Experimentally revealed stochastic preferences for multi-component choice options

Abstract

34Realistic, everyday rewards contain multiple components. An apple has taste and size. 35 However, we choose in single dimensions, simply preferring some apples to others. How can 36 such single-dimensional relationships refer to multi-dimensional choice options? Here, we 37 investigated stochastic choices of two-component milkshakes. The revealed preferences were 38 intuitively graphed as indifference curves that indicated how much of one component was 39 traded-in for obtaining one unit of the other component without a change in preference, thus 40 defining the orderly integration of multiple components into single-dimensional estimates. 41Options on higher indifference curves were preferred to those on lower curves. The 42 systematic, non-overlapping curves satisfied leave-one-out tests, followed decoder 43 predictions and correlated with Becker-DeGroot-Marschak auction-like bids. These single-44 dimensional estimates of multi-component options complied with rigorous concepts of 45 Revealed Preference Theory and encourage formal investigations of normal, irrational and 46 pathological decisions and their neural signals. 47 48 52 53We like apples, in particular if they are sweet. We can state our preference in words, but this 54 may not be accurate because of poor introspection, faulty memory or erroneous report. It 55 would be more accurate to observe our choice between different apples by which we reveal 56 our preference at that moment. But how do we make that choice? When choosing between 57 apples, we may prefer a sweeter one even if it is a bit smaller; we would trade-in some size 58 for more sweetness. As the trade-off illustrates, our preference among apples does not come 59 from any component alone but from their combination. Every reward or economic good 60 constitutes a bundle with multiple components, attributes or dimensions, and thus is formally 61 a vector. The bundle components may be integral parts of a good, like the sweetness and size 62 of the apple, or consist of distinct entities, like the steak and vegetable of a meal. Importantly, 63 each component contributes to the choice of the bundle. Without considering the multi-64 component nature of choice options, we can only study gross choices or exchanges, like 65 between an apple and a pear (not really a choice for an apple lover), or between a movie 66 ticket and a meal (not good when hungry). Thus, to understand realistic, fine-grained choices, 67 we should consider that choice options have multiple components. 68 In contrast to the multi-dimensionality of realistic, vectorial choice options, revealed 69 preferences and subjective reward value ('utility') are single-dimensional. When faced with 70 two options, a rational decision maker can only prefer one option or its alternative or be 71 indifferent to the options (completeness axiom; see Mas-Colell et al. 1995). With repeated, 72 stochastic choices, preferences are revealed by choice probability (McFadden 2004); the 73 probability of choosing one option over its alternative varie...

Single-dimensional human brain signals for two-dimensional economic choice options

“…Each bundle contained the same two separate objects (milkshakes) rather than consisting of single objects that each had multiple components. Our behavioral results (Pastor- In our binary choice task, we elicited revealed preferences with repeated, psychophysically controlled choices (Pastor-Bernier et al 2020;Green, & Swets 1966). Such a multi-trial, stochastic approach is well conceptualized (McFadden & Richter 1990;McFadden 2004), fulfils statistical requirements of neural research, corresponds to standard choice functions (Sutton, & Barto 1998), and allows comparison with animal neurophysiology (Pastor-Bernier et al, 2017).…”

“…The Cambridgeshire Health Authority (Local Research Ethics Committee) approved this study. The behavioral results have been published with more details separately (Pastor-Bernier et al 2020).…”

“…The pump was approved for delivering foodstuffs and was controlled by a National Instruments device (NI-USB-6009) via the Data Acquisition Toolbox in Matlab. We displayed stimuli to participants and recorded behavioral choices using the Psychtoolbox in Matlab running on a Windows (Dell) computer (Pastor-Bernier et al 2020).…”

“…We used a psychophysical staircase method (Pastor-Bernier et al 2020;Green, & Swets, 1966) to estimate the indifference points (IPs) at which, by definition, each of the two bundle options was chosen equally frequently (i.e. probability P = 0.5 for each option), indicating choice indifference for the options.…”

“…The indifference map that resulted from the 3 x 5 IPs was unique for each of the 24 participants. The indifference maps of the 24 participants were presented before (Pastor-Bernier et al 2020).…”