[Paper Review] Crime Aggregation, Deterrence, and Witness Credibility

Harry Pei, Bruno Strulovici|arXiv (Cornell University)|Sep 14, 2020

Experimental Behavioral Economics Studies43 references5 citations

TL;DR

This paper models how crime aggregation under the Aggregate Probabilities Principle (APP) distorts witness incentives by inducing negative correlation in private information, leading to uninformative reports and reduced deterrence. In contrast, treating accusations separately (DPP) preserves report informativeness and enhances deterrence, challenging legal scholarship that advocates APP for efficiency and fairness.

ABSTRACT

We present a model for the equilibrium frequency of offenses and the informativeness of witness reports when potential offenders can commit multiple offenses and witnesses are subject to retaliation risk and idiosyncratic reporting preferences. We compare two ways of handling multiple accusations discussed in legal scholarship: (i) When convictions are based on the probability that the defendant committed at least one, unspecified offense and entail a severe punishment, potential offenders induce negative correlation in witnesses' private information, which leads to uninformative reports, information aggregation failures, and frequent offenses in equilibrium. Moreover, lowering the punishment in case of conviction can improve deterrence and the informativeness of witnesses' reports. (ii) When accusations are treated separately to adjudicate guilt and conviction entails a severe punishment, witness reports are highly informative and offenses are infrequent in equilibrium.

Motivation & Objective

• To analyze the strategic incentives of potential offenders and witnesses when multiple offenses are possible and convictions depend on aggregate or distinct probabilities of guilt.
• To evaluate whether the Aggregate Probabilities Principle (APP), which convicts if the total probability of any offense exceeds a threshold, improves deterrence and fairness compared to the Distinct Probabilities Principle (DPP).
• To investigate how retaliation risk and idiosyncratic reporting preferences affect witness reporting behavior under different legal treatment of multiple accusations.
• To model the endogenous relationship between offense frequency, witness report informativeness, and punishment severity under APP and DPP.
• To challenge the assumption in legal scholarship that APP improves adjudication by showing it can lead to information aggregation failure due to strategic behavior.

Proposed method

• Models a principal (potential offender) who may commit multiple independent offenses, each observed by a distinct witness with private information.
• Each witness decides whether to accuse based on a preference to punish, fear of retaliation, and idiosyncratic private costs or benefits of conviction.
• Uses a Bayesian game framework where witnesses' signals are conditionally independent given the principal's actions, but strategic behavior induces negative correlation in signals under APP.
• Derives equilibrium thresholds for reporting behavior under both APP and DPP, comparing the resulting levels of deterrence and report informativeness.
• Analyzes the impact of punishment severity on deterrence and report quality, showing that lowering punishment can improve deterrence under APP due to reduced retaliation incentives.
• Employs comparative statics to show that increasing the number of witnesses leads to higher offense probabilities under APP, due to strategic negative correlation in reporting.

Experimental results

Research questions

• RQ1 Under what conditions does the Aggregate Probabilities Principle (APP) lead to uninformative witness reports, and why does this undermine its intended benefits?
• RQ2 How does the strategic interaction between potential offenders and witnesses affect the informativeness of reports when multiple offenses are aggregated versus adjudicated separately?
• RQ3 Does lowering the punishment for conviction under APP improve deterrence, and if so, why?
• RQ4 How does the number of witnesses affect the equilibrium frequency of offenses and the informativeness of reports under APP?
• RQ5 Why does the DPP regime lead to more effective deterrence and more informative reports than APP, despite APP’s theoretical appeal in legal scholarship?

Key findings

• Under APP, potential offenders induce negative correlation in witnesses’ private signals, rendering reports uninformative and reducing the effectiveness of deterrence.
• The equilibrium frequency of offenses is higher under APP than under DPP, due to the strategic distortion in witness reporting incentives.
• Lowering the punishment for conviction under APP can improve deterrence and increase report informativeness, contrary to conventional expectations.
• The DPP regime results in more informative witness reports and lower offense frequencies because it avoids the strategic negative correlation induced by APP.
• As the number of witnesses increases, the probability of offense under APP rises, due to the cumulative effect of strategic negative correlation in reporting behavior.
• The model shows that the independence assumption in prior legal scholarship on APP is violated in equilibrium, invalidating its core conclusions about improved adjudication.