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The Crowd Within and the Benefits of Dialectical Bootstrapping

Can the “wisdom of crowds” (Surowiecki, 2004) be exploited within a single mind? Yes, one can increase accuracy by averaging multiple estimates from the same person (Herzog & Hertwig, 2009; Hourihan & Benjamin, 2010; Müller-Trede, 2011; Rauhut & Lorenz, 2011; Stroop, 1932; Vul & Pashler, 2008; White & Antonakis, 2013; Winkler & Clemen, 2004). We proposed boosting this crowd-within effect with what we called dialectical bootstrapping (Herzog & Hertwig, 2009; hereafter, H&H): averaging a person’s first estimate with his or her second, “dialectical” estimate, derived from knowledge and assumptions different from those motivating the first estimate. A dialectical estimate ideally has an error with a different sign relative to the first estimate—which fosters the chance of error cancellation. There are different ways to elicit a dialectical estimate. We tested one, the consider-the-opposite strategy (Lord, Lepper, & Preston, 1984), and found that averaging first and dialectical estimates improved accuracy more than simply asking people to make an estimate anew and averaging the two estimates (i.e., reliability condition). White and Antonakis (2013; hereafter, W&A) reanalyzed our data using a different accuracy measure, concluding that “dialectical instructions are not needed to achieve the wisdom of many in one mind” (p. 116). Here, we delineate where we agree and disagree with W&A. We concur with W&A that the crowd within works. W&A observed (as have we and other researchers) that averaging two estimates from the same person improves accuracy. Moreover, they obtained this result across different measures of accuracy. We also agree with W&A that “dialectical instructions are not needed to achieve the wisdom of many in one mind” (p. 116); in our previous article, we pointed out (H&H, p. 236) that passage of time appears to be enough to boost the gains obtained by averaging (Vul & Pashler, 2008). Additionally, we highlighted that “accuracy in [our] reliability condition increased as a result of aggregation” (p. 234). Our disagreement with W&A concerns the following question: Can dialectical bootstrapping boost the crowd-within effect beyond the gains observed in the reliability condition (i.e., gains expected to occur when averaging any noisy estimates)? Dialectical Bootstrapping: Does It Have Surplus Value?