Turing, Randomness and Economics.
Héctor Zenil · arXiv (Cornell University) · 2013
This is a review of aspects of the theory of algorithmic information (AIT) that may constitute an appropriate framework for formulating questions related to economics. We start by surveying classical results from algorithmic complexity and algorithmic probability, highlighting their deep connection and possible relevance to frequency distribu-tions common in the study of price movement and volatility. Keynes on (statistical) induction and von Mises ’ approach to probability and randomness suggest that AIT may legitimately serve as a framework for approaching such matters. 1 Algorithmic (Program-size) Complexity The concept of algorithmic complexity addresses the question of the com-plexity of individual objects, e.g. binary strings (is 1111111111 less random than 0110101100?). The algorithmic complexity K(s) of a string s is the length of the shortest program p that produces s running on a universal Turing machine U. More formally, KU(s) = min{|p|, U(p) = s} (1) ∗Based on an invited talk under the same title delivered at the Centro de Investigaciones