Abstract
In this paper, we show how game theoretic work on conversation combined with a theory of discourse structure provides a framework for studying interpretive bias and how bias affects the production and interpretation of linguistic content. We model the influence of author bias on the discourse content and structure of the author’s linguistic production and interpreter bias on the interpretation of ambiguous or underspecified elements of that content and structure. Interpretive bias is an essential feature of learning and understanding but also something that can be exploited to pervert or subvert the truth. We develop three types of games to understand and to analyze a range of interpretive biases, the factors that contribute to them, and their strategic effects.
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Notes
A considerable amount of research especially in computational linguistics has been done in this area; see May et al. (2019), Lauscher and Glavaš (2019), Blodgett et al. (2020). We note also that Blodgett et al. (2020) show that restricting oneself to lexical biases paints a very imperfect picture of what bias is.
That is, an SDRS must be a graph G with just one element that has no incoming arrows; in addition, there are no elements a, b of G such that the transitive closure of the arcs in G give us the arrows \(a \rightarrow b\) and \(a \leftarrow b\).
SDRT provides SDRSs with a well-defined relation of consequence as well as a notion of coherence (Asher et al. 2017; Asher and Paul 2016b). So we can define an equivalence relation \(\sim \) on V based on the coherent and consistent continuations they allow. \(\upphi _1 \sim \upphi _2\), if for any SDRT formula \(\uppsi \), \(\upphi _1. \uppsi \) is a consistent and coherent continuation just in case \(\upphi _2.\uppsi \) is. A \(\sim \) equivalence class of V is a class of discourse moves. Thus, when we talk of a “move”, we shall actually be referring to its class.
In some cases it is important to impose a consistency constraint in the following sense for a winning condition: for every play \(\uprho \) of the ME game, \(\uprho \in Win _i\) iff \({\mathfrak {h}}(\uprho )\subset Win _i\). We do not do this here because some ME games we will explore in the next section feature a ulf as the contribution of one player, while the other provides an interpretation of the ulf. For other constraints see Asher and Paul (2018).
Because the set of strategies is uncountable, we need to restrict ourselves to measurable functions and measurable sets—for details see Asher and Paul (2018). For our simple examples of finite plays, this restriction is satisfied, because they are all basic open sets in \((V_0\cup V_1)\). For the infinitary games of Sect. 4, matters are more delicate but we gloss over the details here.
\({\hat{\upbeta }}^\uprho _{\mathcal {J}}=({\upbeta }^\uprho _{\mathcal {J}},\upxi ^\uprho _{\mathcal {J}})\) where the \({\mathsf {belief function}}\) \({\upbeta }^\uprho _i\) and the \({\mathsf {interpretation function}}\) \(\upxi ^\uprho _i\) are defined as:
$$\begin{aligned}&{\upbeta }^\uprho _{\mathcal {J}}: T_{\mathcal {J}}\times {{\mathcal {H}}}(\uprho ) \rightarrow \Delta (T_0)\times \Delta (S^\uprho _0)\times \Delta (T_1)\times \Delta (S^\uprho _1)\\&{\upxi }^\uprho _{\mathcal {J}}: T_{\mathcal {J}}\times T_0 \times T_1 \rightarrow \Delta ({{\mathcal {H}}}(\uprho )) \end{aligned}$$That the interpretation function returns a probability distribution over histories is consonant with the way computational linguists like Afantenos et al. (2015) model how various features of the play lead to a probability distribution over full SDRSs.
Winning conditions define a notion of utility and together with the belief functions of each player this yields a notion of expected utility. For the technical details, see Asher and Paul (2018).
A function \(f: A_1\times A_2\times \ldots A_n \rightarrow B\) is \({\mathsf {independent}}\) of the jth component, \(1\le j\le n\), if for all \(a_j, a'_j\in A_j\), \(f(a_1,a_2,\ldots ,a_j,\ldots ,a_n) = f(a_1,a_2,\ldots ,a'_j,\ldots ,a_n)\).
Self-reinforcing biases of nonlinguistic facts are also echoed in popular analyses, for instance ‘The Evangelical Roots of Our Post-Truth Society’ by Molly Worthen, New York Times, 16.04.2017. But as far as we know, only Asher and Paul (2018) have provided at least a partial formal analysis of this phenomenon.
