# [REVIEW] Foundations of Neuroeconomic Analysis

Neuroeconomics is the application of advances in neuroscience to the fundamentals of economics: choice and valuation. _[Foundations of Neuroeconomic Analyis](http://www.amazon.com/dp/0199744254/?tag=vglnk-c319-20)_ by Paul Glimcher, an active researcher in this area, presents a summary of this relatively new field to psychologists and economists. Although written as a serious work, the presentation is made across disciplines, so it should be accessible to anyone interested without much background knowledge in either area. Although the writing is so-so, the book covers multiple Less Wrong-relevant themes, from reductionism to neuroscience to decision theory. If nothing else, the results discussed provide a wonderful example of how [no one knows what science doesn't know](/lw/kj/no_one_knows_what_science_doesnt_know/). I doubt many economists are aware researchers can point to something very similar to utility on a brain scanner and would scoff at the very notion.

Because of the book's wide target audience, there is not enough detail for specialists, but possibly a little too much for non-specialists. If you are interested in this topic, the best reason to pick up the book would be to track down further references. I hope the following summary does the book justice for everyone else.

Are book summaries of this sort useful? The recent review/summary of [_Predictably Irrational_](/r/discussion/lw/5lb/book_review_predictably_irrational_by_dan_ariely/) appears to have gone over well. Any suggestions to improve possible future reviews?

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### Introduction

Many economists think economics is fundamentally separate from psychology and neuroscience; since they take choices as primitives, little if any knowledge would be gained from understanding the mechanisms underlying choice. However, science steadily brings reduction and linkages between previously unrelated disciplines. A striking amount has already been discovered about the exact processes in the brain governing choice and valuation. On the other side, neuroscientists and psychologist underestimate the ability of economists to say whether claims about the brain are logically coherent or not.

### Section I: The Challenge of Neuroeconomics

Consider a man and woman who have an affair with each other at a professional conference, which they later consider a mistake. An economist looking at this situation would treat their choice to sleep together as revealing a preference, regardless of their verbal claims. A psychologist would consider how mental states mediated this decision, and would be more willing to consider whether the decision was a mistake or not. Biologists would be more likely to point to ancestral benefits of extra-pair copulations, not considering the reflective judgements as directly relevant. These explanations largely speak past each other, hinting that a unified theory could do much better in predicting behavior.

The key to this is establishing linkages between the logical primitives of each discipline. Behavior could be explained on the level of physics, biology, psychology, or economics, but whether low-level explanations are practical is a different matter. Realistically, linking disciplines will strengthen both fields by mutually constraining the theories available to them.

With the neoclassical revolution, economics developed concepts of utility as reflecting ordinal relationships over revealed preferences. Choices that satisfied certain [consistency conditions](http://en.wikipedia.org/wiki/Revealed_preference#The_strong_axiom_of_revealed_preference) could be treated as if generated by a utility function. [Additional axioms](http://en.wikipedia.org/wiki/Expected_utility_hypothesis#The_von_Neumann-Morgenstern_axioms) allowed consistent choice under uncertainty to be added to the theory. There are notable problems with this approach, but the core ideas of utility and maximization have surprisingly close neural analogues. Rather than operating "as if" individuals act on the basis of utility, a hard theory of "because" is being developed.

A look at visual perception reveals our subjective experience of light intensity varies subtantially depending on the wavelength of the light. Brightness is concept that resides in the mind, and furthermore sensitivity to different wavelengths corresponds precisely to the absorption spectra of the chemical _rhodopsin_ in our retinas. All perceptions are represented in the mind along a [power scale](http://en.wikipedia.org/wiki/Stevens'_power_law) with some variance. Because the distributions of perceptions overlap, subjects can report accurately that a dimmer light is perceptually brighter. This suggests random utility models developed for statisical purposes might be directly explain what happens in the brain. One interesting consequence about the power scaling law is that [risk aversion](http://en.wikipedia.org/wiki/Risk_aversion) would be embedded at the level of perception.

