Paper:
Magnitude-sensitive preference formation
Our understanding of the neural computations that underlie the ability of animals to choose among options has advanced through a synthesis of computational modeling, brain imaging and behavioral choice experiments. Yet, there remains a gulf between theories of preference learning and accounts of the real, economic choices that humans face in daily life, choices that are usually between some amount of money and an item. In this paper, we develop a theory of magnitudesensitive preference learning that permits an agent to rationally infer its preferences for items compared with money options of different magnitudes. We show how this theory yields classical and anomalous supply-demand curves and predicts choices for a large panel of risky lotteries. Accurate replications of such phenomena without recourse to utility functions suggest that the theory proposed is both psychologically realistic and econometrically viable.

Review:
This paper presents a rational model of economic choice, where values are replaced by inferences about relative rank in a context. The model is shown to provide a good fit to pricing data and risky-choice experiments.Overall, I found the paper interesting, but somewhat too narrow and inaccessible for a NIPS audience. There was lots of insufficiently explained economic jargon (e.g. Veblen and Giffen goods), which are key for understanding the contribution. Moreover, the point of the model was hard for me to pull out of the paper. The model was motivated as psychological realistic alternative to utility calculations, but then uses Bayesian inference as a psychological calculation (not as rational model). Other points:-Good intro, but a bit too aggressive against the values of utilities. Well-written and fairly clear.-Variables not obvious in equations. For example, o seems to be observations, but that is never mentioned.-To reiterate, something not above, I was very confused about the point of this model. It was motivated as psychological realistic alternative to utility calculations, but then uses Bayesian inference as psychological calculation (not as rational model). I don’t see how this improves over the Decision-by-Sampling model, which provides a more realistic psychological grounding and already covers the some of the key features oWhat is the contribution? Is it the rational model/analysis? -Hanging a lot hang on number frequency means there should be all sorts of weird quirks at large, common numbers (e.g., $100 vs $101). Is there any evidence or data that these frequency anomalies exist? And, I don’t see how this guarantees a Pareto distribution? Little support is given to the key claim that number space will follow this distribution, and, intuitively, I don’t see it all. The numbers are certainly not strictly descending in frequency in many contexts. Imagine buying car. $10 is a lot less frequent than $15000. Finally, there is a lot of work on subjective number representation that is not cited here, but also very relevant. Number (as do most senses) follows Weber’s law, whereby larger numbers are less discriminable than smaller numbers (think 1 vs. 2 or 200 vs. 201; see, for example, Dehaene, 2003, in Trends in Cognitive Science). - Figures 2 and 3 had tones of information, but very little guidance, and I had lots of trouble making sense of them. For example, in Figure 2, what is m (in s, m, d) in top two panels on left? Normal? Not n? And what are the three plots on the topmost panel (presumably hill, valley, and forest, but that’s not labeled). Also, in Fig 2., I like the attempt to explain the pieces of the equation intuitively, but was admittedly baffled by what the bottom 3 panels on the right are supposed to represent. pmf = ? The text only covers some of the figure and is thus unhelpful. Minor points:line 080: direct utile estimation = ?line 082: “from the history of past choices” (missing article)line 107: identitied?lines 145: sampling a representative context sounds far from simpleline 151: could be more simply stated in words than the equation, to wit: “when x is the most preferred option in a context”. At the very least, unpack the equation.line 194. “in via”line 267. [?]line 363. Is q or p(x) the lottery probability?line 377. computatationline 409-411. A bizarre claim to make about RL and back up with the Sutton & Barto book.Ref 19 is mangled: The Sutton & Barto book (not Barto & Sutton) was published by MIT press, which is in Cambridge, Mass. (not U of Cambridge).