able to create money on demand.
The issue would be to find something useful to do to allow you to
redeem the money you want to spend! This at the outset is pretty
damned impressive change of focus.
Basically, nearly all the activities we use voting and money for can
be subsumed by this new system with little or no change and would
finally provide humanity with a means to make rational collective
choice.