Probability fixed points, (in)adequate concept possession and COVID-19 irrationalities

ABSTRACT

We argue that probability mistakes indicate that at least some of us often do not adequately possess the concept of probability (and its cognates) and that the digital dissemination of such misinformation helps foster collective irrationalities (e.g., COVID-19 underestimation and vaccination hesitancy), with detrimental effect for society. Such probability mistakes betray that at least some of us often do not grasp necessary conditions on the concept of probability, what we call probability fixed points. Our case study that illustrates this phenomenon in action is the recent COVID-19 pandemic. We present paradigmatic examples of probability mistakes during the COVID-19 pandemic and explain how such mistakes are especially prone to help create digital epistemic bubbles and echo chambers (cf. Nguyen (2020)) that foster collective irrationalities, such as COVID-19 underestimation and skepticism and vaccination hesitancy.

KEYWORDS:

• Probability fixed points
• conceptual competence
• COVID-19 irrationalities

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. See Kahneman, (2011), Haigh, (2012) and Evans, (2017) for discussion. See Mellor, (2004) and Gillies, (2012) for some philosophical discussion of probability.

2. For nudge theory, see Thaler and Sunstein, (2008).

3. Another timely example of the phenomenon would, presumably, be climate change skepticism.

4. Other factors involved in COVID-19 irrationalities are intellectual vices and cognitive biases, see Meyer et al., (2021) for discussion.

5. We call them “fixed points” in reminiscence of Cuneo and Shafer Landau, (2014) moral fixed points. They are necessary truths about probability that constrain the correct application of the concept of probability. That is, our reliable truth-tracking of objective chance. By our lights, Lewis, (1986) principal principle is also such a probability fixed point. To clarify, the term should not be confused with the identical mathematical term.

6. See Handfield, (2012) for some discussion of Lewis, (1986) Principal Principle.

7. There is some debate about the role probability should play (if any) in epistemic theorizing and our epistemic lives. Some, for example Harman, (1986), have argued that probability is not a concept that can be very practical for our epistemic lives and Williamson, (2000) has argued that evidential probability is explainable in terms of more basic knowledge. We have no space to delve into such questions here and we will facilely assume that probability constrains epistemically rational probabilistic belief. But we think that in contexts where the practical stakes are high and probabilities are practically relevant, we should consult epistemically rational probabilistic belief. For discussion of epistemic probability, see Cuneo and Kyriacou (2018).

8. For the importance of conditional probabilities during the COVID-19 pandemic, see Lewis, (2021).

9. We take it that beliefs in vaccination hesitancy and skepticism and COVID-19 underestimation and skepticism are irrational because they exhibit evidence-resistance i.e., they are not sensitive to ample available empirical evidence and reliable expert testimony. As a result, evidence-resistance beliefs violate an evidential epistemic rationality norm and Lewis, (1986) principal principle because they fail to adjust subjective credence to objective chance, given evidence. For some discussion of the relation of probability and rationality, see Goldman (1986:305-323). Goldman (1986) is skeptical about whether probability mistakes are irrational, but we cannot delve into the issue here.

10. Needless to say, we all fall prey to mistakes of reasoning or irrationality, including mathematicians, philosophers and scientists. There is extensive literature supporting the fact that no matter training and education, people can be flawed in their interpretation of statistics and probabilistic information, especially when it comes to health-related issues (See Slovic, (2000), Gigerenzer et al., (2007), Harman et al., (2021)).

11. Ismael, (2011, p. 418) has already identified the confusion that arises from the failure to distinguish between the two objective concepts of probability: general probability and single-case probability (or chance).

12. For example, Von Mises, (1964, p. 15) expresses his frequency absolutism in the following aphorism: “probability cannot be applied to … [single-cases] any more than the physical concept of work can be applied to the calculation of the ‘work’ done by an actor in reciting his part in a play”.

13. For intellectual virtues and vices see Zagzebski, (1996) and Baehr, (2011), and for cognitive biases Kahneman, (2011), Thaler and Sunstein, (2008) and Evans, (2017). For the epistemic threat they pose, see Hannon, (2021), Wallbridge, (2021) and Carter and McKenna, (2020). Allen and Lynch, (2022) provide some optimism about how we can find our way out of such a skeptical quandary. For empirical work supporting the claim that unrealistic optimism bias during the COVID-19 pandemic is negatively associated with the adoption of protective behaviors see Mccoll et al., (2021).

14. For a comprehensive discussion on frequentism and the problem of the single case, see Hájek, (1996).

15. We think that there can always be some evidence that supports assigning some probability value to an event, even if it is a single case, but we cannot digress further here.

