Using results from neurobiology on perceptual decision making and value-based decision making, the problem of decision making between lotteries is reformulated in an abstract space where uncertain prospects are mapped to corresponding active neuronal representations. This mapping allows us to maximize non-extensive entropy in the new space with some constraints instead of a utility function. To achieve good agreements with behavioral data, the constraints must include at least constraints on the weighted average of the stimulus and on its variance. Both constraints are supported by the adaptability of neuronal responses to an external stimulus. By analogy with thermodynamic and information engines, we discuss the dynamics of choice between two lotteries as they are being processed simultaneously in the brain by rate equations that describe the transfer of attention between lotteries and within the various prospects of each lottery. This model is able to give new insights on risk aversion and on behavioral anomalies not accounted for by Prospect Theory.
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