Decomposition Patterns in Problem Solving

The paper develops a theory of biases in decision making, where biases are intended as deviations from the decisions that should be prescribed on the ground of (theoretically) unlimited rationality. Systematic biases in decision making are interpreted as stable strategies built up in a boundedly rational context. Strategies are built by problem decomposition, and it is shown that generally a solution of a problem obtained by decomposition is suboptimal, while the solutions of any single sub-problem are optimal. The conditions under which a decomposition process gives rise to a sub-optimal solution are explored, and it is shown that the sub-optimalities ultimately originate from the process of categorization that governs the creation of a decomposition pattern. It is shown that the processes of abstraction and categorization used by players to identify a pattern of decomposition use some salient features of the game as a guide; salience and simplification lead to categorizations which do not usually reflect correctly the "metric" of the problem, and therefore players do not evaluate correctly the "distance" to the goal. They are guided by the categorization and decomposition to discover general abstract procedures, simple to be applied in any condition of the game, even though sub-optimal in some game conditions. This means that they found a decomposition pattern that prescribes a nearly optimal strategy: a strategy that is non optimal in limited sub-domains of the game and therefore gives rise to "errors" hidden into the categorization, and therefore very difficult to be detected and corrected. The persistence of biased behaviours, observed in many experiments, is therefore explained showing to the stability of non optimal decomposition patterns. Along this line, the variety of different sub-optimal behaviors is interpreted through a "fitness landscape" in which many suboptimal solutions are locally stable under small changes in the strategy. An application to a simplified version of Rubik cube is developed, showing that individuals stay locked-in simple strategies, slightly sub-optimal, based on an imperfect decomposition pattern