Abstract
In recent decades, empirical investigation has increasingly illuminated how experts in the legal domain, including judges, evaluate evidence and hypotheses, reason and decide about them. Research has highlighted both the cognitive strategies employed in legal reasoning, and the cognitive pitfalls judges and other experts tend to fall prey to. In this paper, we focus on the “conjunction fallacy”, a widespread phenomenon showing that human reasoners systematically violate the rules of probability calculus. After presenting the fallacy as documented in judicial reasoning, we present two formal accounts of the phenomenon, respectively based on the notions of confirmation (evidential support) and truthlikeness (closeness to the truth) as studied in the philosophy of science. With reference to the “story-model” of legal decision-making, we clarify the role that “cognitive utilities” like truth, probability, and information play in legal reasoning, and how it can account for the documented fallacies. We conclude by suggesting some directions for further investigation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
For a survey, see Rachlinski and Wistrich (2017).
- 2.
Tversky and Kahneman (1983).
- 3.
- 4.
- 5.
- 6.
- 7.
Guthrie et al. (2009).
- 8.
While already discussed by Tversky and Kahneman (1983), double conjunction fallacies have been rarely investigated in the literature, also because they are hardly reconciled with most suggested accounts of the (single) conjunction fallacy (Crupi et al. 2018a). The phenomenon is also reported in a recent study of legal decision-making by Wojciechowski and Pothos (2018), even if it is limited to a group of participants with no legal background.
- 9.
In this connection, it is perhaps worth noting that the discussion in Guthrie et al. (2009) does not fully clarify whether the Dina experiment is construed as an instance of the “M-A paradigm” or of the “A-B paradigm”, in the terminology of Tversky and Kahneman (1983, pp. 304 ff.). Roughly, the difference is that, in the former experimental paradigm, a “model” (e.g., Linda story) is positively associated (in terms of representativeness, probability, etc.) to one of the conjuncts (“feminist”) and negatively associated to the other (“bank teller”); whereas in the A-B paradigm, one conjunct is positively associated to the other, even if the latter is not positively associated with the model. Since the two paradigms have different theoretical implications, this point would need further discussion in order to properly assess and interpret the experimental results.
- 10.
- 11.
- 12.
Cevolani and Crupi (2015).
- 13.
Tversky and Kahneman (1983), p. 311.
- 14.
Carnap’s (1962), pp. xv–xx.
- 15.
Cf. Fitelson (2005).
- 16.
See, e.g., Peijnenburg (2012) for a recent discussion.
- 17.
Good (1968), p. 134.
- 18.
- 19.
- 20.
Crupi et al. (2008), p. 188.
- 21.
Popper (1963, ch. 10) proposed the notion of truthlikeness in order to defend the idea that, while likely false, scientific hypotheses and common beliefs can still be close the truth, thus making possible the progress of science and human knowledge in general as a gradual approximation to the truth. His ideas were further elaborated and refined by other scholars (Niiniluoto 1987, 1998; Oddie 2016). For recent discussion, see Cevolani (2017) and Cevolani and Festa (2020).
- 22.
A point also hinted at by Tversky and Kahneman themselves: (1983), p. 312.
- 23.
- 24.
Cevolani et al. (2010).
- 25.
- 26.
The long and spirited debate between two leading philosophers like Karl Popper and Rudolf Carnap (and their followers) is an example of such a discussion; since then, scholars working on so called cognitive decision theory have explored these issues in great detail, providing a solid formal background to the analysis of different cognitive utilities (Levi 1967; Niiniluoto 1987, ch. 12, 2011).
- 27.
- 28.
Scholars in different fields have proposed different measures of the information content of a hypothesis h; for all of them, if h has greater content than g, then h is not more probable than g. One simple such measure, proposed by Popper (1934/1959) among others, amounts to defining informativeness as the plain improbability 1 – P(h), thus making obvious the above inverse relation between the two notions. For a survey of different formal accounts of information as applied to human cognition and information search, see Crupi et al. (2018b).
- 29.
- 30.
- 31.
It “has all its parts”, Pennington and Hastie (1993), pp. 198–199.
- 32.
Vorms and Lagnado (2019), p. 108.
- 33.
- 34.
Cf. Simon (1998).
- 35.
Cf. Heller (2006).
- 36.
Rachlinski and Wistrich (2017).
- 37.
- 38.
