Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov’s probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice–Bob EPR paradigm, non-contextuality means that the identity of Alice’s spin (i.e., the probability space on which it is defined as a random variable) is determined only by the axis $\alpha _{i}$ chosen by Alice, irrespective of Bob’s axis $\beta _{j}$ (and vice versa). Here, we study contextual KPT models, with two properties: (...) (1) Alice’s and Bob’s spins are identified as $A_{ij}$ and $B_{ij}$ , even though their distributions are determined by, respectively, $\alpha _{i}$ alone and $\beta _{j}$ alone, in accordance with the no-signaling requirement; and (2) the joint distributions of the spins $A_{ij},B_{ij}$ across all values of $\alpha _{i},\beta _{j}$ are constrained by fixing distributions of some subsets thereof. Of special interest among these subsets is the set of probabilistic connections, defined as the pairs $\left( A_{ij},A_{ij'}\right) $ and $\left( B_{ij},B_{i'j}\right) $ with $\alpha _{i}\not =\alpha _{i'}$ and $\beta _{j}\not =\beta _{j'}$ (the non-contextuality assumption is obtained as a special case of connections, with zero probabilities of $A_{ij}\not =A_{ij'}$ and $B_{ij}\not =B_{i'j}$ ). Thus, one can achieve a complete KPT characterization of the Bell-type inequalities, or Tsirelson’s inequalities, by specifying the distributions of probabilistic connections compatible with those and only those spin pairs $\left( A_{ij},B_{ij}\right) $ that are subject to these inequalities. We show, however, that quantum-mechanical (QM) constraints are special. No-forcing theorem says that if a set of probabilistic connections is not compatible with correlations violating QM, then it is compatible only with the classical–mechanical correlations. No-matching theorem says that there are no subsets of the spin variables $A_{ij},B_{ij}$ whose distributions can be fixed to be compatible with and only with QM-compliant correlations. (shrink)

Probability can be used to measure degree of belief in two ways: objectively and subjectively. The objective measure is a measure of the rational degree of belief in a proposition given a set of evidential propositions. The subjective measure is the measure of a particular subject’s dispositions to decide between options. In both measures, certainty is a degree of belief 1. I will show, however, that there can be cases where one belief is stronger than another yet both beliefs (...) are plausibly measurable as objectively and subjectively certain. In ordinary language, we can say that while both beliefs are certain, one belief is more certain than the other. I will then propose second, non probabilistic dimension of measurement, which tracks this variation in certainty in such cases where the probability is 1. A general principle of rationality is that one’s subjective degree of belief should match the rational degree of belief given the evidence available. In this paper I hope to show that it is also a rational principle that the maximum stake size at which one should remain certain should match the rational weight of certainty given the evidence available. Neither objective nor subjective measures of certainty conform to the axioms of probability, but instead are measured in utility. This has the consequence that, although it is often rational to be certain to some degree, there is no such thing as absolute certainty. (shrink)

We tested the hypothesis that choices determined by Type 1 processes are compelling because they are fluent, and for this reason they are less subject to analytic thinking than other answers. A total of 104 participants completed a modified version of Wason's selection task wherein they made decisions about one card at a time using a two-response paradigm. In this paradigm participants gave a fast, intuitive response, rated their feeling of rightness for that response, and were then allowed free time (...) to reconsider their answers. As we predicted, answers consistent with a matching heuristic were made more quickly than other answers, were given higher FOR ratings, and received less subsequent analysis as measured by rethinking time and the probability of changing answers. These data suggest that reasoning biases may be compelling because they are fluently generated; this is turn creates a strong FOR, which acts as a signal that further analysis is not necessary. (shrink)

How can probabilities make sense in a deterministic many-worlds theory? We address two facets of this problem: why should rational agents assign subjective probabilities to branching events, and why should branching events happen with relative frequencies matching their objective probabilities. To address the first question, we generalise the Deutsch–Wallace theorem to a wide class of many-world theories, and show that the subjective probabilities are given by a norm that depends on the dynamics of the theory: the 2-norm in the (...) usual Many-Worlds interpretation of quantum mechanics, and the 1-norm in a classical many-worlds theory known as Kent’s universe. To address the second question, we show that if one takes the objective probability of an event to be the proportion of worlds in which this event is realised, then in most worlds the relative frequencies will approximate well the objective probabilities. This suggests that the task of determining the objective probabilities in a many-worlds theory reduces to the task of determining how to assign a measure to the worlds. (shrink)

