Sunday, September 05, 2010

Faustian Agents

"Two souls, alas, do dwell within this breast. The one is ever parting from the other" -– Goethe
"He [i.e., Dickens] told me that all the good simple people in his novels, Little Nell, even the holy simpletons like Barnaby Rudge [Slater comments parenthetically that this must have been Dostoevsky's description, not Dickens' -- indeed] are what he wanted to have been, and his villains were what he was (or rather, what he found in himself), his cruelty, his attacks of causeless enmity towards those who were helpless and looked to him for comfort, his shrinking from those whom he ought to love, being used up in what he wrote. There were two people in him, he told me: one who feels as he ought to feel and one who feels the opposite. From the one who feels the opposite I make my evil characters, from the one who feels as a man ought to feel I try to live my life. Only two people? I asked." -- Fyodor Dostoevsky
I have previously described agents that assess an action by ranking outcomes among a number of incommensurable dimensions. By Arrow's impossibility theorem, such an agent in general cannot have a single aggregate ranking of the outcome of actions. I was able to list all best choices for my simple example. That is, for each menu, I listed best choices, with ties being possible. (By the way, a budget constraint is a menu.) If one wants to generalize this approach, one would need to specify methods for specifying best choices when listing all possible menus by hand becomes impractical. Pairwise voting is not a good idea, since the results depend on the voting order in which pairs are compared. Furthermore, one would not want to specify one such method, but allow for many different possibilities. Ulrich Krause has done this. He calls the method for choosing out of these rankings of different aspects an agent's "character". As I understand it, he allows for these rankings to change, based on the agents experience. And so he ends up with a formal model of opinion dynamics. I don't know if or how this relates to Akerlof's identity dynamics, but, I think, that would be an interesting question to explore. References
  • K. J. Arrow (1963) Social Choice and Individual Values (2nd. Edition), John Wiley & Sons.
  • Ulrich Krause (2010) "Collective Dynamics of Faustian Agents", in Economic Theory and Economic Thought: Essays in Honour of Ian Steedman (ed. by J. Vint, J. S. Metcalfe, H. D. Kurz, N. Salvadori, and P. Samuelson), Routledge.
  • S. Abu Turab Rizvi (2001) "Preference Formation and the Axioms of Choice", Review of Political Economy, V. 13, N. 2: pp. 141-159.
  • A. K. Sen (1969) "Quasi-Transitivity, Rational Choice and Collective Decisions", Review of Economic Studies, V. 36, N. 3 (July): pp. 381-393.
  • A. K. Sen (1970) "The Impossibility of a Paretian Liberal", Journal of Political Economy, V. 78, N. 1 (Jan.-Feb.): pp. 152-157.
To read:
  • G. A. Akerlof and R. E. Kranton (2010) Identity Economics: How Our Identities Shape Our Work, Wages, and Well-Being, Princeton University Press.
  • J. B. Davis (2003) The Theory of the Individual in Economics: Identity and Value, Routledge.
  • A. Kirman and M. Teschl (2004) "On the Emergence of Economic Identity" Revue de Philosphie Économique, V. 9, N. 1: pp. 59-86
  • U. Krause (2009) "Compromise, Consensus and the Iteration of Means", Elemente der Mathematik, V. 64: pp. 1-8
  • I. Steedman and U. Krause (1986) "Goethe's Faust, Arrow's Possibility Theorem and the Individual Decision-Taker" in The Multiple Self: Studies in Rationality and Social Change (ed. by J. Elster), Cambridge University Press.

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