This paper reports the results of an experiment designed to uncover the stochastic structure of individual preferences over lotteries. Unlike previous experiments, which have presented subjects with pair-wise choices between lotteries, our design allowed subjects to choose between two lotteries or (virtually) any convex combination of the two lotteries. We interpret the mixtures of lotteries chosen by subjects as a measure of the stochastic structure of choice. We test between two alternative interpretations of stochastic choice: (...) the random utility interpretation and the deterministic preferences interpretation. The main findings of the experiment are that the typical subject prefers mixtures of lotteries rather than the extremes of a linear lottery choice set. The distribution of choices does not change between a first and second asking of the same question. We argue that this provides support for the deterministic preferences interpretation over the random utility interpretation of stochastic choice. As a subsidiary result, we find a small proportion of subjects make choices that violate transitivity, but the level of intransitive choice falls significantly over time. (shrink)

Models of choice over menus aim at capturing the effect of some behavioral or non-standard element of decision-making on the behavior of a single decision-maker. These models are usually compared with the standard model of choice over menus, in which the decision-maker chooses a menu whose best item is better than that of all other available ones. However, in many empirical settings such as experimental studies, choice data come from a population of decision-makers with possibly heterogeneous attitudes (...) and tastes. This heterogeneity can make the observed choices over menus stochastic. This fact calls for a stochastic characterization of models of choice over menus to be able to better compare and contrast different models empirically. In this paper, I do this task for the standard model, which would be an extension of the random utility model to the realm of choice over menus. In particular, I provide the necessary and sufficient conditions, i.e., axioms on choice data over menus for it to be consistent with a population of decision-makers each of whom behaves according to the standard model. The axioms that characterize the model are the axiom of revealed stochastic preferences over singletons and three rationality axioms. (shrink)

We consider random choice rules that, by satisfying a weak form of Luce’s choice axiom, embody a form probabilistic rationality. We show that for this important class of stochastic choices, the law of demand for normal goods—arguably the main result of traditional consumer theory—continues to hold on average when strictly dominated alternatives are dismissed.

In this article, we illustrate experimentally an important consequence of the stochastic component in choice behaviour which has not been acknowledged so far. Namely, its potential to produce ‘regression to the mean’ (RTM) effects. We employ a novel approach to individual choice under risk, based on repeated multiple-lottery choices (i.e. choices among many lotteries), to show how the high degree of stochastic variability present in individual decisions can distort crucially certain results through RTM effects. We demonstrate (...) the point in the context of a social comparison experiment. (shrink)

This paper provides an experimental test of stochastic choice models of decisions. Models that admit Fechnerian structure are tested through the repeated pairwise choice problems. Results refute the Fechner hypothesis that characterizing the probability of selecting a given prospect increases in how strongly it is preferred to alternative choices. However, the experimental data lend support to characterizing an individual’s binary choice probability as some scalable functions of the von Neumann–Morgenstern utilities in the risky context.

This article explores rationalizability issues for finite sets of observations of stochastic choice in the framework introduced by Bandyopadhyay et al. (Journal of Economic Theory, 84(1), 95–110, 1999). It is argued that a useful approach is to consider indirect preferences on budgets instead of direct preferences on commodity bundles. A new rationalizability condition for stochastic choices, “rationalizable in terms of stochastic orderings on the normalized price space” (rsop), is defined. rsop is satisfied if and only if (...) there exists a solution to a linear feasibility problem. The existence of a solution also implies rationalizability in terms of stochastic orderings on the commodity space. Furthermore it is shown that the problem of finding sufficiency conditions for binary choice probabilities to be rationalizable bears similarities to the problem considered here. (shrink)

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background (...) uncertainty about the choiceworthiness of one's options, many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty. But, even under these conditions, stochastic dominance will not require agents to accept options whose expectational superiority depends on sufficiently small probabilities of extreme payoffs. The sort of background uncertainty on which these results depend looks unavoidable for any agent who measures the choiceworthiness of her options in part by the total amount of value in the resulting world. At least for such agents, then, stochastic dominance offers a plausible general principle of choice under uncertainty that can explain more of the apparent rational constraints on such choices than has previously been recognized. (shrink)

