Response: “Commentary: Utility-free heuristic models of two-option choice can mimic predictions of utility-stage models under many conditions”

Citation: Piantadosi ST and Hayden BY (2015) Response: " Commentary: Utility-free heuristic models of two-option choice can mimic predictions of utility-stage models under many conditions. " Front. Neurosci. 9:299. Response: " Commentary: Utility-free heuristic models of two-option choice can mimic predictions of utility-stage models under many conditions " A commentary on Commentary: Utility-free heuristic models of two-option choice can mimic predictions of utility-stage models under many conditions by Padoa-Schioppa C. In his accompanying commentary on our recent paper, Dr. Padoa-Schioppa identifies two putative errors in our manuscript (Piantadosi and Hayden, 2015). Both reflect basic misunderstandings of our arguments, as well as those of Tversky (1969), whose work ours is an extension of. First, he argues that some commodities are inherently incommensurate, such as different juice flavors (" there is no parametric dimension along which two flavors can be assigned a scalar value "). This argument seems appealing because it is difficult to think of a single algorithmic function that would describe a juice flavor as a single number. So in a colloquial sense, juices could indeed by called incommensurate. However, most models of choice assume, either tacitly or explicitly, that there is an intermediate stage during which each dimension is represented in a scalar manner and may there be deformed. A famous example is prospect theory (Kahneman and Tversky, 1979). In PT, gains are transformed using a convex utility curve and probability is deformed by a different curve; these transformed scalars are then combined into a single utility variable (Figure 1A). The same concept can be extended to thinking about very abstract goods like juice flavor, the funniness of a joke, or the intellectual appeal of a novel theory (Figure 1B). To do so, one may use a lookup table, as illustrated in our example. One example of a model that involves such a lookup table is Padoa-Schioppa and Assad (2006). In that paper, the authors propose that juices can be given a scalar value parameter, and that this parameter can be experimentally observed through preferences. These idea of an intermediate stage is a critical part of several famous economic models, including Padoa-Schioppa's own work, and has a direct neural correlate in the orbitofrontal cortex (Blanchard et al., 2015). A different possibility would be that it is impossible to construct an intermediate-stage model for a given choice process (Figure 1C). In such cases our ideas do not apply, nor would …