Cf. Vorms and Lagnado (2019), p. 104.
- 39.
- 40.
Schum (2001).
- 41.
- 42.
Cf. Vorms and Lagnado (2019), p. 118.
- 43.
Cf. Cevolani and Crupi (2015).
References
Bovens L, Hartmann S (2003) Bayesian epistemology. Oxford University Press, Oxford
Carnap R (1962). Logical foundations of probability, 2nd edn., 1st edn. University of Chicago Press, Chicago, p 1950
Cevolani G (2017) Truthlikeness and the problem of measure sensitivity. In: Massimi M, Romeijn J, Schurz G (eds) EPSA15 selected papers. Springer, pp 257–271
Cevolani G, Crupi V (2015) Subtleties of naive reasoning. Probability, confirmation, and verisimilitude in the Linda paradox. In: Bianca M, Piccari P (eds) Epistemology of ordinary knowledge, Cambridge Scholars
Cevolani G, Festa R (2020) A partial consequence account of truthlikeness. Synthese 197(4):1627–1646
Cevolani G, Crupi V, Festa R (2010) The whole truth about Linda: probability, verisimilitude, and a paradox of conjunction. In: D’Agostino M, Giorello G, Laudisa F, Pievani T, Sinigaglia C (eds) SILFS new essays in logic and philosophy of science. College Publications, London, pp 603–615
Cevolani G, Crupi V, Festa R (2011) Verisimilitude and belief change for conjunctive theories. Erkenntnis 75(2):183–202
Crupi V (2020) Confirmation. In: Zalta EN (ed) The Stanford Encyclopedia of Philosophy. Spring 2020 Edition, URL = https://plato.stanford.edu/archives/spr2020/entries/confirmation/
Crupi V, Fitelson B, Tentori K (2008) Probability, confirmation and the conjunction fallacy. Think Reason 14:182–199
Crupi V, Elia F, Aprà F, Tentori K (2018a) Double conjunction fallacies in physicians’ probability judgment. Med Decis Mak 38(6):756–760
Crupi V, Nelson JD, Meder B, Cevolani G, Tentori K (2018b) Generalized information theory meets human cognition: introducing a unified framework to model uncertainty and information search. Cogn Sci 42(5):1410–1456
Fitelson B (2005) Inductive logic. In: Pfeifer J, Sarkar S (eds) Philosophy of science. An encyclopedia. Routledge, New York, pp 384–393
Gigerenzer G and The ABC group (1999) Simple heuristics that make us smart. Oxford University Press
Good IJ (1968) Corroboration, explanation, evolving probability, simplicity, and a sharpened razor. Br J Philos Sci 19:123–143
Griffin LK (2013) Narrative, truth, and trial. Georgetown Law J 101:281–335
Guthrie C, Rachlinski JJ, Wistrich AJ (2009) The hidden ‘judiciary’: an empirical examination of executive branch justice. Duke Law J 58(7):1477–1530
Heller KJ (2006) The cognitive psychology of circumstantial evidence. Mich Law Rev 105:241
Huber F (2008) Assessing theories, bayes style. Synthese 161:89–118
Kahneman D, Frederick S (2002) Representativeness revised: attribute substitution in intuitive judgment. In: Gilovich T, Griffin D, Kahneman D (eds) Heuristics and biases: the psychology of intuitive judgment. Cambridge University Press, New York, pp 49–81
Kuipers TAF (2012) A realist partner for Linda: confirming a theoretical hypothesis more than its observational sub-hypothesis. Synthese 184:63–71
Lagnado D (2011) Thinking about evidence. In: Dawid P, Twining W, Vasilaki M (eds) Evidence, inference and enquiry. OUP/British Academy, pp 183–223
Lagnado DA, Shanks DR (2002) Probability judgment in hierarchical learning: a conflict between predictiveness and coherence. Cognition 83:81–112
Levi I (1967) Gambling with truth. Alfred A. Knopf, New York
Levi I (1985) Illusions about uncertainty. Br J Philos Sci 36:331–340
Levi I (2004) Comments on Jaakko Hintikka. Synthese 140(1/2):37–41
Niiniluoto I (1987) Truthlikeness. Reidel, Dordrecht
Niiniluoto I (1998) Verisimilitude: the third period. Br J Philos Sci 49:1–29
Niiniluoto I (2011) The development of the Hintikka program. In: Gabbay DM, Woods J, Hartmann S (eds) Handbook of the history of logic. Elsevier, pp 311–356
Oddie G (2016) Truthlikeness. In: Zalta EN (ed) The Stanford Encyclopedia of Philosophy. URL = http://plato.stanford.edu/archives/spr2014/entries/truthlikeness/
