Bayesian decision theory can guide legal factfinding

• Pages: 181-198
• Date: 01 July 2026
• Published date: 01 July 2026
• Author: Mario Günther
• Subject Matter: Derecho Procesal

Quaestio facti. Revista Internacional sobre Razonamiento Probatorio / International Journal on Evidential Legal Reasoning

Año 2026 11 pp. 181-198 DOI: 10.33115/udg_bib/qf.i11.23280

Quaestio facti. Revista Internacional sobre Razonamiento Probatorio

Quaestio facti. International Journal on Evidential Legal Reasoning

Sección: Conjeturas y refutaciones

2026 l 11 pp. 181-198

Madrid, 2026

DOI: 10.33115/udg_bib/qf.i11.23280

Marcial Pons Ediciones Jurídicas y Sociales

© Mario Günther

ISSN: 2604-6202

Recibido: 07/05/26 | Aceptado: 16/06/26 | Publicado online: 26/06/2026

Editado bajo licencia Reconocimiento 4.0 Internacional de Creative Commons

BAYESIAN DECISION THEORY

CAN GUIDE LEGAL FACTFINDING

Mario Günther*

Panthéon Sorbonne

ABSTRACT: I argue that Bayesian decision theory can guide legal factnding. I do so by oering an

account of legal proof on which judges should minimize expected justice costs. My account entails

a judge’s credence threshold for nding guilty and his prior credence of guilt. Hence, it can guide

a judge in his decision based on the lawful evidence presented at trial—unlike the Bayesian model

Mackor presents.

KEYWORDS: Philosophy of Law, Legal Proof, Bayesianism, Decision eory, Retributive Justice,

Undeserved Punishment.

SUMMARY: 1. INTRODUCTION.— 2. THE PRINCIPLE OF EXPECTED UTILITY MAXI-

MIZATION.— 3. JUSTICE COSTS: 3.1. A Simpler Credence reshold; 3.2. e Severity

of Undeserved Punishment; 3.3. e Severity of the Crime and Appropriate Punishments.— 4.

BAYESIAN EVIDENCE EVALUATION: 4.1. How to Determine the Prior Credence of Guilt?;

4.2. e Strength of the Evidence Required for Conviction.— 5. CONCLUSION.— APPEN-

DIX.— REFERENCES

* Please contact Mario.Gunther@univ-paris1.fr for any inquiries. ORCID: https://orcid.org/0000-

0001-6208-448X.

182 MARIO GÜNTHER

Quaestio facti. Revista Internacional sobre Razonamiento Probatorio / International Journal on Evidential Legal Reasoning

Año 2026 11 pp. 181-198 DOI: 10.33115/udg_bib/qf.i11.23280

1. INTRODUCTION

Mackor (2026) asks whether ‘the’ Bayesian model can and should guide the ju-

dicial evaluation of evidence in criminal cases as a whole. She focuses on Dutch

criminal law, which allows a judge to convict a defendant for an oense only if the

judge is convinced that the defendant committed it in light of the lawful evidence

presented at trial. However, a judge may not convict even if the presented lawful

evidence convinces him that the defendant is guilty. Mackor points out that this

freedom of choice leaves the judge “helpless” in his decision (p.364). For he lacks

further guidance on whether or not he should convict the defendant. Dutch criminal

law leaves open when the presented lawful evidence is sucient for a nding of guilt.

It leaves open how the judge should decide.

e Bayesian decision criterion is often conceptualized as a threshold for the pos-

terior probability that the defendant committed the alleged oence—the nal prob-

ability that the defendant is guilty after learning all the lawful evidence presented at

trial (Günther & Friedrich, 2026). However, a judge has only a posterior of guilt if

he starts out with a prior probability of guilt—the probability of guilt with which a

judge begins to evaluate the lawful evidence received at trial. Mackor suggests that

the judge’s prior of guilt could be based on some reference class. is poses the ques-

tion what reference class of the many possible ones should be used to estimate the

prior (fn.4). If there is no suitable reference class, she suggests relegating the task of

determining the prior of guilt to “the court”—without giving any further guidance

(pp.366-7&fn. 11).

Surprisingly, Mackor does not oer a Bayesian standard of proof in terms of a

probability threshold. She neither says when a nal probability of guilt suces for

nding a defendant guilty, nor what a judge’s prior of guilt should be in general.

e Bayesian model Mackor presents leaves open how a judge should decide. As it

stands, the model cannot guide judges in their decisions.

Here I argue that Bayesian decision theory can guide a judge’s factnding. I do

so by oering a decision-theoretic account of legal proof which does not leave open

how a judge should decide. e account is based on the heart of Bayesian decision

theory—the principle of expected utility maximization (EUM). But it goes beyond

the formalism of decision theory by making a substantive assumption about the

justice costs of the possible trial outcomes. e normative assumption entails with

the principle of EUM a probability threshold for nding guilty from which I derive

a prior probability of guilt. e result is a Bayesian account for how a judge should

decide in criminal trials. e account shows that Bayesian decision theory can guide

legal factnding in principle.

e plan is as follows. Section 2 explains how the principle of EUM can gure

as the decision criterion in legal factnding. Section 3 argues for an assignment of

utilities or justice costs to the possible trial outcomes based on the substantive as-