# Blog #3: A Game Theoretic Analysis of the Hearsay Rule

Since our last blog post, we have spent a significant amount of time expanding our literature review. Our new discoveries have encouraged us to change the shape of our research. We were happily surprised to find more research done that addresses Game Theoretic and Bayesian applications to Hearsay evidence in law. Some of the literature that we incorporated with particular usefulness include “Hearsay, Double Hearsay, and Bayesian Updates” from Less Wrong, “Why Type 1 Errors Are More Important Than Type 2 Errors” from The 20% Statistician, and “Criminal Justice Policy Preference: Blackstone Ratios and the Veil of Ignorance” by Nicholas Scurich of the Stanford Law & Policy Review. As a result of our new findings, our research is evolving into a relative analysis of hearsay evidence and its applications to bayesian law deliberations.

We’ve begun to answer some of the research questions that we proposed in our last post. To achieve a bayesian subgame perfect equilibrium, we must set conditions that narrow our research focus and simplify our game. We’ve also decided that our games will be of incomplete and imperfect information, and that we’ll use bayesian probabilities to make our games solvable, although they will still be deficient in terms of available information. A new question we’ve begun working on is “At what time will it be most beneficial to include hearsay evidence?” and “How is hearsay evidence influenced by the rest of the evidence presented?”.

We’ve discovered that the jury deliberation process has already been presented using game theory in several model formats. These models assume that jurors receive utility, or satisfaction, from maximizing the probability that they will convict a guilty suspect while minimizing the probability that they will convict an innocent suspect. Our goal is to model hearsay evidence taking into account that jurors recognize the information that they are receiving may or may not be true.

Two important ideas we’re exploring now are:

1. The more relatively reliable the information is that the jurors receive, the easier it will be for them to judge the veracity of the hearsay evidence.
2.  Jurors ask themselves how their fellow jurors are likely to react to the hearsay evidence as they form their own reaction. In essence, they are preparing for the deliberative process where the jury works collectively to produce a verdict. Each juror acts as a player in a game which involves the other jurors as players, similar to the famous Wooly Mammoth game in Game Theory. In it, each player shares a collective responsibility where they are simultaneously influenced by and influencing other players. This idea is specifically shaping our research.

We intend now to consider the judge as a determinant of the environment in which the jurors deliberate, as opposed to being a player. The game, as a result, would be between the jurors themselves. At this point, we feel we have all the tools to start constructing games using the information we’ve gathered.