Testing Decision Makers without Counterfactuals

Computer Science > Computer Science and Game Theory [Submitted on 1 Jun 2026] Title:Testing Decision Makers without Counterfactuals View PDF HTML (experimental)Abstract:A decision-maker (DM) repeatedly makes choices under uncertainty in a bandit environment, where only the realization of the chosen arm is observed. Another competing agent, the adviser (AD), repeatedly provides recommendations, but the realizations of these recommendations are unobserved unless they coincide with the DM's choice. Both agents possess partial information about the arms' realizations. The central question we focus on is whether, in the long run, an outside observer can identify which agent is more informed based solely on the observed decisions, recommendations, and arm realizations. A test selects one of the agents based on the observed data. We focus primarily on the class of scoring tests, which assign a numerical score to each observation and select the agent according to the average score. We study strategic agents whose objective is to be selected by the test. For simultaneous arm choices, we show that there exists a scoring test that successfully identifies the more-informed agent. For sequential arm choices, however, no such scoring test exists. Finally, we explore the tension between identifying the more-informed agent and maximizing welfare. A DM whose objective is to pass the test may not necessarily make welfare-maximizing decisions. In a binary-arm environment, we show that no scoring test can simultaneously identify the more informed agent and achieve more than half of the welfare attained by welfare-maximizing decisions. Current browse context: cs.GT References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.