Evolution would favor organisms that can make recurrent decisions in accordance with classical probability (CP) theory, because such choices would be optimal in the long run. This is illustrated by the base-rate fallacy and probability matching, where nonhumans choose optimally but humans do not. Quantum probability (QP) theory may be able to account for these species differences in terms of orthogonal versus nonorthogonal representations.

Some propositions add more information to bodies of propositions than do others. We start with intuitive considerations on qualitative comparisons of information added . Central to these are considerations bearing on conjunctions and on negations. We find that we can discern two distinct, incompatible, notions of information added. From the comparative notions we pass to quantitative measurement of information added. In this we borrow heavily from the literature on quantitative representations of qualitative, comparative conditional probability. We look at two (...) ways to obtain a quantitative conception of information added. One, the most direct, mirrors Bernard Koopman’s construction of conditional probability: by making a strong structural assumption, it leads to a measure that is, transparently, some function of a function P which is, formally, an assignment of conditional probability (in fact, a Popper function). P reverses the information added order and mislocates the natural zero of the scale so some transformation of this scale is needed but the derivation of P falls out so readily that no particular transformation suggests itself. The Cox–Good–Aczél method assumes the existence of a quantitative measure matching the qualitative relation, and builds on the structural constraints to obtain a measure of information that can be rescaled as, formally, an assignment of conditional probability. A classical result of Cantor’s, subsequently strengthened by Debreu, goes some way towards justifying the assumption of the existence of a quantitative scale. What the two approaches give us is a pointer towards a novel interpretation of probability as a rescaling of a measure of information added. (shrink)

ABSTRACT For changing opinion, represented by an assignment of probabilities to propositions, the criterion proposed is motivated by the requirement that the assignment should have, and maintain, the possibility of matching in some appropriate sense statistical proportions in a population. This ‘tracking’ criterion implies limitations on policies for updating in response to a wide range of types of new input. Satisfying the criterion is shown equivalent to the principle that the prior must be a convex combination of the possible (...) posteriors. Furthermore, this is equivalent to the requirement that prior expected values must fall inside the range spanned by possible posterior expected values. The tracking criterion is liberal; it allows for, but does not require, a policy such as Bayesian conditionalization, and can be offered as a general constraint on policies for managing opinion over time. Examples are given of non-Bayesian policies, both ones that satisfy and ones that violate the criterion. _1_ Introduction _2_ Alternative Updating Policies _3_ Modelling the Situation for Normal Updating _4_ Tracking: A Criterion for Updating Policies _5_ Tracking: Precise Formulation and Relation to Convexity _6_ The Spanning Criterion _7_ Non-Bayesian Policies that Satisfy the Spanning and Tracking Criteria _8_ Policies that Violate the Spanning and Tracking Criteria Appendix Appendix. (shrink)

For changing opinion, represented by an assignment of probabilities to propositions, the criterion proposed is motivated by the requirement that the assignment should have, and maintain, the possibility of matching in some appropriate sense statistical proportions in a population. This ‘tracking’ criterion implies limitations on policies for updating in response to a wide range of types of new input. Satisfying the criterion is shown equivalent to the principle that the prior must be a convex combination of the possible posteriors. (...) Furthermore, this is equivalent to the requirement that prior expected values must fall inside the range spanned by possible posterior expected values. The tracking criterion is liberal; it allows for, but does not require, a policy such as Bayesian conditionalization, and can be offered as a general constraint on policies for managing opinion over time. Examples are given of non-Bayesian policies, both ones that satisfy and ones that violate the criterion. 1 Introduction2 Alternative Updating Policies3 Modelling the Situation for Normal Updating4 Tracking: A Criterion for Updating Policies5 Tracking: Precise Formulation and Relation to Convexity6 The Spanning Criterion7 Non-Bayesian Policies that Satisfy the Spanning and Tracking Criteria8 Policies that Violate the Spanning and Tracking Criteria AppendixAppendix. (shrink)

