Aggregate Choices Research Articles

Dopamine neurons encode trial-by-trial subjective reward value in an auction-like task

The dopamine reward prediction error signal is known to be subjective but has so far only been assessed in aggregate choices. However, personal choices fluctuate across trials and thus reflect the instantaneous subjective reward value. In the well-established Becker-DeGroot-Marschak (BDM) auction-like mechanism, participants are encouraged to place bids that accurately reveal their instantaneous subjective reward value; inaccurate bidding results in suboptimal reward (“incentive compatibility”). In our experiment, male rhesus monkeys became experienced over several years to place accurate BDM bids for juice rewards without specific external constraints. Their bids for physically identical rewards varied trial by trial and increased overall for larger rewards. In these highly experienced animals, responses of midbrain dopamine neurons followed the trial-by-trial variations of bids despite constant, explicitly predicted reward amounts. Inversely, dopamine responses were similar with similar bids for different physical reward amounts. Support Vector Regression demonstrated accurate prediction of the animals’ bids by as few as twenty dopamine neurons. Thus, the phasic dopamine reward signal reflects instantaneous subjective reward value.

The prediction of market-level food choices by the neural valuation signal.

Neuroimaging studies have demonstrated the ability to use the brain activity of a group of individuals to forecast the behavior of an independent group. In the current study, we attempted to forecast aggregate choices in a popular restaurant chain. During our functional magnetic resonance imaging (fMRI) study, 22 participants were exposed to 78 photos of dishes from a new menu of a popular restaurant chain. In addition to self-reported preferences, fMRI data was extracted from an a priori domain-general and task-specific region of interest-the ventral striatum. We investigated the relationship between the neural activity and real one-year sales provided by the restaurant chain. Activity in the ventral striatum, which was defined using the task-specific region of interest, significantly correlated (r = 0.28, p = 0.01) with one-year sales. A regression analysis, which included ventral striatum activity together with the objective characteristics of the products (price and weight), behavioral, and survey data, showed R2 values of 0.33. Overall, our results confirm prior studies, which have suggested, that brain activity in the reward system of a relatively small number of individuals can forecast the aggregate choice of a larger independent group of people.

Risk and rationality: The relative importance of probability weighting and choice set dependence

The literature suggests that probability weighting and choice set dependence influence risky choices. However, their relative importance remains an open question. We present a joint test that uses binary choices between lotteries provoking Common Consequence and Common Ratio Allais Paradoxes and manipulates their joint payoff distribution. We show non-parametrically that probability weighting and choice set dependence both play a role at describing aggregate choices. To parsimoniously account for heterogeneity, we also estimate a structural model using a finite mixture approach. The model uncovers substantial heterogeneity and classifies subjects into three types: 38% Prospect Theory types whose choices are predominantly driven by probability weighting, 34% Salience Theory types whose choices are predominantly driven by choice set dependence, and 28% Expected Utility Theory types. The model predicts type-specific differences in the frequency of preference reversals out-of-sample, i.e., in choices with a different context than the ones used for estimating the model. Moreover, the out-of-sample predictions indicate that the choice context shapes the influence of choice set dependence.

Inferring Cognitive Heterogeneity From Aggregate Choices

Theories of bounded rationality often assume a rich dataset of choices from many overlapping menus, limiting their practical applicability. In contrast, we study the problem of identifying the distribution of cognitive characteristics in a population of agents from a minimal dataset that consists of aggregate choice shares from a single menu, and includes no observable covariates of any kind. With homogeneous preferences, we find that “consideration capacity” and “consideration probability” distributions can both be recovered effectively if the menu is sufficiently large. This remains true generically when tastes are heterogeneous with a known distribution. When the taste distribution is unknown, we show that joint choice share data from three “occasions” are generically sufficient for full identification of the cognitive distribution, and also provide substantial information about tastes.

