Configurative weighting and adding can be a surprisingly effective approximation of multiplicative functions. In thecontext of joint probability judgment, Nilsson et al. (2009) has shown that, when marginal probabilities are only approxi-mately known, the configurative weighted average (CWA) of two probabilities not only predicts a high level of conjunctionfallacies, as observed in data, but also correlates higher with the true joint probability than if the two probabilities are mul-tiplied. Here we show that [1] the surface representing the optimal Bayesian estimate of a joint probability can be closelyapproximated by two planes, [2] configurative weighting and adding, such as the CWA model, constitutes such a two-planeapproximation, and [3] a bias-variance tradeoff is not sufficient to explain the accuracy of the CWA. More generally, thissuggests that the efficiency of heuristics might be due to suitable weighting operations rather than less-is-more effects.

Sampling-based models, which assume that people remember or simulate instances of events and count outcome propor-tions to make probability judgments, account for many apparent biases in human judgment. The success of such modelsis generally dependent on sample size, as particularly large or particularly small samples are often required for a modelto reproduce effects observed in data. Thus, systematically exploring the actual number of instances that people tend tosample is an important criterion in evaluating model credibility. Here we propose a method of estimating sample size byway of inter-judgment variance. We show through model recovery that this method will reliably recover the correct samplesize and subsequently apply the method to two well-supported models of human probability judgment, Probability TheoryPlus Noise and the Bayesian Sampler. Results indicate, in both cases, that human probability judgments are based on arelatively plausible (¡ 10) number of sampled instances.

Individuals make biased and variable probability judgements. Recent models such as the Bayesian Sampler (Zhu, et al., 2020), Probability Theory Plus Noise (Costello & Watts, 2014), and the Quantum Sequential Sampler (Huang et al., 2023) capture a wide range of effects by assuming people are biased towards indifference (i.e., 0.5). However, in some experiments participants instead showed asymmetric bias, defined as a pull toward non-0.5 values. We investigated asymmetric bias in 5 experiments, where participants judged the probabilities of dice rolls. While participants' judgements were independent of whether they were in a high or low probability environment or the number of alternative options displayed, participants showed a bias toward low (<0.5) estimates. Furthermore, participants showed the highest variability for judgements below 0.5. This latter effect can be captured by an asymmetric prior in the Bayesian Sampler, but not by the biasing mechanisms in the other models.