Human Decision-Making under Limited Time
Subjective expected utility theory assumes that decision-makers possess unlimited computational resources to reason about their choices; however, virtually all decisions in everyday life are made under resource constraints-i.e. decision-makers are bounded in their rationality. Here we experimentally tested the predictions made by a formalization of bounded rationality based on ideas from statistical mechanics and information-theory. We systematically tested human subjects in their ability to solve combinatorial puzzles under different time limitations. We found that our bounded-rational model accounts well for the data. The decomposition of the fitted model parameter into the subjects' expected utility function and resource parameter provide interesting insight into the subjects' information capacity limits. Our results confirm that humans gradually fall back on their learned prior choice patterns when confronted with increasing resource limitations.
This paper proposes a model of bounded-rational decision-making using ideas from statistical mechanics and information-theory, in particular assuming that humans adopt a choice policy which maximizes expected subjective utility while minimizing KL divergence from a prior choice distribution, with the trade-off determined by a temperature parameter that is related to the amount of time/computational resources available to the individual for deliberation.  The model is tested on a set of data obtained from human subjects solving a pictorial version of the conunctive normal form (CNF) problem, and finds, based on the results, that subjects' prior choice distributions are similar to the true distribution over solutions, that the estimated temperature parameter varies monotonically with deliberation time allowed, and the estimated subjective utility peaks at the correct solution for well-trained puzzles but rather flat for an untrained puzzle.
Overall, this seems to be an interesting and mathematically sophisticated piece of work, bringing together quantitative tools from diverse feeds to bear on the modeling of bounded-rational decision making.   I feel the conclusions/framing of the paper is somewhat over-reaching, because the model of choice (primarily Eq. 1) is not really a model of decision-making, nor of learning.  What I mean is that the framework allows one to infer an individual's "subjective utility" (which from a normative perspective should be the distribution of correct answers for the trained puzzles), but does not say anything about how those utility preferences get computed, nor explain how these computations are learned or improved over time as the subject gets more experience with a particular puzzle.  The application to the CNF pictorial puzzle data set seems original, but with the way the task is designed (often very short viewing time), the task really seems more like a memory task than a decision-making task. The estimated utility function being flat for an untrained puzzle makes it clear that nontrivial computations & learning are indeed involved. In fact, it's clear from looking at Eq. 1, that if a subject really had access to the utility function Ux(y), then he should just pick the maximal utility response every single time for a given stimulus x, as that would yield better empirical utility (accuracy rate) than maximizing the full Eq. 1.  So Eq. 1 cannot be taken very literally as a model of how subjects make choices on each given trial, but rather is a descriptive model of how the distribution of choices might arise over a set of stimuli and presentations. The authors' feedback on this point did not assuage my concerns. Also, in terms of related work, there was a previous NIPS paper (Frazier & Yu, 2008) entitled "Sequential hypothesis testing under stochastic deadlines" that treated the problem of human decision-making under time pressure. While that took a very different approach at multiple levels, it is surely worth including as a reference in discussing how the current work situates in the ecology of human decision-making modeling literature.  Unfortunately, the actual findings are not very surprising/interesting at a scientific level. That the inferred "subjective utility" should peak at the correct solution for learned puzzles is hardly surprising, if subjects are indeed capable of learning to do this task through repeated trials. However, it does serve as a useful method validation step, to establish for a problem where the "correct" utility is known, that the utility function+beta+prior estimation procedure indeed performs as desired.  I would have liked to see an alternative model being compared to. In general it is good to have a baseline model as comparison so as to give some additional insight to the mechanism, correctness, and generality of the proposed model. In this particular case, because the way the decision-making model set up is so unusual compared to conventional practice, I think the readers would especially benefit from a comparison to (perhaps simpler) alternatives. The authors' feedback on this point did make me feel more reassured.  However, the 80% subject dropout rate mentioned in the rebuttal is extremely high! This would suggest that perhaps the experimental procedure resulted in substantial "subject filtering" to get a good model fit, instead of taking the more sensible "model filtering." AIC was better for the B-R model in 21 out of 30 included subjects, but really it could have actually been only out of a total 120 subjects. That hardly makes this seem like a persuasive model of human decision-making.  My final scores reflect the appearance/persistence of the various concerns that crystalized during the rebuttal phase.  Other comments: - Sec. 2 is rather dense with math, and it is not always clear whether a mathematical statement is an assumption, a derivation, an explanation, or an interesting aside.