Experimental Condition Testing the approach Experimental Condition Control Condition Please wait 3 seconds. 20 3-step planning problems Significant advantage of 3-step planning Experimental condition: Delay penalty based on metacognitive PRs feedback messages Control condition: constant delays with the same average duration after each move no feedback message: “Please wait 5 seconds.” Participants have to spend at least 45 seconds on each trial Each click costs $0.05 Bonus payment: 5% of earnings on a randomly selected trial

Feedback promotes more planning (Lieder*, Krueger*Callaway*, & Griffiths, 2017)

… leading to higher performance (Lieder*, Krueger*Callaway*, & Griffiths, 2017)

Conclusions Resource rationality provides a framework that is realistic yet still systematic as a source of models Many standard heuristics are not just “kluges” but are resource-rational for some architecture This approach lets us tackle questions about how people use their cognitive resources, and how to design systems to overcome those limitations

Availability of extreme events Availability bias: people over-estimate the probability of events that come to mind easily (Tversky & Kahneman, 1973) Extreme events come to mind easily…

Availability of extreme events Task: Estimate the expected utility of an action Architecture: Generate (weighted) samples of possible outcomes of the action Cost: Increases linearly in the number of samples (as with opportunity cost) (Lieder, Hsu, & Griffiths, 2014)

Unbiased sampling is bad… 51 samples required to give 99.99% chance of discovering the bad outcome To take the potential disaster into account with 50% probability when the odds are 1 in one million requires 700 million samples.

Importance sampling q(x) p(x)

The optimal distribution Variance is minimized by… But, the result is biased: with small samples, we will over-represent extreme events (Lieder, Hsu, & Griffiths, 2014)

Over-representing extreme events ρ = 0.53 On average, the extremest event’s frequency (murder, 98% extreme) was overestimated by a factor of 972, whereas the frequency of the least extreme event (headache, 20% extreme) was overestimated by merely 6% (n.s.). (Lieder, Hsu, & Griffiths, 2014)

A simple optimal heuristic When making a decision… generate from the utility-weighted distribution tally the number of pros and cons Reproduces phenomena in decision-making fourfold pattern of risk preferences (Tversky & Kahneman, 1992) Allais paradox (Allais, 1953) outperforms cumulative prospect theory in the Technion dataset (Erev et al., 2010)

Fourfold pattern of risk preferences Overweight gain/loss of risky gamble if p small (since |u(o)-u(p.o)| is greater than |u(p.o)|) Underweight gain/loss of risky gamble if p large

Allais paradox L1: 66% chance of $2400, 33% chance of $2500, 1% chance of $0 L2: 100% chance of $2400 L1: 33% chance of $2500, 67% chance of $0 L2: 34% chance of $2400, 66% chance of $0

Allais paradox

Technion results r = 0.88

Anchoring and adjustment What’s the freezing point of vodka? How long is Mars’ orbit around the sun? People answer these questions by starting with a more familiar example (an anchor) and adjusting away from it (leading to bias) -17F 687 days (Epley & Gilovich, 2006)

Anchoring and adjustment Task: Estimate a quantity based on memory and other cues Architecture: Markov chain Monte Carlo via the Metropolis-Hastings algorithm Cost: Increases linearly in the number of samples (as with opportunity cost) (Lieder, Griffiths, & Goodman, 2012)

Metropolis-Hastings

Bias is resource-rational (Lieder, Griffiths, & Goodman, 2012)

Anchoring and adjustment (data from Epley & Gilovich, 2006) Starting points were initial estimates, cost was estimated to minimize mean-squared error. (Lieder, Griffiths, & Goodman, 2012)

Other predictions Cognitive load, time pressure, and alcohol reduce adjustment (Epley & Gilovich, 2006) Bias increases with anchor extremity (Russo & Schoemaker, 1989) Uncertainty increases anchoring (Jacowitz & Kahneman, 1995) Knowledge can abolish the anchoring bias (Wilson et al., 1996)

Effects of time and error cost

Waiting for the bus

Experiment results

Investment task Two strategies: Take The Best (TTB) vs. weighted combination Two environments: noncompensatory vs. compensatory (Lieder & Griffiths, submitted)

Model predictions (data from Reiskamp & Otto, 2006)

Flexible strategy use (Lieder & Griffiths, submitted)