What Is ‘Real’ in Interpersonal Comparisons of Confidence

ABSTRACT

According to comparativism, comparative confidence is more fundamental than absolute confidence. In two recent AJP papers, Stefánsson has argued that comparativism is capable of explaining interpersonal confidence comparisons. In this paper, I will argue that Stefansson’s proposed explanation is inadequate; that we have good reasons to think that comparativism cannot handle interpersonal comparisons; and that the best explanation of interpersonal comparisons requires thinking about confidence in a fundamentally different way than that which comparativists propose: specifically, we should think of confidence as a dimensionless quantity.

KEYWORDS:

• comparativism
• confidence
• interpersonal comparisons
• degrees of belief
• measurement

Disclosure Statement

No potential conflict of interest was reported by the author.

Notes

1 For detailed discussions of this methodology aimed at philosophical audiences, see Fine [1973: 68ff], Stefánsson [2017, 2018], and Elliott [2020, forthcoming b]; for a formal treatment, see Krantz et al. [1971: 199–21]. The same methodology can also be used to give truth conditions for claims about ratios (not just ratios of differences) whenever ≽_α is coherent and continuous. This is not noted initially by Stefánsson [2017], but the fact is exploited later by him [2018]. It won’t make any difference to my arguments whether we think that confidence is measurable on nothing stronger than an interval scale, or if we think that it’s measurable on a ratio scale. I focus on ratios of differences only because that’s Stefánsson’s earlier [2017] focus.

2 That is, g is a positive affine transformation of f just in case, for all P, g(P) = f(P)r + c, for r > 0 and any constant c. Except in the special case where c = 0, any positive affine transformation of a probability function p will violate Additivity. Almost all positive affine transformations of a probability function will therefore not preserve ratios between the values that function assigns; nevertheless, they will preserve ratios of differences, and that’s all we need.

3 This is an example to which I will return later in the paper.

4 To be explicit, I am assuming that utility-for-α is an interval-preserving measure of α’s preferences; likewise for β. I’m therefore assuming that rational agents have preferences that are measurable as such. This should be generally uncontroversial. I am not arguing that interpersonal utility comparisons are meaningless. I do happen to think that interpersonal utility comparisons are meaningless, but right now I’m only noting that the mere fact that utility-for-α and utility-for-β are psychologically similar does not imply that they’re comparable.

5 I’m here presupposing in what follows that there are some Q and R such that α prefers Q to R; and, to keep things simple, I’m assuming that α is indifferent between Q and (Q∧P), and between R and (R∧¬P).

6 Following Eriksson and Hájek [2007], you might worry here about so-called ‘Zen monk’ cases, or agents who are indifferent amongst all things. I have responded to this problem elsewhere [forthcoming a]. In short, a functional characterisation of α’s confidence states is given in terms, not of how those states interact with her actual utilities/preferences, but instead of their potential interactions with different utility/preference states in which she could be. If α is actually indifferent amongst all things, then she can still be in a state the typical causal role of which would only become apparent if she were no longer to be universally indifferent.

7 I’ll flag here that I think there are further problems with the same-role response. I’ve been granting, for the sake of argument, that if two agents have identical coherent and continuous confidence rankings, then they have identical absolute confidences. But that’s a commitment of Stefánsson’s comparativism, not a self-evident truth. It is, at least arguably, conceptually possible for two agents to have identical confidence rankings and yet to attach different absolute confidences to propositions at the same ‘locations’ within their respective rankings (including the minima and maxima). This includes cases where the differences in absolute confidence between the agents are systematically reflected by differences in their preferences as predicted by an underlying decision theory, and are thus functionally distinct, according to that theory. This is, however, a more general problem for comparativism that I’ve discussed elsewhere [forthcoming b], I don’t want to dwell on it further here.

8 In saying this, I’m taking no stand on whether quantitative facts are anything over and above relational facts. For more discussion, see Dasgupta [2013]. Even if you think that there’s more to the facts about a quantity than its relational facts, you’ll still agree that every quantity determines some relational facts that we can then use to differentiate between them.

9 I thank an anonymous referee for offering this suggestion.

10 Thanks are due to Nick DiBella for helpful discussions on the topic, and to anonymous referees.