Information Value Under Endogenous Feasibility

This paper studies payoff information when past choices constrain future feasible actions. We introduce the Irreversibility Decision Problem, in which an agent navigates an action graph subject to stochastic edge blocking. Along a Blackwell-ordered Gaussian signal family, greater payoff precision can lower expected terminal reward when the agent ranks immediate rewards rather than continuation values. A two-route construction establishes this reversal, and a general-graph extension gives sufficient conditions for it. On depth-d trap trees, the probability of correct navigation decays exponentially in d. A cognitive-depth parameter determines whether welfare is increasing or decreasing in payoff precision; sufficient knowledge of the feasibility graph restores monotonicity. A welfare decomposition separates signal-invariant reachability loss from the agent-dependent residual. On percolated networks, giant-component membership determines when reachability loss vanishes conditionally, while persistent local isolation prevents population-average loss from vanishing. The results attribute non-monotonicity to objective misspecification, not to a failure of Blackwell's comparison theorem.