While Stanley (2015) proposes that such messages are conventional implicatures, Henderson and McCready (2019), Khoo (2017) show that dog whistle content doesn’t behave like other conventional implicatures; in terms of tests about “at issue content”, dog whistle content patterns with other at issue content, not with the content associated with conventional implicatures in the sense of Potts (2005).
This in fact is a precise model of what relevance theorists have called “free enrichment” (Sperber and Wilson 1986).
As far as we know, no other framework can capture the observations below.
Technically, Aumann’s observation relies on common prior probabilities. We don’t see any reason to adopt such an assumption in an analysis of strategic conversations or bias. Our observation is a sort of correlate or converse of Aumann’s.
For a fuller discussion of symmetry, see Asher and Paul (2018).
The mathematical structure of ME games also makes it natural to investigate how ME game analyses of bias interact with information-theoretic analyses proposed by Hilbert (2012).
In those fields “bias” often refers to the divergence between an estimated hypothesis about a parameter and its objective value.
For instance see, http://www.edu.gov.mb.ca/k12/cur/socstud/foundation_gr9/blms/9-1-3g.pdf.
This option encapsulates the problem of optimizing the decision to exploit a bias that has a certain “local” optimality or to explore the space of possible biases further. There is a large body of literature on this issue (Whittle 1980; Lai and Robbins 1985; Banks and Sundaram 1994; Burnetas and Katehakis 1997; Auer et al. 2002; Garivier and Cappé 2011).
References
Afantenos, S., Kow, E., Asher, N., & Perret, J. (2015). Discourse parsing for multi-party chat dialogues. In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing (pp. 928–937). Lisbon, Portugal: Association for Computational Linguistics.
Asher, N. (1993). Reference to abstract objects in discourse. Dordrecht: Kluwer Academic Publishers.
Asher, N., & Hunter, J. (2021). Interpretive blindness and the impossibility of learning from testimony. In Proceedings of the 20th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2021), May 3–7, 2021, London (online).
Asher, N., & Lascarides, A. (2003). Logics of conversation. Cambridge: Cambridge University Press.
Asher, N., & Paul, S. (2013). Conversations and incomplete knowledge. In R. Fernández, & A. Isard (Eds.), Proceedings of the 17th Workshop on the Semantics and Pragmatics of Dialogue (SEMDIAL) (pp. 173–176). Amsterdam: University of Amsterdam.
Asher, N., & Paul, S. (2016a). Evaluating conversational success: Weighted message exchange games. In J. Hunter, M. Simons, & M. Stone (Eds.), Proceedings of the 20th Workshop on the Semantics and Pragmatics of Dialogue (SEMDIAL) (pp. 55–64). Brunswick, NJ: Rutgers University.
Asher, N., & Paul, S. (2016b). Language games. In M. Amblard, P. Groote, W. Pogodalla, & C. Retoré (Eds.) Logical aspects of computational linguistics. Celebrating 20 years of LACL (1996–2016) (pp. 1–17). Berlin: Springer.
Asher, N., & Paul, S. (2018). Strategic conversation under imperfect information: Epistemic message exchange games. Logic, Language and Information, 27(4), 343–385.
Asher, N., Paul, S., & Venant, A. (2017). Message exchange games in strategic conversations. Journal of Philosophical Logic, 46(4), 355–404. https://doi.org/10.1007/s10992-016-9402-1.
Auer, P., Cesa-Bianchi, N., & Fischer, P. (2002). Finite-time analysis of the multiarmed bandit problem. Machine Learning, 47(2–3), 235–256.
Aumann, R. J. (1976). Agreeing to disagree. The Annals of Statistics, 4(6), 1236–1239.
Banks, J. S., & Sundaram, R. K. (1994). Switching costs and the Gittins index. Econometrica: Journal of the Econometric Society, 62, 687–694.
Baron, J. (2000). Thinking and deciding. Cambridge: Cambridge University Press.
Battigalli, P. (2003). Rationalizability in infinite, dynamic games with incomplete information. Research in Economics, 57(1), 1–38.
Beaver, D., & Stanley, J. (2018). Toward a non-ideal philosophy of language. Graduate Faculty Philosophy Journal, 39(2), 503–547.