Calibration inductive logics are based on accepting estimates of relative frequencies, which are used to generate imprecise probabilities. In turn, these imprecise probabilities are intended to guide beliefs and decisions — a process called “calibration”. Two prominent examples are Henry E. Kyburg's system of Evidential Probability and Jon Williamson's version of Objective Bayesianism. There are many unexplored questions about these logics. How well do they perform in the short-run? Under what circumstances do they do better or worse? What is (...) their performance relative to traditional Bayesianism? -/- In this article, we develop an agent-based model of a classic binomial decision problem, including players based on variations of Evidential Probability and Objective Bayesianism. We compare the performances of these players, including against a benchmark player who uses standard Bayesian inductive logic. We find that the calibrated players can match the performance of the Bayesian player, but only with particular acceptance thresholds and decision rules. Among other points, our discussion raises some challenges for characterising “cautious” reasoning using imprecise probabilities. Thus, we demonstrate a new way of systematically comparing imprecise probability systems, and we conclude that calibration inductive logics are surprisingly promising for making decisions. (shrink)

Nebel argues for the Repugnant Conclusion via the “Intrapersonal Repugnant Conclusion,” on which certainty of a mediocre life is better for individuals than a sufficiently small chance of an excellent life. In this article, I deny that acceptance of the Intrapersonal Repugnant Conclusion leads us to the Repugnant Conclusion. I point out that on many views which avoid the Repugnant Conclusion we should discount very small probabilities down to zero. If we do, then Nebel’s crucial premise of Ex Ante Pareto (...) fails, because discounting at the individual level can fail to match up with discounting at the population level. (shrink)

The main difficulty facing no-collapse theories of quantum mechanics in the Everettian tradition concerns the role of probability within a theory in which every possible outcome of a measurement actually occurs. The problem is two-fold: First, what do probability claims mean within such a theory? Second, what ensures that the probabilities attached to measurement outcomes match those of standard quantum mechanics? Deutsch has recently proposed a decision-theoretic solution to the second problem, according to which agents are rationally required (...) to weight the outcomes of measurements according to the standard quantum-mechanical probability measure. I show that this argument admits counterexamples, and hence fails to establish the standard probability weighting as a rational requirement. (shrink)

The ability to recover from official match-play across a single and multiple matches is often considered a key factor in subsequent performance for modern professional basketball. The aims of this study were to: explore the differences in match performances between different match congestion cycles ; and identify the key performance indicators discriminating between winning and losing during different match congestion cycles. The current study indicated that scoring close to or very far away was significantly greater for winning matches separated by (...) 1- and 2-days of rest compared to consecutive matches. Additionally, shooting efficiency, and attaining Defensive Rebounds and Steals, were significant offensive and defensive KPIs that differentiated winning and losing teams. Similarly, opponent quality and match pace were important situational variables that affected match outcome during different match congestion cycles. While match location had an impact on winning following 1- and 2-days of rest, it had no impact for back-to-back matches. The current results will support coaches' offensive, defensive and recovery strategies during various match congestion cycles for a greater probability of winning NBA matches. (shrink)

Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for first-order sentences. Given first-order sentences φ and θ, we consider the structures with domain {1,..., N} that satisfy θ, and compute the fraction of them in which φ is true. We then consider what happens to this fraction as N gets large. This extends the work on 0-1 laws that considers the limiting probability of first-order sentences, by considering asymptotic (...) conditional probabilities. As shown by Liogon'kii [24], if there is a non-unary predicate symbol in the vocabulary, asymptotic conditional probabilities do not always exist. We extend this result to show that asymptotic conditional probabilities do not always exist for any reasonable notion of limit. Liogon'kii also showed that the problem of deciding whether the limit exists is undecidable. We analyze the complexity of three problems with respect to this limit: deciding whether it is well-defined, whether it exists, and whether it lies in some nontrivial interval. Matching upper and lower bounds are given for all three problems, showing them to be highly undecidable. (shrink)

