First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. 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.

In my opinion, this paper deserves the attention of the NIPS audience at least on poster level for sound investigation of an highly interdisciplinary and fundamental question whose answer might eventually have a strong impact on ML. To the best of my knowledge, the proofs and arguments presented are correct. While an experimental evaluation would of course have been very good to back up the theoretical claims, the absence of a device capable of executing the algorithm excuses the authors from my point of view. As far as quantum algorithms go, the results are hence well presented and analyzed. It is clear that this paper stands out in terms of originality and novelty (at least for the NIPS audience).

The main result of the paper is giving tight bounds on the number of n-variable boolean functions that can be expressed as degree d-polynomial threshold functions for any fixed d (d growing very mildly with n) also works. To me the rest of the results while interesting seem to be mostly easy applications of the key result to other more fashionable neural network models. However, the tightness of the main result does not translate to tight bounds when other neuroidal models are considered, because of the kind of non-linearities or weight constraints involved. The main result is highly non-trivial, the proof quite lengthy though elegant, and resolves a 25 year old open problem. Although the proof uses a lot of heavy mathematics, the key contribution seems to be generalizing random matrix theory to a random tensor theory -- the key result being that a large number of stochastically independent random vectors in low-dimension (and hence clearly not linearly indpendent) still yield a high degree of linear independence when tensorized.