Benamara, F., Asher, N., Mathieu, Y. Y., Popescu, V., & Chardon, B. (2016). Evaluation in discourse: A corpus-based study. Dialogue and Discourse, 7(1), 1–49.
Berger, A. L., Pietra, V. J. D., & Pietra, S. A. D. (1996). A maximum entropy approach to natural language processing. Computational Linguistics, 22(1), 39–71.
Besnard, P., & Hunter, A. (2008). Elements of argumentation. Cambridge, MA: MIT Press.
Blodgett, S. L., Barocas, S., Daumé III, H., & Wallach, H. (2020). Language (technology) is power: A critical survey of “bias” in NLP. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics (pp. 5454–5476). Association for Computational Linguistics. https://doi.org/10.18653/v1/2020.acl-main.485.
Burnetas, A. N., & Katehakis, M. N. (1997). Optimal adaptive policies for Markov decision processes. Mathematics of Operations Research, 22(1), 222–255.
Burnett, H. (2017). Sociolinguistic interaction and identity construction: The view from game-theoretic pragmatics. Journal of Sociolinguistics, 21(2), 238–271.
Cesa-Bianchi, N., & Lugosi, G. (2006). Prediction, learning, and games. Cambridge: Cambridge University Press.
Chaterjee, K. (2007). Concurrent games with tail objectives. Theoretical Computer Science, 388, 181–198.
Dung, P. M. (1995). On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence, 77(2), 321–357.
Erev, I., Wallsten, T. S., & Budescu, D. V. (1994). Simultaneous over-and underconfidence: The role of error in judgment processes. Psychological Review, 101(3), 519.
Franke, M. (2009). Signal to act: Game theory in pragmatics. Ph.D. thesis, Universiteit van Amsterdam.
Fudenberg, D., & Levine, D. K. (1998). The theory of learning in games. Cambridge, MA: MIT Press.
Garivier, A., & Cappé, O. (2011). The kl-ucb algorithm for bounded stochastic bandits and beyond. In COLT (pp. 359–376).
Glazer, J., & Rubinstein, A. (2004). On optimal rules of persuasion. Econometrica, 72(6), 119–123.
Griffiths, T. L., Kemp, C., & Tenenbaum, J. B. (2008). Bayesian models of cognition. In R. Sun (Ed.), The Cambridge handbook of computational psychology (p. 59–100). Cambridge: Cambridge University Press.
Harsanyi, J. C. (1967). Games with incomplete information played by “Bayesian” players, parts i–iii. Management Science, 14, 159–182.
Henderson, R., & McCready, E. (2019). Dogwhistles and the at-issue/non-at-issue distinction. In D. Gutzmann, & K. Turgay (Eds.), Secondary Content (pp. 222–245). Leiden: Brill. https://doi.org/10.1163/9789004393127_010.
Hilbert, M. (2012). Toward a synthesis of cognitive biases: How noisy information processing can bias human decision making. Psychological Bulletin, 138(2), 211.
Hintzman, D. L. (1984). Minerva 2: A simulation model of human memory. Behavior Research Methods, Instruments, & Computers, 16(2), 96–101.
Hintzman, D. L. (1988). Judgments of frequency and recognition memory in a multiple-trace memory model. Psychological Review, 95(4), 528.
Hobbs, J. R., Stickel, M., Appelt, D., & Martin, P. (1993). Interpretation as abduction. Artificial Intelligence, 63(1–2), 69–142.
Khoo, J. (2017). Code words in political discourse. Philosophical Topics, 45(2), 33–64.
Konek, J. (2016). Probabilistic knowledge and cognitive ability. Philosophical Review, 125(4), 509–587.
Lai, T. L., & Robbins, H. (1985). Asymptotically efficient adaptive allocation rules. Advances in Applied Mathematics, 6(1), 4–22.
Lakkaraju, H., Kamar, E., Caruana, R., & Horvitz, E. (2016). Discovering blind spots of predictive models: Representations and policies for guided exploration. arXiv preprint arXiv:1610.09064.