The guiding idea of this work is that classical diffusion theory, being nonrelativistic, should be associated with nonrelativistic quantum mechanics. A study of classical diffusion leads to a generalization which should correspond to the relativistic domain. Actually, with a convenient choice of the basic constants, one sees the relativistic features (Lorentz contraction and covariant diffusion equation) emerge in the generalized process. This leads first to a derivation of the nonrelativistic and relativistic wave equations (and to a model of the (...) Dirac fluid); then to a better understanding of several relativistic aspects of quantum mechanics (spin connection with relativity and link of relativity with nonlocalization). No quantum mechanical forces are postulated: they arise as pseudo-forces in the course of the calculations. The physical significance of the stochastic model is examined and shown to give a pictorial description only in certain ideal situations, but to remove several conceptual difficulties. Remarks are presented on the role of idealization in microphysics. (shrink)

We propose a probabilistic interpretation of Propositional Dynamic Logic (PDL). We show that logical and behavioral equivalence are equivalent over general measurable spaces. This is done first for the fragment of straight line programs and then extended to cater for the nondeterministic nature of choice and iteration, expanded to PDL as a whole. Bisimilarity is also discussed and shown to be equivalent to logical and behavioral equivalence, provided the base spaces are Polish spaces. We adapt techniques from coalgebraic (...) class='Hi'>stochastic logic and point out some connections to Souslin's operation A from descriptive set theory. This leads to a discussion of complete stochastic Kripke models and model completion, which permits an adequate treatment of the test operator. (shrink)

In a remarkable confirmation of OT in an empirical domain for which it was not originally intended, phonological and morphological variation has been successfully modeled by partially ranked categorical constraints (Anttila 1997, 2002). Poetic meter is a good place to extend and test this approach to variation, because there is abundant and diverse quantitative data available for it, and because it is typically governed by a relatively small number of well-understood constraints. I report the results of four such studies here. (...) They confirm that choices among metrical options are governed by the interaction of partially ranked constraints, in each case constraints that are grounded, and motivated independently of variation data by related systems in which they have a fixed rank. The partially ranked constraint systems turned out to predict not only the relative preferences among metrical options, but also their actual frequencies in the corpora, with surprising accuracy. These findings support the partial ranking model of variation, and provide an explanatory benchmark beyond the reach of intrinsically weaker stochastic approaches that posit a statistical component for metrical competence (Hayes & MacEachern 1998). (shrink)

The possibility to interpret expected and nonexpected utility theories in purely probabilistic terms has been recently investigated. Such interpretation proposes as guideline for the Decision Maker the comparison of random variables through their probability to outperform a stochastic benchmark. We apply this type of analysis to the model of Becker and Sarin, showing that their utility functional may be seen as the probability that an opportune random variable, depending on the one to be evaluated, does not outperform a non-random (...) benchmark. Further, the consequent choice criterion is equivalent to a sort of probability of ruin. Possible interpretations and financial examples are discussed. (shrink)

The paper presents a set of games of competition between two or three players in which reward is jointly determined by a stochastic biased mechanism and players’ choices. More specifically, a resource can be found with unequal probabilities in one of two locations. The first agent is rewarded only if it finds the resource and avoids being found by the next agent in line; the latter is rewarded only if it finds the former. Five benchmarks, based on different psychological (...) and game-theoretic assumptions are derived and their predictions compared to actual behavior of 120, 40, and 48 participants playing repeatedly. Of the five benchmarks—the unique (Nash) equilibrium, reinforcement learning, trust-based efficiency, maximum unpredictability, and regret-based (Impulse Balance) equilibrium—regret for missed opportunities best accounts for the qualitative aspect of participants’ behavior and regret attenuated by randomization best accounts for the quantitative aspect of behavior. (shrink)

The rationalization of context-based choice is usually based on the assumption that preferences are context-dependent. In this paper, we show that context-based choice can be due to the characteristics of the choice procedure applied by the individual and not to the dependence of preferences (stochastic or deterministic) on the context. Our arguments are illustrated focusing on the much-studied dominated-alternative effects.

