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:

  1. Number of labeled groupoids with n elements
  2. Number of nonisomorphic groupoids with n elements
  3. Forests of rooted trees
  4. Enumerating distinct topologies, or transitive digraphs with n unlabeled nodes
  5. Number of different quasi-orders (or topologies, or transitive digraphs) with n labeled elements.
  6. Number of partially ordered sets ("posets") with n labeled elements (or labeled acyclic transitive digraphs)
  7. Number of partially ordered sets ("posets") with n unlabeled elements
  8. 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]

Created by Mathematica  (June 5, 2006)