Laugel, T., Lesot, M. J., Marsala, C., Renard, X., & Detyniecki, M. (2019a). The dangers of post-hoc interpretability: Unjustified counterfactual explanations. arXiv preprint arXiv:1907.09294.
Laugel, T., Lesot, M. J., Marsala, C., Renard, X., & Detyniecki, M. (2019b). Unjustified classification regions and counterfactual explanations in machine learning. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases, Part II (pp. 37–54). Wiesbaden: Springer.
Lauscher, A., & Glavaš, G. (2019). Are we consistently biased? Multidimensional analysis of biases in distributional word vectors. arXiv preprint arXiv:1904.11783.
Lewis, D. (1969). Convention: A philosophical study. Cambridge, MA: Harvard University Press.
Mann, W. C., & Thompson, S. A. (1987). Rhetorical structure theory: A framework for the analysis of texts. International Pragmatics Association Papers in Pragmatics, 1, 79–105.
May, C., Wang, A., Bordia, S., Bowman, S. R., & Rudinger, R. (2019). On measuring social biases in sentence encoders. arXiv preprint arXiv:1903.10561.
Mitchell, T. M. (1980). The need for biases in learning generalizations. Technical report, Rutgers University.
Moss, S. (2013). Epistemology formalized. Philosophical Review, 122(1), 1–43.
Parikh, P. (1991). Communication and strategic inference. Linguistics and Philosophy, 14, 473–514.
Parikh, P. (2001). The use of language. Stanford: CSLI Publications.
Parikh, P. (2006). Pragmatics and games of partial information. In A. Benz, G. Jäger, & R. van Roiij (Eds.), Game theory and pragmatics (pp. 101–122). London: Palgrave MacMillan.
Potts, C. (2005). The logic of conventional implicatures. Oxford: Oxford University Press.
Saul, J. (2018). Dogwhistles, political manipulation, and philosophy of language. In D. Fogal, D. W. Harris, & M. Moss (Eds.), New Work on Speech Acts. Oxford: Oxford University Press. https://doi.org/10.1093/oso/9780198738831.003.0013.
Sobot, B. (2009). Games on Boolean algebras. Ph.D. thesis, University of Novi Sad, Serbia.
Sperber, D., & Wilson, D. (1986). Relevance. Oxford: Blackwell.
Stanley, J. (2015). How propaganda works. Princeton: Princeton University Press.
Tversky, A., & Kahneman, D. (1973). Availability: A heuristic for judging frequency and probability. Cognitive Psychology, 5(2), 207–232.
Tversky, A., & Kahneman, D. (1981). The framing of decisions and the psychology of choice. Science, 211(4481), 453–458.
Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90(4), 293.
Tversky, A., & Kahneman, D. (1986). Judgment under uncertainty: Heuristics and biases. In H. R. Arkes & K. R. Hammond (Eds.), Judgment and decision making: An interdisciplinary reader (pp. 38–55). Cambridge: Cambridge University Press.
van Rooij, R. (2004). Signalling games select horn strategies. Linguistics and Philosophy, 27, 493–527.
Venant, A. (2016). Structures, semantics and games in strategic conversations. Ph.D. thesis, Université Paul Sabatier, Toulouse.
Whittle, P. (1980). Multi-armed bandits and the Gittins index. Journal of the Royal Statistical Society: Series B (Methodological), 42, 143–149.
Wilkinson, N., & Klaes, M. (2012). An introduction to behavioral economics. London: Palgrave Macmillan.
Wolpert, D. H. (1996). The lack of a priori distinctions between learning algorithms. Neural Computation, 8(7), 1341–1390.
Wolpert, D. H., & Macready, W. G. (1995). No free lunch theorems for search. Technical report SFI-TR-95-02-010, Santa Fe Institute.
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We thank the ANR PRCI Grant SLANT and the 3IA Institute ANITI funded by the ANR-19-PI3A-0004 Grant for research support. We thank anonymous reviewers from Linguistics and Philosophy, as well as the editor, for extensive and helpful comments on a previous draft.
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Asher, N., Hunter, J. & Paul, S. Bias in semantic and discourse interpretation. Linguist and Philos 45, 393–429 (2022). https://doi.org/10.1007/s10988-021-09334-x
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DOI: https://doi.org/10.1007/s10988-021-09334-x