16. See Hájek, (2007) for the reference class problem.

17. See Kahneman, (2011) for discussion of the law of large numbers.

18. See Botzen et al., (2022) for empirical work supporting the claim that people’s risk perceptions are related to their personal experiences with COVID-19 as well as experiences of people close to them. That is the availability heuristic operating at its best.

19. See Kahneman, (2011) for the availability and representativeness biases and Evans, (2017) for the focusing bias.

20. See Kahneman, (2011) for the base rate fallacy.

21. There is also the question of moral and social obligations and responsibility. Arguably, even if John were prudentially wise, he would not be morally wise because he does not fulfil the moral obligation of socially responsible action. We think that our practical deliberation should take into account both prudential and moral and social considerations into account, but again this is a topic we cannot delve into here.

22. The condition of the total relevant probability is in essence a version of the total evidence requirement on justification.

23. See Kahneman, (2011) for our intuitive causal understanding of the world and Evans, (2017) for the fact that we are better in processing frequencies rather than probability values.

24. We demur about how prevalent in the general population such mistakes are, which is an interesting empirical question in its own right.

25. See Peacocke, (1992), Smith, (1994), Brandom, (2000), Cuneo and Shafer Landau, (2014).

26. They lack characteristic prototypes such as flight and feathers and have a swimming ability, unlike most birds. See Rosch, (1975) for the prototype theory of concepts and Burge, (1979, pp. 89–92, Burge, 1988) for discussion of a partial understanding of concepts.

27. See Margolis and Laurence (2019: Section 2.1) for discussion of the classical theory of concepts.

28. See Williamson (2007, 2018) and McGinn, (2012) for discussion of conceptual analysis.

29. Redacted [XXX].

30. For instance, Alston, (2005) has called the project of a reductive conceptual analysis of epistemic justification “quixotic”, Williamson, (2000) has questioned the feasibility and the necessity of a reductive conceptual analysis of knowledge and Crick, (2002) has questioned the feasibility and necessity of a reductive conceptual analysis of democracy.

31. One reason for thinking that reliable application of a concept is not sufficient for adequate concept possession is that we may conceive of cases where someone is mechanically applying (i.e., “parroting”) the concept without really possessing the concept. Plausibly, some meta-conceptual awareness condition is required for full-er concept possession.

32. The full list of necessary conditions for judgmental and inferential reliability should be jointly sufficient for judgmental and inferential reliability. We only present what we take to be some necessary conditions for judgmental and inferential reliability.

33. The full list of necessary conditions for judgmental and inferential reliability should be jointly sufficient for judgmental and inferential reliability. We only present what we take to be some necessary conditions for judgmental and inferential reliability.

34. See Christensen, (2004) for the gradability of rational belief and credence.

35. Some of these probability fixed points, such as the gradability condition, seem more basic than others and we would expect minimally competent users of the concept of probability to grasp. Others, such as the base rates condition, seem much more cognitively demanding and there is empirical evidence that even well-educated agents can miss them (cf. Kahneman, (2011)). For the purposes of this paper, we do not distinguish between more basic minimal probability fixed points and more demanding, more advanced probability fixed points.

36. See Stojanovic et al., (2021) about the fact that COVID-19 is a more serious threat to health than flu (and with a higher mortality rate).

37. For the purpose of this paper, “collective irrationality” is understood to be the state of affairs where individual irrationalities are shared by a collective of individuals. Not every member of that collective need share the irrational belief for the collective to be irrational, but some sufficiently high percentage must share (if we are to speak of collective irrationality).

38. Goldman, (2001, pp. 94–7) distinguishes between direct and indirect argumentative justification for relying on an experts’ testimony. Roughly, direct argumentative justification involves the hearer understanding and endorsing one’s argument, while indirect argumentative justification involves an inference to the best explanation from the dialectical performance of the speaker. Either of the two strategies could be used to evaluate whether we should rely on the testimony of the digital conspiracy theorist, who often pretends to be an expert about a subject-matter.

39. For how Facebook nudges climate change skeptics toward misinformation and conspiracy theories, see the discussion in B.B.C here: https://www.bbc.com/news/technology-60905348. See also Spence, (2020) for discussion of the Cambridge Analytica case and about how Facebook’s operation does not perform according to normative standards of social responsibility (e.g., information sharing users’ information, fake news detection).

40. See Evans, (2017) for discussion.

41. See Cassam, (2019) on conspiracy theories.

42. We would like to thank two anonymous reviewers for helpful critical comments. XXX.

Additional information

Funding

The work was supported by the Alexander von Humboldt-Stiftung.