Nonlinear dynamics of belief updating and decision making

An equivalence is derived between the recursive two parametric belief-adjustment model of Hogarth and Einhorn (1992) for estimation type belief updating tasks and processes modeled by the Logistic equation with a single control parameter Λ, yielding 1 ≤ Λ ≤ 2 under Hogarths assumptions. It follows that for a sufficiently large number of belief updates the belief in a hypothesis in Hogarth´s model always approaches a stationary state. An increase of the control parameter to Λ ≥ 3 yields the well known universal period doubling bifurcations at critical values Λ_n. The transition from quadratic to cosinuidal maps yields node type bifurcations, which have been experimentally realized by photonic, interferometric equivalent circuits. In agreement with the catastrophe theoretical approach to human decision making they exhibit discontinuous transitions between different stationary levels including hysteresis effects. In terms of Synergetics this process corresponds to the spontaneous symmetry breaking of a (belief-) potential energy function. It determines the belief state as a macroscopic order parameter which is driven by a conservative force as derivative of the potential and which enslaves the microscopic neural states.