Heterogeneous Society in Binary Choices with Externalities

We study a two-strategy model with negative externalities proposed by Schelling, in a dynamical setting where a society consists of two interacting populations with different behaviors derived from experiments with human participants. The resulting dynamics is a three-dimensional piecewise smooth map with one discontinuity, which inherits some of the characteristics of each homogeneous population dynamics, while others are lost and new ones emerge. We propose a technique to represent the dynamics on a bidimensional space and prove that the heterogeneous society dynamics can be obtained as a linear combination of the dynamics of the two homogeneous populations. As expected, complexity arises with respect to some aspects. Firstly, the number of equilibria expands to infinity and we were able to determine possible focal equilibria in the sense of Schelling. Secondly, when heterogeneity is introduced, the period adding structure of cycles is replaced by a period incrementing structure. Thirdly, the phenomenon of overreaction and cyclic oscillations can be mitigated even if it never completely disappears. We also derive the orbits of cycles of period two and provide numerical evidences of coexistence of cycles with different periods. It is worth noticing that with the heterogeneous society, the dynamics does not depend on the society aggregate choices only, rather on each population choice; neglecting it will make impossible to determine the future evolution of the system. The implications are important as heterogeneity makes the system path-dependent and a policy maker, considering aggregate society choice only, would be unable to make the proper decisions, unless further information is considered.

A laboratory experiment on the heuristic switching model

We present results from the first laboratory experiment on the seminal heuristic switching model introduced by Brock and Hommes (1997, 1998). Subjects choose between two alternatives, a sophisticated and stabilizing, but costly, heuristic, and a destabilizing, but cheap, heuristic, and are paid according to the performance of the chosen heuristic. Aggregate choices determine the evolution of a state variable and, consequently, the performance of both heuristics. Theoretically, an increase in the costs for the stabilizing heuristic generates instability and leads to endogenous fluctuations in both the state variable and the fraction of agents using that heuristic.We vary the costs of the stabilizing heuristic in the experiment and find that the predictions of the heuristic switching model are partially confirmed. For low costs the dynamics are stable. For high costs, the dynamics initially are unstable and exhibit the type of bubbles and crashes emblematic for the heuristic switching model. However, over time the pattern of bubbles and crashes disappears and the dynamics become more stable. We estimate a standard discrete choice model on aggregate choice data and observe that subjects have a tendency to become less sensitive to payoff differences when the environment is less stable, which has important implications for the application of heuristic switching models.

A formal and empirical comparison of two score measures for best–worst scaling

Best–worst scaling (BWS) is a method that asks individuals to choose the most and the least preferred option from a set of available options. There has been extensive discussion and evaluation of the use of scores (data summaries) in the analysis of such data. Here we motivate, summarize, and compare the usefulness of two such score measures: the analytical closed form solution (Lipovetsky and Conklin, 2014, Journal of Choice Modelling) and normalized best–worst scores (Louviere et al., 2015, Cambridge University Press). We conclude that both have underlying motivations in the maxdiff model of best–worst choice and that the analytical closed form solution provides better fits to the aggregate choices in several best–worst choice data sets.

Observational Learning with Large Choice Sets - Crowds, Contrarians, and Congestion

We study the formation of market shares in environments where customers choose from among multiple options for which they observe the aggregate choices of previous customers (the sales of each option). With imperfect information regarding the true quality of the different options, the choices of better informed customers turn sales into informative signals, allowing less informed customers to learn about the options' quality. Besides such informational externalities, we consider possible direct negative externalities that characterize many economic environments - customers often derive lower utility from options chosen by more other customers, ceteris paribus. Our equilibrium analyses demonstrate a moderating, and counterintuitive, effect of negative externalities on observational learning. For example, when negative externalities are negligible, the option with the highest sales might seem like the obvious choice as it is a cheap signal of quality, but we find that rational uninformed customers instead choose a option with lower sales. We test our theory in a controlled laboratory environment with human subjects, and find strong evidence for observational learning predicted by our equilibrium analyses, with one notable exception: With negligible negative externalities, uninformed subjects ignore minority options and choose majority options instead. We explain this behavior via random choice theory.

Efficient Bayesian analysis of multivariate aggregate choices

In estimating individual choice behaviour using multivariate aggregate choice data, the method of data augmentation requires the imputation of individual choices given their partial sums. This article proposes and develops an efficient procedure of simulating multivariate individual choices given their aggregate sums, capitalizing on a sequence of auxiliary distributions. In this framework, a joint distribution of multiple binary vectors given their sums is approximated as a sequence of conditional Bernoulli distributions. The proposed approach is evaluated through a simulation study and is applied to a political science study.