### Section II: The Choice Mechanism

Due to its relative simplicity, eye movement serves as a model for motor control and perhaps decisions broadly. The _superior colliculus_ represents possible eye movements topographically with "hills" of activity. Eventually, the tissue transitions to a bursting state where the most active hill becomes much more active and the rest are inhibited via a "winner-take-all" or "argmax" mechanism. All inputs have to eye motion have to pass through the _superior colliculus_, so this represents a common final pathway of processed sensory signals. By giving monkeys varying awards for eye-motion tasks, activity in the _lateral intraparietal area_ (LIP) correlates strongly with the probability and size of reward in an area known to trigger action before the action is taken. In other words, this appears to be a direct neural representation of subjective expected valuation. If monkey subjects play a game with mixed strategies in equilibrium, neuron firing rates are all roughly equal, matching the conclusion that expected utilities of actions are equalized when an opponent is mixing.

Cortial neurons fire almost like independent Poisson processes, resulting in neurons down the line being able to easily extract the mean firing rate of the inputs. Interneuronal correlation can vary according to the task at hand, resulting in greater or lesser variation of the final decision, so descriptive decision theories must incorporate randomness in choice. This also provides support for mixed strategies being represented directly in the brain.

Subjective valuations are normalized, and are only considered relative to the other options at hand. This normalization maximizes the joint information of neurons, increasing the efficiency of value representation. One consequence is that as the choice set increases, valuations start overlapping, and choice becomes essentially random. Activity also varies according to the delay of rewards, matching previous findings of hyperbolic discounting. While these findings are largely based on eye-movements in monkeys, this provides a clear path of how choice can be reduced to neural mechanisms.

### Section III: Valuation

Back to visual perception, our judgements are made relative to other elements in the environment. Color looks roughly the same indoors and outdoors, even though there can be six orders of magnitude more illumination outside. Drifting reference points make absolute values unrecoverable. Local irrationalies due to reliance on a reference point arise because evolution is trading off between accurate sensory encoding and the costs of these irrationalities.

One promising way to specify the reference point is as the discounted sum of our future wealth. Learning depends on the difference between actual and expected rewards, so valuation compared to a reference point arises from the learning process. In the brain, reward prediction errors are encoded through dopamine. Dopamine firing rates are well-described by an exponentially weighted sum of previous awards subtracted from the most recent award. Hebb's law, which says "cells that fire together, wire together", describes how long-term predictions work.

Valuation appears to be orginally constructed in the striatum and medial prefrontal cortex. The reference level encoded there can be directly observed with brain scanners. Various other regions provide inputs to construct value. For instance, the orbitofrontal cortex (OFC) provides an assessment of risk. Subjects with lesions in this area exhibit almost perfect risk neutrality. Values might also be stored in the OFC, again in a compressed and encoded way. Longer-term valuations might be stored in the amygdala.

Because valuations are encoded relatively and don't work well over large choice sets, humans might edit out options by sequentially considering particular attributes until the choice set become manageable. Sorting by attributes can lead to irrational choices, unsurprisingly.

Probabilistic valuations depend on whether the expectation was learned experientially or symbolically. Symbolically communicated probabilities, where the person is told a number, are overweighed near zero and underweighted near one. Experientially communicated probabilities, where the person samples the lotteries directly, exhibit the opposite pattern. This suggests at least two mechanisms at work, especially with the ability to deal with symbolic probabilities arising relatively late in our evolutionary history. Also, while experiential expected values incorporate probabilities implicitly, this information can't be extracted. When probabilities change, the only means to change valuations is to relearn them from scratch.

### Section IV: Summary and Conclusions

Here the author presents formalized models of the descriptive theory. The normative uses of this theory are still unclear. Even if we can identify subjective valuations in the brain, does this have any relation to welfare?

The four critical observations of neuroeconomics are reference-dependence, the lack of an absolute measure of anything in the brain, stochasticity in choice, and the influence of learning on choice. Along with the question of the welfare implications of these findings, six primary questions are currently unanswered:

1.  Where is subjective value stored and how does it get to choice?
2.  What part of the brain governs when it is "time to choose"?
3.  What neural mechanism guides complementarity between goods?
4.  How does symbolic probability work?
5.  How does the state of the world and utility interact?
6.  How does the brain represent money?