We derive the exact inefficiency upper bounds of the multiclass C-Logit stochastic user equilibrium in a transportation network. All travelers are classified on the basis of different values of time into M classes. The multiclass CL-SUE model gives a more realistic path choice probability in comparison with the logit-based stochastic user equilibrium model by considering the overlapping effects between paths. To find efficiency loss upper bounds of the multiclass CL-SUE, two equivalent variational inequalities for the multiclass CL-SUE (...) model, i.e., time-based variational inequality and monetary-based VI, are formulated. We give four different methods to define the inefficiency of the multiclass CL-SUE, i.e., to compare multiclass CL-SUE with multiclass system optimum, or to compare multiclass CL-SUE with multiclass C-Logit stochastic system optimum, under the time-based criterion and the monetary-based criterion, respectively. We further investigate the effects of various parameters which include the degree of path overlapping, the network complexity, degree of traffic congestion, the VOT of user classes, the network familiarity, and the total demand on the inefficiency bounds. (shrink)

People often face preferential decisions under risk. To further our understanding of the cognitive processes underlying these preferential choices, two prominent cognitive models, decision field theory (DFT; Busemeyer & Townsend, 1993) and the proportional difference model (PD; González‐Vallejo, 2002), were rigorously tested against each other. In two consecutive experiments, the participants repeatedly had to choose between monetary gambles. The first experiment provided the reference to estimate the models’ free parameters. From these estimations, new gamble pairs were generated for the second (...) experiment such that the two models made maximally divergent predictions. In the first experiment, both models explained the data equally well. However, in the second generalization experiment, the participants’ choices were much closer to the predictions of DFT. The results indicate that the stochastic process assumed by DFT, in which evidence in favor of or against each option accumulates over time, described people’s choice behavior better than the trade‐offs between proportional differences assumed by PD. (shrink)

The paper develops models of statistical experiments that combine propensities with frequencies, the underlying theory being the branching space-times (BST) of Belnap (1992). The models are then applied to analyze Bell's theorem. We prove the so-called Bell-CH inequality via the assumptions of a BST version of Outcome Independence and of (non-probabilistic) No Conspiracy. Notably, neither the condition of probabilistic No Conspiracy nor the condition of Parameter Independence is needed in the proof. As the Bell-CH inequality is most likely experimentally falsified, (...) the choice is this: contrary to the appearances, experimenters cannot choose some measurement settings, or some transitions, with spacelike related initial events, are correlated; or both. (shrink)

Adapting a definition introduced by Milgrom (1981) we say that a signal about the environment is good news relative to some initial beliefs if the posterior beliefs dominate the initial beliefs in the sense of first-order stochastic dominance (the assumption being that higher values of the parameter representing the environment mean better environments). We give an example where good news leads to the adoption of a more pessimistic course of action (we say that action a, reveals greater pessimism than (...) action a„ if it gives higher payoff in bad environments and lower payoff in good environments). We then give sufficient conditions for a signal not to induce a more pessimistic choice of action. (shrink)

If one starts from de Broglie's basic relativistic assumptions, i.e., that all particles have an intrinsic real internal vibration in their rest frame, i.e., hv 0 =m 0 c 2 ; that when they are at any one point in space-time the phase of this vibration cannot depend on the choice of the reference frame, then, one can show (following Mackinnon (1) ) that there exists a nondispersive wave packet of de Broglie's waves which can be assimilated to the (...) nonlinear soliton wave U 0 introduced by him in his double solution model of wave mechanics. (2) Since de Broglie's linear pilot waves can be considered to be real waves propagating as collective motions on a covariant subquantum chaotic “aether,” (3) these new solition waves can be considered as describing the particle's immediate neighborhood, i.e., the aether's reaction to the particle's motion in the stochastic interpretation of quantum mechanics. The existence of such a physical aether (which provides a perfectly causal interpretation of the action-a-distance implied by the Einstein-Podolsky-Rosen experiments) can now be proved by establishing the reality of de Broglie's waves in realizable experiments. (shrink)