Is equilibrium in transport pure Nash, mixed or Stochastic?

The classical theory of transport equilibrium is based on the Wardrop’s first principle that describes a Nash User Equilibrium (UE), where in no driver can unilaterally change routes to improve his/her travel times. A growing number of economic laboratory experiments aiming at testing Nash-Wardrop equilibrium have shown that the Pure Strategy Nash Equilibrium (PSNE) is not able to explain the observed strategic choices well. In addition even though Mixed Strategy Nash Equilibrium (MSNE) has been found to fit better the observed aggregate choices, it does not explain the variance in choices well. This study analyses choices made by users in three different experiments involving strategic interactions in endogenous congestion to evaluate equilibrium prediction. We compare the predictions of the PSNE, MSNE and Stochastic User Equilibrium (SUE). In SUE, the observed variations in choices are assumed to be due to perception errors. The study proposes a method to iteratively estimate SUE models on choice data with strategic interactions. Among the three sets of experimental data the SUE approach was found to accurately predict the average choices, as well as the variances in choices. The fact that the SUE model was found to accurately predict variances in choices, suggests its applicability for transport equilibrium models that attempt to evaluate reliability in transportation systems. This finding is fundamental in the effort to determining a behaviourally consistent paradigm to model equilibrium in transport networks. The study also finds that Fechner error which is the inverse of the scale parameter in the SUE model is affected by the group sizes and the complexity of the cost function. In fact, the larger group sizes and complexity of cost functions increased the variability in choices. Finally, from an experimental design standpoint we show that it is not possible to estimate a noise parameter associate to Fechner error in the case when the choices are equally probable.

Preference reversals: The impact of truth-revealing monetary incentives

Researchers vigorously debate the impact of incentives in preference reversal experiments. Do incentives alter behavior and generate economically consistent choices? Lichtenstein and Slovic (1971) document inconsistencies (reversals) in revealed preference in gamble pairs across paired choice and individual pricing tasks. The observed pattern is inconsistent with stable underlying preferences expressed with simple errors. Lichtenstein and Slovic (1973) and Grether and Plott (1979) introduce incentives, but aggregate reversal rates change little. These results fostered numerous replications and assertions that models of non-stable preferences are required to explain reversals. Contrary to this research, we find that incentives can generate more economically consistent behavior. Our reevaluation of existing experimental data shows that incentives have a clear impact by better aligning aggregate choices and prices. The effect is sufficiently large that, with truth-revealing incentives, a stable-preferences-with-error model not only explains behavior, but fits the data as well as any model possibly could.

Towards a brain-to-society systems model of individual choice

Canonical models of rational choice fail to account for many forms of motivated adaptive behaviors, specifically in domains such as food selections. To describe behavior in such emotion- and reward-laden scenarios, researchers have proposed dual-process models that posit competition between a slower, analytic faculty and a fast, impulsive, emotional faculty. In this paper, we examine the assumptions and limitations of these approaches to modeling motivated choice. We argue that models of this form, though intuitively attractive, are biologically implausible. We describe an approach to motivated choice based on sequential sampling process models that can form a solid theoretical bridge between what is known about brain function and environmental influences upon choice. We further suggest that the complex and dynamic relationships between biology, behavior, and environment affecting choice at the individual level must inform aggregate models of consumer choice. Models using agent-based complex systems may further provide a principled way to relate individual and aggregate consumer choices to the aggregate choices made by businesses and social institutions. We coin the term “brain-to-society systems” choice model for this broad integrative approach.

