Loss Aversion Without Loss-Averse Preferences
Irreversible failure can make a rational agent look psychologically biased.
Provoking question
How much of what we call “bias” is actually optimal behavior near an irreversible boundary?
Some behaviors that look psychologically biased may emerge from the structure of the world.
This paper studies a simple Markov decision process in which an agent chooses between a safe action and a risky action. The agent is risk-neutral. Rewards are linear. There is no built-in loss aversion, no probability weighting, and no framing effect. But the environment contains an absorbing catastrophe boundary: once the agent falls into failure, the failure is irreversible.
That boundary is enough to produce prospect-theory-like behavior.
In growth environments, the risky action has higher immediate expected value. But near catastrophe, one bad outcome can end everything, so the Bellman-optimal agent plays safe. In decline environments, the safe action has lower immediate expected loss. But near catastrophe, safety only leads to certain ruin more slowly, so the optimal agent gambles. The same agent, with the same objective, shows opposite risk attitudes depending on the direction of the environment.
The paper also derives a closed-form formula for endogenous loss sensitivity and shows that loss-aversion-like slope ratios can arise even with symmetric payoffs. The effect persists under model-free Q-learning and stochastic transitions.
In AI safety, reinforcement learning, economics, and institutional design, we often interpret risk aversion or desperate risk-taking as a property of the agent. This paper shows that irreversible boundaries can create those behaviors structurally.
When failure is irreversible, the world itself becomes loss-sensitive.