The voting paradox occurs when a democratic society seeking to aggregate individual preferences into asocialpreference reaches an intransitive ordering. However it is not widely known that the paradox may also manifest for anindividualaggregating over attributes of risky objects to form a preference over those objects. When this occurs, the relation ‘stochastically greater than’ is not always transitive and so transitivity need not hold between those objects. We discuss the impact of other decision paradoxes to address a series of philosophical and (...) economic arguments against intransitive (cyclical) choice, before concluding that intransitive choices can be justified. (shrink)

This paper focuses on the comparison of individual and group decision-making, in a stochastic inter-temporal problem in two decision environments, namely risk and ambiguity. Using a consumption/saving laboratory experiment, we investigate behaviour in four treatments: individual choice under risk; group choice under risk; individual choice under ambiguity and group choice under ambiguity. Comparing decisions within and between decision environments, we find an anti-symmetric pattern. While individuals are choosing on average closer to the theoretical optimal predictions, (...) compared to groups in the risk treatments, groups tend to deviate less under ambiguity. Within decision environments, individuals deviate more when they choose under ambiguity, while groups are better planners under ambiguity rather than under risk. Our results extend the often observed pattern of individuals behaving more optimally under risk, to its dynamic dimension. (shrink)

Considering three monetary policy rules, together with two endogenous macroprudential policies that are credit constraints for households and counter-cyclical capital for bankers, this paper establishes a dynamic stochastic general equilibrium model. Based on the welfare analysis of different combinations of macroprudential rules and monetary policy rules, this paper identifies the optimal policy combinations and analyzes the coordination effects between macroprudential policies and monetary policies. The results show that no matter what kind of monetary policy rules is implemented, the introduction (...) of macroprudential rules has improved the level of total social welfare. In the optimal “two pillars” framework of monetary policies and macroprudential rules, the main objective of monetary policy is to stabilize price inflation, and the macroprudential policy to be implemented is the CRR macroprudential policy. This combination can effectively promote the stability of the real estate market, financial market, and macroeconomy, while maximizing the improvement of total social welfare. (shrink)

In public goods experiments, stochastic choice, censoring and motivational heterogeneity give scope for disagreement over the extent of unselfishness, and whether it is reciprocal or altruistic. We show that these problems can be addressed econometrically, by estimating a finite mixture model to isolate types, incorporating double censoring and a tremble term. Most subjects act selfishly, but a substantial proportion are reciprocal with altruism playing only a marginal role. Isolating reciprocators enables a test of Sugden’s model of voluntary contributions. (...) We estimate that reciprocators display a self-serving bias relative to the model. (shrink)

This study extends experimental tests of (cumulative) prospect theory (PT) over prospects with more than three outcomes and tests second-order stochastic dominance principles (Levy and Levy, Management Science 48:1334–1349, 2002; Baucells and Heukamp, Management Science 52:1409–1423, 2006). It considers choice behavior of people facing prospects of three different types: gain prospects (losing is not possible), loss prospects (gaining is not possible), and mixed prospects (both gaining and losing are possible). The data supports the distinction of risk behavior into (...) these three categories of prospects, Further, probability weighting and diminishing sensitivity of utility as predicted by PT are observed. Loss aversion is, however, less pronounced, except for choices where one prospect is degenerate. The data suggests that the probability of losing may be relevant for loss aversion. (shrink)

Are risk preferences stable over time? To address this question we elicit risk preferences from the same pool of subjects at two different moments in time. To interpret the results, we use a Fechner stochastic choice model in which the revealed preference of individuals is governed by some underlying preference, together with a random error. We take cumulative prospect theory as the underlying preference model (Kahneman and Tversky, Econometrica 47:263–292, 1979; Tversky and Kahneman, Journal of Risk and Uncertainty (...) 5:297–323, 1992). We observe that the aggregate pattern of preferences is very similar in both sessions, and it matches the results reported in the literature. Most subjects are risk averse for gains, and risk seeking for losses. However, the subjects that jointly agree with the reflection effect of prospect theory are around 50%. The percentage of individuals that change their responses across sessions is quite high, 63%. Estimating the stochastic choice model we find that 72% of the subjects have an underlying preference which agrees with the reflection effect of prospect theory. The remaining 28% are mainly classified as risk averse for both gains and losses. The results reinforce the empirical validity of the reflection effect. Deviations from the reflection effect can be attributed to noise, as well as to the existence of a fraction of risk averse subjects. (shrink)