New measures and tests of temporal and spatial pattern of crops in agricultural landscapes

Crops are allocated to their fields by growers according to rotational principles and such rotations may be defined and classified. Rotations evolve through the aggregate choices of crops by growers over time which create the characteristic agricultural landscapes for a given region. As agriculture becomes ever more competitive, growers increasingly should use such rotational principles to maximise efficiency. Their choices of crop allocations alter the observed temporal heterogeneity and spatial pattern of cropped landscapes. Within the European Union the forms of heterogeneity studied here are increasingly evident at the landscape scale. We present techniques to study these patterns of crops in time and space. This is essential in order to build realistic simulators of large-scale cropped landscapes within which farming practices may be studied across national boundaries. Simulation is required to provide realistic arenas to extend current models of gene flow from the field to the landscape scale, in furtherance of studies of coexistence between genetically modified and conventional and organic crops. We provide simple, empirical descriptors of cropped landscapes in terms of the degree of the non-randomness of the allocation. Non-randomness of fields is assessed in terms of (i) spatial pattern, (ii) temporal heterogeneity, and (iii) spatio-temporal heterogeneity. Four formal statistical tests of significance are presented: one of spatial pattern, two of temporal heterogeneity and one of spatio-temporal heterogeneity that may also be used to test for spatial pattern. The tests were exemplified using data taken from a study landscape of 72 arable fields farmed by 10 different growers in Burgundy, France, from 1994 to 1997. Two of the tests were based on simple χ 2 -statistics; two were randomisation tests. The χ 2 -test of spatial pattern demonstrated clustering in the distribution of set aside fields. The χ 2 -test of temporal heterogeneity demonstrated non-randomness for eight growers who employed 15 rotations. The randomisation test of temporal heterogeneity found significant non-randomness for one grower in three of the five crops examined. The common 3-year rotation of oilseed rape, wheat, winter barley was employed by one grower on 10 of their fields, for which significant spatio-temporal heterogeneity was shown by the proposed randomisation test. It is possible to extend the analysis of these test-statistics between – and within – units in a hierarchy, so that the methods could be used to study pattern at larger scales than landscapes, say at regional or national scales.

Bilateralism, Multilateralism, or Regionalism? Japan's Trade Forum Choices

The Japanese government today is actively and strategically choosing among various institutional forums to deal with its trade partners, namely bilateral venues, multilateral settings, and even preferential regional arrangements. This ongoing high-profile institutional selection is somewhat unprecedented for Japan, and demands a review of the historical and analytical reasons that drive decisionmakers to select one forum over another. Overall, the Japanese case suggests that the aggregate trade forum choices are influenced both by the desire to institutionalize mechanisms for stabilizing a range of expectations and by the necessity of guaranteeing market access and protection of investment in the fastest time possible.

Ecological Transfers in Non-Human Communities Parallel Economic Markets in a General Equilibrium Ecosystem Model

Synopsis: The oft-cited analogies between ecological and economic systems are exploited to develop a many-species model of population dynamics. In economies, markets are the fundamental institutions in which the interaction of demands and supplies determine the quantities and prices of goods. However, economic markets are not appropriate for ecological communities, because markets rely on voluntary exchange, whereas plants and animals engage in involuntary transfers of biomass. A properly defined counterpart to markets based on biomass transfers permits a general equilibrium model of predator/prey and competitive interactions in a many-species community. Functional response from optimal foraging and predation risk provide the demand and supply, respectively, in the biomass transfers. Energy per unit time is scarce and predators and prey make optimum choices with respect to functional response and risk avoidance based on required energy expenditures. The energy expenditures are similar to economic prices: they determine foraging strategies and are beyond the control of the predators and prey, yet they are determined by the aggregate choices of all predators and prey and by population densities. The energies acquired from foraging are used in a new way to construct difference equations that determine the population dynamics.

Whom or What Does the Representative Individual Represent?

Macroeconomic models often assume that the choices of all the diverse agents in one sector— consumers for example—can be considered as the choices of one “representative” standard utility maximizing individual whose choices coincide with the aggregate choices of the heterogeneous individuals. My basic point is that the reduction of the behavior of a group of heterogeneous agents even if they are all themselves utility maximizers, is not simply an analytical convenience as often explained, but is both unjustified and leads to conclusions which are usually misleading and often wrong. First, such models are particularly ill-suited to studying macroeconomic problems like unemployment, which should be viewed as coordination failures. Furthermore these models, instead of being a hive of activity and exchange, are frequently, ones in which no trade at all takes place. And this is just the beginning of a list of problems with this approach. Finally I will consider more positive alternatives to the representative individual approach—approaches that focus on heterogeneity of agents may and interaction between individuals. It is clear that the “representative” agent deserves a decent burial, as an approach to economic analysis that is not only primitive, but fundamentally erroneous.