Loss Aversion as Optimal Attention Allocation: Mismatches Are the Squeaky Wheel

Abstract

We study an agent who tracks several independent, unobserved, slowly drifting states and is paid by how well a chosen action matches each state but who can process only a bounded amount of information per period. The payoff environment is deliberately symmetric—quadratic matching losses, Gaussian drift, Gaussian observation noise—and the agent’s objective contains no asymmetry: we treat both the risk-neutral (linear) objective and the long-run log-growth (Kelly) objective. Within this symmetric environment, we show that the value of attentionis sharply asymmetric in the sign of the agent’s surprise. Because the matching payoff is maximized when action equals state, a surprisingly low payoff is strong evidence of a state mismatch that is worth correcting, whereas a surprisingly high payoff is evidence either of noise or of a match already achieved—in both cases carrying little decision-relevant information. We prove (Theorem 1) that the posterior expected mismatch, and hence the value of information, is strictly decreasing in the realized payoff, negligible for good surprises and rising steeply for bad ones, with a correspondingly asymmetric slope. We then show that an information-constrained agent optimally adopts a threshold attention policy (Theorem 2), which, under one explicit and standard bridge—that valuation inherits attention weight, as in salience and rational-inattention theories of choice—projects onto a reference-dependent value function with a kink at the expected payoff and a loss-side slope strictly steeper than its gain-side slope (Corollary 1): precisely the signature of loss aversion. The mechanism supplies the structure of loss aversion—its sign, its reference point, and how it varies with the environment—while its magnitude is one calibrated parameter that places the implied coefficient in the empirical range. Risk aversion follows as a corollary (Theorem 3): the kink induces first-order risk aversion over small symmetric gambles, inverting the usual hierarchy in which (second-order) risk aversion is primitive, and loss aversion is an add-on. The mechanism is immune to the Rabin calibration critique. Simulations benchmark the myopic policy against the computed optimum, map the mechanism’s robustness across noise tails, and locate the implied coefficient; we close with extensions to endogenous gain-seeking in convex (“gold-rush”) environments, population heterogeneity through learned priors, and a reading of hedonic affect as the Lagrange multiplier that prices a scarce attentional resource.