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Updating on Biased Probabilistic Testimony

Dealing with Weasels Through Computational Pragmatics

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We frequently hesitate concerning the reports of others. We balance the opposite circumstances, which cause any doubt or uncertainty[.] —David Hume, An Enquiry concerning Human Understanding

Abstract

In this paper, I use a framework from computational linguistics, the Rational Speech Act framework, to model deceptive probabilistic communication. This account allows agents to discount for the biases they perceive their interlocutors to have. This way, agents can update their credences with the perceived interests of others in mind.

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Notes

  1. There is other inspiring literature on deception, e.g., the work of Oey et al. (2019) and of Ransom et al. (2019).

  2. There is a strong flavour of plausible deniability here.

  3. See Mahon (2016) and Meibauer (2019) for a more complete overview.

  4. I would like to thank Jeroen Frans and Bram Sterkendries for pointing out that acknowledging a competitor as being in the same ball park can actually build trust. Moreover, one might lose an air of expertise by boasting that one is the best all the time.

  5. I draw upon many fields in this article, ranging from philosophy of language over information theory to cognitive science. Since this paper is written for philosophers, I mainly review literature that is least familiar to them.

  6. Anyone interested in doing empirical work based on this paper should look into what the best operationalization of PEs is to use in combination with the proposed frameworks. Since this is not an empirical paper, however, I will not commit to any part of the literature.

  7. Throughout this paper, I will set C(u) to 0 for two reasons: (1) the cost of an utterance is an empirical matter, and (2) it simplifies the calculations.

  8. As Huttegger (2017) points out, probabilistic choice has been unduly neglected in philosophy. The edifying work of this field is undoubtedly Luce’s (1959) monograph Individual Choice Behavior. The interested reader is advised to consult Pleskac (2015) and Huttegger (2017). The formulation of this choice theory I use here derives from the work of McFadden (1967, 2001).

  9. For a good overview, see Horn (2004).

  10. I am grateful to Jan Heylen for sharing his intuitions and thorough knowledge of the literature with me.

  11. Of course, the aforementioned degree semantics literature has a way more sophisticated approach to these expressions. So, will I, later on in the paper. I use this simplistic semantics here to keep the toy model tractable, whilst still being able to make the point.

  12. \(\chi _X: S \rightarrow \{ 0, 1 \}\) is the indicator function for X, i.e., the function that maps a state s to 1 if \(s \in X\) and that maps s to 0 otherwise.

  13. For the sake of simplicity, the model is presented in terms of discrete random variables. However, it is easy to extend this approach to the continuous case.

  14. Another nice feature of the Hellinger distance is its relatively low computational complexity (deterministic polynomial time). For our models, it will also mean that speakers can “stretch the truth”.

  15. That this listener does not infer o and a, is a design choice. In Bergen and Goodman’s (2015) model, the literal listener does infer observations.

  16. One can establish this by going to the combinatorics, but this effect will barely influence very small toy models. I discovered it by running a simulation, as models and implementation were developed in parallel.

  17. Suppose one does know something more about what the speaker might observe. Akin to Herbstritt and Franke (2019), one might consider a set of possible distributions one believes the speaker might have observed. One can then draw (categorically or uniformly depending on the available information) from this set of possibly observed distributions and use a some kind of information distance as the epistemic utility function.

  18. Again, one can choose one’s favorite information distance.

  19. Since we assume that the speaker only wants to communicate one specific probability distribution P, there is no reason to conditionalize \(\mathbb {U}_2\) on this distribution. This merely is a design choice.

  20. In principle, when one does not assume that listener and speaker share priors and perceptions about the honesty of the speaker, one can actually run two models side by side: one for the listener and one for the speaker with the respective parameters—i.e., P, \(\lambda\), interpretations of utterances, and so on. These models will then proscribe the behavior of the respective agents.

  21. I.e., inhabitants of the Array{Float64}-type, the components of which sum to 1.

  22. I am grateful to an anonymous referee for pointing me in this direction.

  23. For a nice historical tracing of the development of epistemic game theory from classical game theory, one can consult (Perea 2014).

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Acknowledgements

First and foremost, I would like to thank my supervisors, Sylvia Wenmackers and Lorenz Demey for their help in writing this paper. I would also like to thank my colleagues at the Center for Logic and Philosophy of Science in Leuven for their support and time. I would also like to thank Jan Heylen, Jeroen Frans, Wouter Voorspoels and the referees for their valuable feedback. Finally, I am very grateful to the participants of FMSPh III, PhDs in Logic XI and the Philosophical Engineering Summer School for their feedback.

Funding

This research was conducted with funds from my Research Foundation–Flanders (FWO) PhD-fellowship 1139420N.

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  1. Centre for Logic and Philosophy of Science (CLPS), Institute of Philosophy, KU Leuven, Kardinaal Mercierplein 2 – bus 3000, Leuven, Belgium

    Leander Vignero

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Vignero, L. Updating on Biased Probabilistic Testimony. Erkenn 89, 567–590 (2024). https://doi.org/10.1007/s10670-022-00545-7

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