Abstract
The study of people’s ability to engage in causal probabilistic reasoning has typically used fixed-point estimates for key figures. For example, in the classic taxi-cab problem, where a witness provides evidence on which of two cab companies (the more common ‘green’/less common ‘blue’) were responsible for a hit and run incident, solvers are told the witness’s ability to judge cab color is 80%. In reality, there is likely to be some uncertainty around this estimate (perhaps we tested the witness and they were correct 4/5 times), known as second-order uncertainty, producing a distribution rather than a fixed probability. While generally more closely matching real world reasoning, a further important ramification of this is that our best estimate of the witness’ accuracy can and should change when the witness makes the claim that the cab was blue. We present a Bayesian Network model of this problem, and show that, while the witness’s report does increase our probability of the cab being blue, it simultaneously decreases our estimate of their future accuracy (because blue cabs are less common). We presented this version of the problem to 131 participants, requiring them to update their estimates of both the probability the cab involved was blue, as well as the witness’s accuracy, after they claim it was blue. We also required participants to explain their reasoning process and provided follow up questions to probe various aspects of their reasoning. While some participants responded normatively, the majority self-reported ‘assuming’ one of the probabilities was a certainty. Around a quarter assumed the cab was green, and thus the witness was wrong, decreasing their estimate of their accuracy. Another quarter assumed the witness was correct and actually increased their estimate of their accuracy, showing a circular logic similar to that seen in the confirmation bias/belief polarization literature. Around half of participants refused to make any change, with convergent evidence suggesting that these participants do not see the relevance of the witness’s report to their accuracy before we know for certain whether they are correct or incorrect.
Highlights
While causal Bayesian reasoning, and reasoning under uncertainty in general are major research programs within the judgment and decision-making literature, problems presented to participants have typically only studied this under first order uncertainty
While 33% might still be our best guess, with such a small sample size to estimate this, a substantial range of other probabilities are possible. How would this affect our decision over which bet to take? This uncertainty about our first order uncertainty is known as second order uncertainty (e.g., Kleiter, 2018), and we currently know little about how classic findings in the judgment and decision-making literature apply under such conditions
In this paper we aimed to examine responses to a modified version of the classic taxi cab problem including second order uncertainty
Summary
While causal Bayesian reasoning, and reasoning under uncertainty in general are major research programs within the judgment and decision-making literature, problems presented to participants have typically only studied this under first order uncertainty ( known as ‘risk’ in the economics literature). The participant might be given a betting choice between a sure win of £25 or a 33% chance of £100 (e.g., Kahneman and Tversky, 1979). While in the latter option it is uncertain whether we will get the £100, we can quantify this uncertainty precisely, and the problem yields to an expected utility calculation. While 33% might still be our best guess, with such a small sample size to estimate this, a substantial range of other probabilities are possible How would this affect our decision over which bet to take? How would this affect our decision over which bet to take? This uncertainty about our first order uncertainty is known as second order uncertainty (e.g., Kleiter, 2018), and we currently know little about how classic findings in the judgment and decision-making literature apply under such conditions
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