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).
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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