A combinatorial theory of minimal social situations

A minimal social situation is a game‐like situation in which there are two actors, each of them has two possible actions, and both evaluate the outcomes of their joint actions in terms of two categories (say, ‘success’ and ‘failure'). By fixing actors and actions and varying ‘payoffs’ the set of 256 ‘configurations’ is obtained. This set decomposes into 43 ‘structural forms’, or equivalence classes with respect to the relation of isomorphism defined on it. This main theorem and other results concerning related configurations (minimal decision situations) are derived in this paper by means of certain tools of group theory. Some extensions to larger structures are proved in the Appendix. In the introductory section after a brief explanation of the meaning given to the terms ‘structure’ and ‘isomorphism’ in mathematics (Bourbaki) it is shown how these terms can be used to formalize the concept of ‘social form’.

Key words::

• Combinatorial theory
• decision making
• game theory
• minimal social situation
• social form
• structure