Logic Seminar - Boning Yu / Comparing solutions to the Judy Benjamin Problem
Logic Seminar - Boning Yu / Comparing solutions to the Judy Benjamin Problem
Wednesday March 6, Bo leads the Logic Seminar with a presentation on the Judy Benjamin Problem, abstracted below.
Abstract: When it comes to updating beliefs about conditional probabilities, i.e., in a case like the Judy Benjamin problem, there are two mainstream solutions, the intuitive solution and relative entropy minimization (REM). Adam Grove and Joseph Halpern (1997) provide a justification for the intuitive solution, while Anubav Vasudevan (2020) justifies the use of REM. In this paper, I demonstrate that the two arguments follow a similar approach: they identify a probability space that allows agents to condition on information about conditional probabilities. Despite the fact that the two arguments propose different ways of creating a probability space, I argue that Vasudevan is wrong to claim that REM is motivated by Judy’s trust in her commander while taking the intuitive solution as conservative. In addition, I show that Grove and Halpern’s formalization is missing some important cognitive aspects. Meanwhile, I agree with Grove and Halpern’s conclusion that, theoretically, the context of the Judy Benjamin problem does not provide sufficient information to determine a uniquely correct answer. I then use computer simulations to examine the two solutions and argue that the intuitive solution is superior.