>
> In the early days of the Soviet Union there was an attempt to match
> people to jobs (or tasks) through some central bureaucracy. Of course
> bureaucracies don't work very well, but even if they did work,
> perfectly, they could not have accomplished that task because of the
> combinatorial explosion of possibilities.
>
In the early days of the soviet union, when most of
the marxist theorists haven't been killed by
the civil/intervesionist war or later, Stalin,
there was a genuine strife for democracy and
a wide range of new/modern concepts of freedom
for those times.
However, their failure has not much to do
with any combinatorial tasks, but with the
facts, that most people couldn't read or
write, most people had not enough to eat
or place to live, most people had never heard
of the concept of thinking for themselves rather
than being told what to do by their landlord/
clergy or the tsar.
> In graph theory and computer science the problem of matching workers
> to jobs (or any equivalent bipartite matching problem) is called the
> assignment problem.
>
> Good modern algorithms for solving the assignment problem are roughly
> O(3), which means that they scale up as to the cube of the number of
> nodes. Using my aging 120 MHz Pentium it takes about half an hour to
> solve an assignment problem with a few thousand nodes. To solve a
> problem with a few million nodes would not take 1000 times as long,
> but the cube of that, one billion times as long. So there is probably
> not enough computing power in the world today to solve the assignment
> problem the Soviet bureaucracy set themselves.
>
Even this estimate doesn't sound that dounting
in the view of the present and possible future
computing capabilities. However, there would be several
different level of assigning anyway, say by
local housing groups, education groups,
workplace groups, district, town, country etc
areas of collective decisions.
Hey, if there is an energy problem/hiccup, it can even be
done without computers...
> OK, this is an oversimplification. But the basic point should be
> clear. The organization of society is the kind of combinatorial
> optimization problem that is hard to solve. Actually as combinatorial
> problems go, it is one of the easy ones, most are not just hard but
> virtually impossible. But somehow most economists don't address the
> combinatorial explosion. A flaw in the economics curriculum, I suppose.
>
Even the present system managed to work upto a point
without a lot of combinatorics so far...
> Unemployment is a good example. One constantly hears governments
> talking about job creation, as if there just aren't enough jobs to go
> around. To me unemployment is evidence that it is hard to FIND a job,
> not that there are too few jobs. Lots of women fail to find a
> husband, but you don't hear governments talking about man-creation or
> a shortage of men.
>
Well, the fact is, that while more and more people
come to the job-market, there are less and less jobs.
When last time there was an advertisement for a
middle grade technician
job in our department, there was 102 applications,
6 of them with Phds.
If you into sharing the existing job-hours,
basic income or other ideas mentioned on this list,
you have to think of an economic structure that could
work with such a human needs and not profit oriented
problemsolving.
> For each individual to find a good job, society as a whole must solve
> a very difficult combinatorial optimization problem, a bipartite
> matching or assignment problem. Not an impossible problem, but we
> certainly won't solve it as long as we ignore the combinatorial problem
> altogether and try to do job-creation.
>
I wish it was the question of just a bit of
clever mathematics... It would have been solved by
now; we have teams of able mathematicians all over the
place looking for decent Phd projects...
Eva
> So, there you have it -- after complaining about Jay Hanson's
> mistreatment of economists I go on to criticize them myself. But,
> people, please, it's not personal, and it's not a prejudice, I just
> think the universities need to add a few graph theory and computer
> science courses to their economics curriculum.
>
> dpw
>
> Douglas P. Wilson [EMAIL PROTECTED]
> http://www.island.net/~dpwilson/index.html
>