Peijnenburg J (2012) A case of confusing probability and confirmation. Synthese 184(1):101–107
Pennington N, Hastie R (1986) Evidence evaluation in complex decision making. J Pers Soc Psychol 51:242–258
Pennington N, Hastie R (1993) The story model for juror decision making. In: Hastie R (ed) Inside the juror. Cambridge University Press, Cambridge, pp 192–222
Popper KR (1934/1959) Logic of scientific discovery. Routledge and Kegan Paul, London
Popper KR (1963) Conjectures and refutations. Routledge and Kegan Paul, London
Rachlinski JJ, Wistrich AJ (2017) Judging the judiciary by the numbers: empirical research on judges. Ann Rev Law Soc Sci 13(1):203–229
Samuels R, Stich S, Bishop M (2002) Ending the rationality wars: how to make disputes about human rationality disappear. In: Elio R (ed) Common sense, reasoning and rationality. Oxford University Press, New York, pp 236–268
Schum DA (2001) The evidential foundations of probabilistic reasoning. Northwestern University Press, Evanston
Sides A, Osherson D, Bonini N et al (2002) On the reality of the conjunction fallacy. Mem Cogn 30:191–198
Simon D (1998) A psychological model of judicial decision making. Rutgers Law J 30(1):1–142
Sprenger J, Hartmann S (2019) Bayesian philosophy of science. Oxford University Press, New York
Taroni F, Biedermann A, Bozza S, Garbolino P, Aitken C (2014) Bayesian networks for probabilistic inference and decision analysis in forensic science. John Wiley & Sons, Chichester
Teichman D, Zamir E (2014) Judicial decision-making: a behavioral perspective. In: The Oxford handbook of behavioral economics and the law. Oxford University Press, Oxford, pp 664–702
Tenenbaum JB, Griffiths TL (2001) Generalization, similarity, and Bayesian inference. Behav Brain Sci 24(4):629–640
Tentori K, Crupi V (2012) How the conjunction fallacy is tied to probabilistic confirmation: some remarks on Schupbach (2009). Synthese 184:3–12
Tentori K, Crupi V, Russo S (2013) On the determinants of the conjunction fallacy: probability vs. inductive confirmation. J Exp Psychol Gen 142:235–255
Thagard P (2000) Coherence in thought and action. Bradford Books
Tversky A, Kahneman D (1982) Judgments of and by representativeness. In: Kahneman D, Slovic P, Tversky A (eds) Judgment under uncertainty: heuristics and biases. Cambridge University Press, New York, pp 84–98
Tversky A, Kahneman D (1983) Extensional vs. intuitive reasoning: the conjunction fallacy in probability judgment. Psychol Rev 90:293–3l5
Vorms M, Lagnado D (2019) Coherence and credibility in the story-model of jurors’ decision-making: does mental simulation really drive the evaluation of the evidence? In: Nepomuceno-Fernández Á, Magnani L, Salguero-Lamillar F, Barés-Gómez C, Fontaine M (eds) Model-based reasoning in science and technology. Springer, Cham
Wedell DH, Moro R (2008) Testing boundary conditions for the conjunction fallacy: effects of response mode, conceptual focus, and problem type. Cognition 107:105–136
Wojciechowski BW, Pothos EM (2018) Is there a conjunction fallacy in legal probabilistic decision making? Front Psychol 9
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Additional information
Gustavo Cevolani acknowledges financial support from the Italian Ministry of Education, Universities and Research (MIUR) through the grant n. 201743F9YE (PRIN 2017 project “From models to decisions”).
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Cevolani, G., Crupi, V. (2022). Truth, Probability, and Evidence in Judicial Reasoning: The Case of the Conjunction Fallacy. In: Bystranowski, P., Janik, B., Próchnicki, M. (eds) Judicial Decision-Making. Economic Analysis of Law in European Legal Scholarship, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-031-11744-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-031-11744-2_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-11743-5
Online ISBN: 978-3-031-11744-2
eBook Packages: Social SciencesSocial Sciences (R0)