An attainable answer can be worth less than perfect information

In another constructed decision, two feasible investments have already been valued on a common date. The receiver uses expected value, with the risk treatment embedded in the stipulated value basis. A contributes 20 in a favorable state and −10 otherwise. B contributes 8 in either state. The supported probabilities for this illustration are one half each, so A has expected contribution 5 and B has 8. Choose B on present information.

Perfect knowledge before commitment would permit A in the favorable state and B otherwise. Expected contribution would be 14, a gain of 6 over the present choice. An available signal is less informative: favorable and unfavorable signals occur equally often, and the favorable-state probabilities conditional on them are 0.75 and 0.25. These premises are mutually consistent with the prior one half. After a favorable signal, A’s expected contribution is 12.50 and exceeds B’s 8; after an unfavorable signal, A’s −2.50 does not. The signal therefore supports expected contribution 10.25 before its cost, improving the current choice by 2.25.

A signal costing 1 plus a separately valued delay cost of 0.50 leaves an expected improvement of 0.75. A cost of 3 alone exceeds the attainable gain. If the signal arrives after the commitment deadline, it supplies no improvement to this choice. These calculations demonstrate how advice about inquiry can be completed. They neither estimate a real signal’s reliability nor require a numerical information-value model for every recommendation.