When Humans and Machines Make Joint Decisions: A Non-Symmetric Bandit Model

As machine learning algorithms have become on par or even superior to humans in a number of decision making problems (Rajpurkar et al., 2017; Silver et al., 2018), the idea that humans might be assisted by computer programs across a large variety of tasks has gained momentum. Already today, automated decision making systems are being used to predict cardiac arrests, credit scores, and recidivism (Tonekaboni et al., 2018; Board of Governors, 2007; Angwin et al., 2016). An emerging literature asks how humans, who often remain the final decision makers, can and should interact with such systems (Tonekaboni et al., 2019; Lucic et al., 2020). Machine learners, in turn, want to understand how algorithms should be designed such that interaction with humans is as fruitful as possible (Carroll et al., 2019). In most real-world decision making problems, humans have access to information that is unobservable to any algorithm. In the medical domain, doctors can obtain important information from personal interaction with patients (Goldenberg and Engelhardt, 2019). In judicial bail, judges may base their decision on the behavior of the defendant in the courtroom (Lakkaraju et al., 2017). From a machine learning point of view, such unobserved variables arise not due to a failure of the algorithm's designer to collect them. Instead, it is a property of many real-world decision problems that formulating all relevant aspects as inputs to an algorithm is impossible. 1