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Toward Enumeration of All Possible Economic Systems
Jonathan Vos Post
Computer Futures, Inc.
The question, “Can one map the space of all possible economic
systems?” is the 9th of 22 topic questions posed by Stephen
Wolfram in the Request for Papers of the NKS 2006 Wolfram Science
Conference. As a precursor to such a mapping, it is worth scoping the
problem by attempting to answer the question, “Is it possible to
enumerate all possible economic systems?” This paper summarizes
the meaning of this in terms of axiom sets for systems of stupid
autonomous economic agents, and introduces a dozen different
approaches to combinatorial enumeration problems already in the
literature, with suggestions for how they might be extended to
problems of classification or “mapping” of the spaces to
which they are associated.
We defer providing a definition of “all possible economic
systems” because virtually all such definitions in the economics
literature presuppose that past and present terrestrial economic
systems, with perhaps certain modifications, cover the search
space. To the contrary, this author believes that other economic
systems as significant as capitalism, communism, and potlatch are
possible with humans on Earth, but have either not been thought of
yet, or are considered impossible to implement. We believe that, once
sufficient people and computational resources are devoted to Stephen
Wolfram’s provocative question, the scientific community may be
able to constructively reframe the questions, with a sound
quantitative basis. The fact that we have not begun to exhaust the
space of possible economic systems is due (in Sir Arthur
C. Clarke’s terminology) to two main reasons: (1) Failure of
imagination [since we have limited the scope of that imagination,
basing it too firmly on already-known models, and failed to use
computers adequately as our imaginative tools]; and (2) Failure of
nerve [e.g., a valuable model is imagined, and the discoverer fails to
publish or attempt implementation, frightened by the implications].
Instead, we limit this paper to various oversimplifications of
economic system models that strip away most of what is usually
addressed in Economics, to focus on a range of “kernels”
or “skeletons” upon which more realistic models of
economic systems might be based, but are in any case capable of
enumeration, and thus an assessment of computational resources needed
for certain categories of mapping of the related spaces.
These include:
- Number of labeled groupoids with n elements
- Number of nonisomorphic groupoids with n elements
- Forests of rooted trees
- Enumerating distinct topologies, or transitive digraphs with n
unlabeled nodes
- Number of different quasi-orders (or topologies, or transitive
digraphs) with n labeled elements.
- Number of partially ordered sets ("posets") with n
labeled elements (or labeled acyclic transitive digraphs)
- Number of partially ordered sets ("posets") with n
unlabeled elements
- Other models, such as hypergraphs, and economic systems as
strong attractors in trajectories of economies in transition
Some of these kernels or skeletons are so stripped of the details
normal to economics (i.e. money) that they may easily be modified to
models of all possible social systems. As an example of how
theory diverges from practice, we point out that it is well known that
a theoretical optimum social system is to find someone who is always
right, and make him king. The mathematical countermodel is:
find someone who is always wrong, and make him anti-king and always
do exactly the opposite of what he says.
A series of arguments are made on science fiction as a source of
economic models, especially on the economics of abundance. Some short
comments are included on the pointlessness of modeling a plethora of
flavors of socialism and communism, and on economies in transition.
[presentation
materials]
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