There are results which show that measure-theoretic deterministic models and stochastic models are observationally equivalent. Thus there is a choice between a deterministic and an indeterministic model and the question arises: Which model is preferable relative to evidence? If the evidence equally supports both models, there is underdetermination. This paper first distinguishes between different kinds of choice and clarifies the possible resulting types of underdetermination. Then a new answer is presented: the focus is on the choice (...) between a Newtonian deterministic model supported by indirect evidence from other Newtonian models which invoke similar additional assumptions about the physical systems and a stochastic model that is not supported by indirect evidence. It is argued that the deterministic model is preferable. The argument against underdetermination is then generalised to a broader class of cases. Finally, the paper criticises the extant philosophical answers in relation to the preferable model. Winnie’s (1998) argument for the deterministic model is shown to deliver the correct conclusion relative to observations which are possible in principle and where there are no limits, in principle, on observational accuracy (the type of choice Winnie was concerned with). However, in practice the argument fails. A further point made is that Hoefer’s (2008) argument for the deterministic model is untenable. (shrink)

Contemporary theories of deterrence place a strong emphasis on coherency between model and theory. Schelling’s contention of irrational threats for successful deterrence abandons the rationality assumption to explain how a player can deter, thereby departing from the standard game theoretic solution concepts. It is a misfit model in relation to a deterrence theory and, therefore, excluded. The article defends and remodels Schelling’s intuition by employing the level-k model. It is shown that an unsophisticated player that randomizes over its strategies brings (...) about an advantageous outcome. The model also shows that the belief that a player randomizes has the same deterrent effect, as an actual stochastic choice, like Schelling suggested. While this means Schelling’s idea can be saved, it is still problematic how we should view contributions of bounded rationality in relation to current deterrence theory. The article suggests that separating the purpose of a model in conjunction with allowing other scientific ideals than model-theory coherence permits a broader and philosophically sounder approach. (shrink)

The evolution of the human mind through natural selection mandates that our conscious experiences are causally potent in order to leave a tangible impact upon the surrounding physical world. Any attempt to construct a functional theory of the conscious mind within the framework of classical physics, however, inevitably leads to causally impotent conscious experiences in direct contradiction to evolution theory. Here, we derive several rigorous theorems that identify the origin of the latter impasse in the mathematical properties of ordinary differential (...) equations employed in combination with the alleged functional production of the mind by the brain. Then, we demonstrate that a mind--brain theory consistent with causally potent conscious experiences is provided by modern quantum physics, in which the unobservable conscious mind is reductively identified with the quantum state of the brain and the observable brain is constructed by the physical measurement of quantum brain observables. The resulting quantum stochastic dynamics obtained from sequential quantum measurements of the brain is governed by stochastic differential equations, which permit genuine free will exercised through sequential conscious choices of future courses of action. Thus, quantum reductionism provides a solid theoretical foundation for the causal potency of consciousness, free will and cultural transmission. (shrink)

Defenders of deontological constraints in normative ethics face a challenge: how should an agent decide what to do when she is uncertain whether some course of action would violate a constraint? The most common response to this challenge has been to defend a threshold principle on which it is subjectively permissible to act iff the agent's credence that her action would be constraint-violating is below some threshold t. But the threshold approach seems arbitrary and unmotivated: what would possibly determine where (...) the threshold should be set, and why should there be any precise threshold at all? Threshold views also seem to violate ought agglomeration, since a pair of actions each of which is below the threshold for acceptable moral risk can, in combination, exceed that threshold. In this paper, I argue that stochastic dominance reasoning can vindicate and lend rigor to the threshold approach: given characteristically deontological assumptions about the moral value of acts, it turns out that morally safe options will stochastically dominate morally risky alternatives when and only when the likelihood that the risky option violates a moral constraint is greater than some precisely definable threshold (in the simplest case, .5). I also show how, in combination with the observation that deontological moral evaluation is relativized to particular choice situations, this approach can overcome the agglomeration problem. This allows the deontologist to give a precise and well-motivated response to the problem of uncertainty. (shrink)

