Reasoning in teaching and misleading situations - eScholarship

Reasoning in teaching and misleading situations Russell E. Warner, Todd Stoess, Patrick Shafto Department of Psychological and Brain Sciences, University of Louisville Abstract Much of human inference occurs in social situations. While in many cases people cooperate, as in teaching settings, people can misdirect others in order to protect their own interests. Shafto and Goodman (2008) formal- ized teaching and learning from teachers as Bayesian inference, in which learners use knowledge about the teacher’s intent to facilitate inference. This same model provides a basis for exploring reasoning about mis- leading. We present two new experiments compar- ing reasoning about teaching and misleading. In both experiments, participants play the role of informant (teacher/misleader) or learner. Our model predicts and our results show that people’s behavior differs in teach- ing and misleading conditions, both when intentions are explicitly known as well as when they are not. Further, the model provides close fits to informants’ and learners’ behavior. Introduction Learning about the world is a daunting task. From the fact that so much of the evidence is underdetermined, to the fact that we have limited time to explore, making inferences about the world is a difficult problem. But what if we are not on our own in this task? Having people around to help us learn about the world might ease some of the difficulty. If knowledgeable informants (mothers, fathers, teachers, friends) helped by choos- ing the evidence that one saw, learners stand to gain in knowledge about the world–potentially much more rapidly than they could alone. Indeed, knowledgeable and helpful informants play a central feature of many accounts of cognition and cog- nitive development (Csibra & Gergely, 2009; Tomasello, Carpenter, Call, Behne, & Moll, 2005; Vygotsky, 1978). For instance, Csibra (2007) claims that children (and not other animals) have an ability to understand inten- tional teaching as conveying both information about the data, and about the hypothesis that the teaching intends to communicate. This ability is seen as so essential to explaining children’s rapid pace of learning, that Csibra and Gergely (2009) suggest that it may in fact be innate. However, opposite our ability to choose evidence help- fully comes an ability to mislead others with true, but otherwise unhelpful or downright misleading evidence. For this reason, it becomes critical to be able to dis- cern the intentions of individuals sharing information (Sperber et al., 2010). Consider, for example, the game in Figure 1. In the game, there are concepts (here, boats) of different sizes, and an informant chooses which evidence to supply to the learner. The learner, then must infer the true state of the world, based on the information provided. Clearly, the intention of the informant matters considerably. For instance, in situation A, a teacher would choose to pro- vide the two ends, allowing the learner to infer that the middle must also be a part of the concept. A misleader, on the other hand, would provide either of the other two possibilities, thus leaving the learner uncertain whether A or B/C was true. Building off of work by Shafto & Goodman (2008), we present a model of teaching/misleading, and infer- ence in each of these situations. We present two exper- iments testing the predictions of the model, first when the learner knows the informant’s intent, and second, when the learner does not know the informant’s intent. The results show strong fits to the model’s predictions, and show that learners can accurately infer intent based on the evidence alone. We conclude by discussing rela- tionships to other models of inference, and implications cognition. A model of teaching, misleading, and infer- ence We formalize reasoning as a problem of probabilistic in- ference in which learners observe data, d. Given this data, learners update their beliefs about a hypothesis, h, that represents a particular set of concepts. Bayes’ rule states that posterior beliefs about hypotheses given data, P (h|d) are proportional to the product of the learner’s prior beliefs about the hypothesis, P (h), and the proba- bility of the data given the hypothesis, P (d|h): P L (h|d) ∝ P (d|h)P L (h), where L indicates learner, and P (d|h) is an appropriate sampling model (e.g. random sampling). In this paper, we consider data that are sampled by an individual whose intent is to either teach or mislead. That is, we consider informants who choose data inten- tionally, to either facilitate or impede learning. Our ap- proach builds of that of Shafto & Goodman (2008), who proposed a model of pedagogical data selection. They modeled teaching as choosing data that tend to increase learners’ beliefs about the correct hypothesis: P I (d|h) ∝ P L (h|d) α .