## 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.

## Blog #2: A Game Theoretic Analysis of the Hearsay Rule

Since our last blog post, we have acquired two law review journal articles that examine two very different viewpoints with respect to the application of the hearsay rule, which we found to be very useful for our studies. The first is a Harvard Law review article titled, “The History of the Hearsay Rule” which was written in 1904 by John H. Wigmore. The second, “Jack Weinstein and the Missing Pieces of the Hearsay Puzzle” appeared in the DePaul Law Review much more recently in 2015. Friedman’s review stresses the positive information content obtained through cross examination from witnesses offering hearsay testimony. Wigmore, on the other hand, considers the balance between additional information and its veracity.  He also considers the impact of dubious hearsay testimony on the legal rights of the defendant. The reviews helped us to shape our research and in deciding which aspects of game theory are most relevant to the benefits and costs of hearsay testimony. The articles also extended our understanding of the history and evolution of the hearsay rule.

In “The History of The Hearsay Rule,” Wigmore discusses the strongest objection of the hearsay rule being applied between the 16th and 18th century. At that time, it was important to the court that the accused not directly engage with their accuser. Wigmore argued that the pragmatics dictated that, by its very nature, the hearsay rule is not subject to direct cross examination. Over time, this perspective has dramatically changed. The modern view of hearsay evidence stresses this exact opportunity for cross examination as essential in determining if evidence is admissible. In the review, Wigmore also explored the general reluctance of hearsay testimony with a set of exceptions which included deathbed testimony.

Friedman takes a slightly different approach than Wigmore in “Jack Weinstein and the Missing Pieces of the Hearsay Puzzle.” Friedman and Wigmore differ critically in a major aspect of the hearsay rule. This is mainly due to the time period in which the journal articles were written and the evolution that has occurred in law, which stresses cross examination and a defendant’s right to confront their accuser. Within his review, Friedman analyzed Judge Jack Weinstein’s monumental treatise from 1975 that is still widely accepted today. His review also took a look at his most important contributions to modern hearsay rules, which stress a discretionary approach. The treatise argues that the Hearsay rules be functionally oriented and procedurally sensitive. We will use this review to define and understand modern hearsay rules within the context of balancing legal rights against information of uncertain value.

Friedman believes that some constraint on hearsay evidence is necessary for it to be probative. Friedman is not in favor of deathbed testimony being admitted in hearsay. He also makes it clear that he would not be in favor of admitting a signed affidavit as evidence. This all supports the modern value of the right to cross examination. Friedman stressed the importance of cross examination and testimonial hearsay to protect the rights of the defendants. He continued to relate hearsay to confrontational rights. He even went as far as stating that even if the Supreme Court were to reverse these confrontational rights, they should be ingrained into the law. Friedman also believed in giving discretion to the judge and the value of incorporating more information, at the risk of some of that information not being credible. We intend to tie this into subgame perfection which requires that information admitted must be credible in every subgame of the game.

We will be analyzing hearsay information using concepts of information asymmetries and bayesian probabilities used in Game Theory. Information is either imperfect or incomplete, corresponding to the problematic aspects involving hearsay evidence.  Game Theory is expected to illuminate this issue with greater clarity. Some questions we want to ask include:

1. Under what conditions are we more likely to achieve a bayesian subgame perfect equilibrium?
2. With the potential for multiple equilibria, under what conditions does bayesian information become admissible?
3. Are we in a game of imperfect or incomplete information? (We’re making the assumption that it depends on how verifiable the information is.)

Our goal is to minimize the type 1 error of convicting an innocent. We hope to determine a probability distribution that can be translated into a rule of law.

Our next step is to deepen our understanding of the evolution of the hearsay rule and obtain more research to assist our studies. We also plan to begin constructing games. We imagine this can go in the direction of two 3-player games; the first between the two parties of the case and the judge, and the second between the two parties and the jury where the judge and jury can act as players or bayesian probability distributions in their acceptance of the evidence given to them at various stages of a combination simultaneous-sequential game. Some stages of the game could include the judge accepting evidence and another could include the jury determining if they want to accept or nullify the evidence if the judge chose to accept it. If successful, we intend to develop a way to test this game out with students. Specifically, we would focus on testing their processing and accepting of the information given to them, as a jury would.

## Blog #1: A Game Theoretic Analysis of the Hearsay Rule

Our research aims to analyze the Hearsay Rule from a game theoretic perspective. Our objective is to understand how exceptions to the Hearsay Rule may or may not contribute to the ability of judges and juries reaching a just decision, with emphasis on which Hearsay evidence is incorporated into the fact pattern and information available in any given case.

The Hearsay Rule has a rich tradition in common law and in both criminal and civil jurisprudence. The need to provide a fair trial while providing sufficient evidence to a judge or jury may be mutually incompatible. In the case of The Hearsay Rule, the presentation of hearsay evidence may enrich the information content of case or may conceivably diminish that content given the quality and veracity of that evidence.

In order to balance efficiency and equity it would be highly desirable to perform a cost and benefit analysis of the advantages and disadvantages of the inclusion of hearsay information among the facts of the case. Although it is impossible to determine whether the hearsay evidence is correct of incorrect it is possible to analyze, from a probabilistic standpoint, the likely impact of creating irreversible error in judicial decision making. The techniques of Applied Game Theory are uniquely suitable for this type of analysis.

Introducing information into a strategic decision making environment is well supported in Game Theory. For example, when economists specify the characteristics of a game’s equilibrium, with respect to existence identification and robustness. Research employed will investigate the application of concepts including cheaptalk, babbling equilibrium, signaling, screening, and Bayesian perfection. Special attention will be applied to the most common exceptions to The Hearsay Rule in light of their implied tradeoff between efficiency and equity.