CONCEPTIONS OF COMPLEXITY AND IMPLICATIONS FOR ECONOMICS Stuart A. Umpleby The George Washington University Washington, DC

Three conceptions of complexity Complexity -- Systems with large numbers of variables and many relationships among them Self-organizing systems -- Systems composed of numerous autonomous (usually preprogrammed) actors or agents or algorithms which interact, often producing unexpected results (emergence) Reflexive systems -- Systems involving knowing participants acting in systems in which they have an interest in the outcome

Three conditions define reflexivity There is circular reasoning – observe, act, observe, act… The observer is included in what is observed Descriptions on two levels are required – observation and participation These conditions seem to involve fallacious reasoning – circular reasoning, the ad hominem fallacy -- and self-reference

The situation in economics For many years economists have been using an equilibrium model of economic systems Economists assume that if some incident affects an economy, it will quickly return to a stable equilibrium This model is taken from thermodynamics in physics Equilibrium theory is based on some very unrealistic assumptions about human behavior

Reflexivity theory as an alternative George Soros has proposed reflexivity theory as an alternative to equilibrium theory Reflexivity theory assumes that social systems are different from physical systems because they are composed of thinking participants Each person observes what is happening, thinks about alternatives, chooses a course of action and then participates to implement it

Why has reflexivity theory not been accepted? When I explain reflexivity theory to economists, most say they have not heard of it Some say that reflexivity theory would encounter logical difficulties By “logical difficulties” they usually mean Russell’s Paradox and self-reference

Are logical difficulties an obstacle to a more realistic theory of economics? This is a question I have been pondering for several months The answer is yes and no, but both yes and no are complex I shall describe the situation as I see it now

Yes, logical difficulties are an obstacle Clearly self-reference is a difficult problem Paradox is a form of inconsistency and leads to undecideability The informal fallacies, whether known explicitly or only implicitly, also lead social scientists to want to avoid a reflexive point of view

No, logical difficulties are not the obstacle The problem with believing that self-reference is the primary obstacle to adopting reflexivity theory is that most social scientists have not heard of self-reference Most social scientists have not heard of the Russell set – the set of all sets that do not contain themselves Also, some philosophers and mathematicians familiar with Russell’s paradox interpret it narrowly and say it is not related to social systems

Yes, nevertheless One possible reply is that many people believe that there are logical problems, even if they do not know a formal representation The problems have been known for a very long time, at least since Epimenides’s paradox (circa 600 B.C.) of the Cretan liar We have laws governing self-incrimination, conflicts of interest, corruption Hence, we have devised ways of dealing with self- reference through legal arrangements and judgments about human behavior

The goals of social scientists Currently social scientists, particularly economists, are trying to create a social science similar to physics Paradox, inconsistency, and undecideability do not fit their image of what science should look like Economists want a quantitative, mathematical theory, similar to physics, even if the foundational assumptions are unrealistic

The siren song of physics It is not so much the logical problems of self- reference that stand in the way of reflexivity theory Rather the problem is that the image of physics constitutes a greatly desired “fantastic object” Like ancient mariners, economists do not worry about being ship-wrecked on rocks, instead they listen to the music of the lorelei

Underlying assumptions Because of the strong desire to create economics in the image of physics, economists are willing to adopt many highly unrealistic assumptions Some of these assumptions are being corrected with behavioral economics The ergodic assumption may be addressed next There are also two philosophical assumptions that have not yet been addressed by economists

A practical solution to the problem As noted, we already have devised solutions to the problem of self-reference in social systems through laws against conflicts of interest, corruption and self-incrimination Another corrective action is business ethics

Experts vs. decision-makers An expert who is advising a decision-maker can think of himself as giving objective advice However, a decision-maker sees himself as a participant in the social system and must take responsibility for his decisions Of course the expert is also a participant in that he seeks to maintain his reputation as an expert and seeks to maintain his position as an adviser But experts usually ignore this kind of participation in an effort to claim objectivity

Self-reference is an issue for decision-makers When an expert sees himself as uninvolved and objective, he is saying he is outside the system But a decision-maker is deliberately trying to influence a social system Since the decision-maker is inside the system, there is ambiguity and undecideability Is the decision-maker acting to benefit himself, his firm, society or some combination?

A formal solution to the problem Rather than A or not A Describe a process A leads to B leads to C leads to D leads to A Describing a process implicitly adds time as an additional dimension System dynamics and recursive function theory are possible representations

Conclusion Methods rather than theories may be the best way to describe management. The observer is then included Economics needs to expand its conception of science to include the observer and the effects of economic theories on the operation of economic systems

Contact information Stuart A. Umpleby Department of Management The George Washington University Washington, DC

Presented at Capital Science 2012 A conference of the Washington Academy of Sciences Washington, DC 2012 March 31 to April 1, 2012