Empirical research often requires a method how to convert a deterministic economic theory into an econometric model. A popular method is to add a random error term on the utility scale. This method, however, ignores stochastic dominance. A modification of this method is proposed to account for stochastic dominance. The modified model compares favorably to other existing models in terms of goodness of fit to experimental data. The modified model can rationalize the preference reversal phenomenon. An intuitive axiomatic (...) characterization of the modified model is provided. Important microeconomic concept of risk aversion is well defined in the modified model. (shrink)

A decision maker bets on the outcomes of a sequence of coin-tossings. At the beginning of the game the decision maker can choose one of two coins to play the game. This initial choice is irreversible. The coins can be biased and the player is uncertain about the nature of one (or possibly both) coin(s). If the player is an expected-utility maximizer, her choice of the coin will depend on different elements: the nature of the game (namely, whether (...) she can observe the outcomes of the previous tosses before making her next decision), her utility function, the prior distribution on the bias of the coin. We will show that even a risk averter might optimally choose a riskier coin when learning is allowed. We will express most of our results in the language of stochastic orderings, allowing comparisons that are valid for large classes of utility functions. (shrink)

The paper outlines various concepts of rationality, their characteristics and consequences. In the first, most general part, the metaphysical, instrumental and discursive rationality is distinguished. The following part focuses on instrumental rationality and the rational choice theory and ordinal and cardinal utility, expected utility and game theory, respectively. All those concepts are summarised as being the most mathematically elegant and mostly decidable and helpful in the decision-making process. Giving primacy to individual preferences and withholding the judgment on their “objective” (...) value, they are also devoid of double standards. They are, however, strongly normative and weakly coincide with actual agents’ behaviour. Empirical findings on agents’ decision making seem to demonstrate their irrationality, unless we introduce into the analysis different concepts of rationality, namely based on costs efficient heuristics, inclusive fitness and ecological rationality. They are discussed respectively, and although they seem better to explain the set of humans’ seemingly irrational behaviour, they are likely week in predicting that behaviour. They are also losing their normative dimension and thus cease to be helpful in decision making. Applying the particular theory of rationality, either descriptively or normatively, seems to depend strongly on the environment, which can be characterised by its extension from a small to a large world. The more the small world’s features an environment reveals, the more effective is the application of the particular model of rationality. Beyond the small worlds, rule stochasticity, underspecification and misspecification and the only reasonable method are consecutive trials and errors, which eventually may reduce the large world to the small one. (shrink)

By employing binary committee choice problems, this paper investigates how varying or eliminating feedback about payoffs affects: subjects’ learning about the underlying relationship between their nominal voting weights and their expected payoffs in weighted voting games; the transfer of acquired learning from one committee choice problem to a similar but different problem. In the experiment, subjects choose to join one of two committees and obtain a payoff stochastically determined by a voting theory. We found that: subjects learned to (...) choose the committee that generates a higher expected payoff even without feedback about the payoffs they received; there was statistically significant evidence of “meaningful learning” only for the treatment with no payoff-related feedback. This finding calls for re-thinking existing models of learning to incorporate some type of introspection. (shrink)

According to the local risk-neutrality theorem an agent who has the opportunity to invest in an uncertain asset does not buy it or sell it short iff its expected value is equal to its price, independently of the agent's attitude towards risk. Contrary to that it is shown that, in the context of expected utility theory with differentiable vNM utility function, but without the assumption of stochastic constant returns to scale, nondegenerate intervals of no-trade prices may exist. With a (...) quasiconcave expected utility function they do if, and only if, the agent is risk averse of order one. (shrink)

The defence of The No Alternatives Argument in a recent paper by R. Dawid, S. Hartmann and J. Sprenger rests on the assumption that the number of acceptable alternatives to a scientific hypothesis is independent of the complexity of the scientific problem. This note proves a generalisation of the main theorem by Dawid, Hartmann and Sprenger, where this independence assumption is no longer necessary. Some of the other assumptions are also discussed, and the limitations of the no-alternatives argument are explored.