TY - JOUR
T1 - Classical probabilities and belief functions in legal cases
AU - Meester, Ronald
PY - 2020/3
Y1 - 2020/3
N2 - I critically discuss a recent suggestion in Nance (Belief Functions and Burdens of Proof. Law, Probability and Risk, 18:53-76, 2018) concerning the question which ratios of beliefs are appropriate when in criminal or civil cases one works with belief functions instead of classical probabilities. I do not call into question the use of belief functions themselves in this context, and I agree with in Nance (Belief Functions and Burdens of Proof. Law, Probability and Risk, 18:53-76, 2018) that so-called 'uncommitted support', possible in the framework of belief functions, should not be taken into account in a decision-theoretic framework. However, I argue against in Nance (Belief Functions and Burdens of Proof. Law, Probability and Risk, 18:53-76, 2018) in that, at least in criminal law, relative sizes of beliefs should not be used for decision-making at all. I will argue that only the individual, absolute beliefs should be considered. Since belief functions generalize classical probabilities, this position seems at first sight to conflict with the fact that odds are abundant when we use classical probabilities in a legal context. I will take the opportunity, then, to point out that also in the classical setting, odds are not our primary concern either. They are convenient since they appear, together with the likelihood ratio, in the odds form of Bayes' rule. Apart from that, they do not have any individual significance. I also note that in civil law the conclusions might be different.
AB - I critically discuss a recent suggestion in Nance (Belief Functions and Burdens of Proof. Law, Probability and Risk, 18:53-76, 2018) concerning the question which ratios of beliefs are appropriate when in criminal or civil cases one works with belief functions instead of classical probabilities. I do not call into question the use of belief functions themselves in this context, and I agree with in Nance (Belief Functions and Burdens of Proof. Law, Probability and Risk, 18:53-76, 2018) that so-called 'uncommitted support', possible in the framework of belief functions, should not be taken into account in a decision-theoretic framework. However, I argue against in Nance (Belief Functions and Burdens of Proof. Law, Probability and Risk, 18:53-76, 2018) in that, at least in criminal law, relative sizes of beliefs should not be used for decision-making at all. I will argue that only the individual, absolute beliefs should be considered. Since belief functions generalize classical probabilities, this position seems at first sight to conflict with the fact that odds are abundant when we use classical probabilities in a legal context. I will take the opportunity, then, to point out that also in the classical setting, odds are not our primary concern either. They are convenient since they appear, together with the likelihood ratio, in the odds form of Bayes' rule. Apart from that, they do not have any individual significance. I also note that in civil law the conclusions might be different.
KW - belief functions
KW - decision
KW - evidence
KW - likelihood ratio
KW - posterior and prior odds
KW - relative size of beliefs
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U2 - 10.1093/lpr/mgaa005
DO - 10.1093/lpr/mgaa005
M3 - Article
AN - SCOPUS:85093984947
SN - 1470-8396
VL - 19
SP - 99
EP - 107
JO - Law, Probability and Risk
JF - Law, Probability and Risk
IS - 1
ER -