In this paper, we use an experimental design to compare the performance of elicitation rules for subjective beliefs. Contrary to previous works in which elicited beliefs are compared to an objective benchmark, we consider a purely subjective belief framework. The performance of different elicitation rules is assessed according to the accuracy of stated beliefs in predicting success. We measure this accuracy using two main factors: calibration and discrimination. For each of them, we propose two statistical indexes and we compare the (...) rules’ performances for each measurement. The matching probability method provides more accurate beliefs in terms of discrimination, while the quadratic scoring rule reduces overconfidence and the free rule, a simple rule with no incentives, which succeeds in eliciting accurate beliefs. Nevertheless, the matching probability appears to be the best mechanism for eliciting beliefs due to its performances in terms of calibration and discrimination, but also its ability to elicit consistent beliefs across measures and across tasks, as well as its empirical and theoretical properties. (shrink)

Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of (...) dynamic-probabilistic logics as well. Finally, we discuss how our basic update rule can be parameterized for different update policies, or learning methods. (shrink)

Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of (...) dynamic-probabilistic logics as well. Finally, we discuss how our basic update rule can be parameterized for different update policies, or learning methods. (shrink)

The preferential attachment mechanism that forms scale-free network cannot display assortativity, i.e., the degree of one node is positively correlated with that of their neighbors in the network. Given the attributes of network nodes, a cultural trait-matching mechanism is further introduced in this paper. Both theoretical analysis and simulation results indicate that the higher selection probability of such mechanism, the more obvious the assortativity is shown in networks. Further, the degree of nodes presents a positive logarithm correlation with (...) that of adjacent ones. Finally, this study discusses the theoretical and practical significances of the introduction of such a cultural trait-matching mechanism. (shrink)

In the standard and traditional view, the concept of conditional probability is defined with what is known as the ratio formula: the probability of B given A is the ratio between the probability of A and B and the probability of A. It is well known that this definition does not match the conceptual and mathematical expectations that we have from conditional probability, especially for the probability values at the limits. Thus, as pointed out (...) by several philosophers such as Popper and Hájek, it is fair to conclude that we have yet to have a satisfactory definition for the concept of conditional probability. E.J. Lowe, in a debate with Dorothy Edgington, proposed two different definitions of conditional probability, and unfortunately his definitions have gone unnoticed in the literature. In this paper, my main aim is to renew interest in Lowe’s definitions. I achieve this aim by showing that E.J. Lowe’s definitions have great potential in providing us with a satisfactory definition of conditional probability.Standard Olasılık kuramında bir olayın bir diğer olaya koşullu olasılığı rasyo formülü olarak bilinen bir formül ile tanımlanmaktadır. Bu formüle göre B olayının A olayına koşullu olasılığı olayının olasığının sadece A olayının olasılığına bölünmesi ile bulunan değerdir. Bu standard tanımın özellikle limitlerdeki olasılık değerleri için kavramsal ve matematiksel beklentilerimizi karşılamadığı bilinen bir durumdur. Aralarında Popper ve Hájek gibi isimlerin de bulunduğu birçok felsefecinin de belirttiği gibi, bu durumdan elimizde tatmin edici bir koşullu olasılık tanımı olmadığını çıkarsamak yanlış olmayacaktır. E.J. Lowe, Dorothy Edgington ile girdiği bir tartışma bağlamında koşullu olasılığın iki alternatif tanımını önermiştir. Ne yazık ki, literatürde bu tanımlara gereken önem verilmemiştir. Literatürdeki bu eksikliği gidermeyi hedefleyen bu makalenin genel amacı, Lowe’ün önerilerinin tatmin edici bir koşullu olasılık tanımı sunma potansiyeline sahip olduğunu göstermektir. (shrink)

Research on preference reversals has demonstrated a disproportionate influence of outcome probability on choices between monetary gambles. The aim was to investigate the hypothesis that this is a prominence effect originally demonstrated for riskless choice. Another aim was to test the structure compatibility hypothesis as an explanation of the effect. The hypothesis implies that probability should be the prominent attribute when compared with value attributes both in a choice and a preference rating procedure. In Experiment 1, two groups (...) of undergraduates were presented with medical treatments described by two value attributes (effectiveness and pain-relief). All participants performed both a matching task and made preference ratings. In the latter task, outcome probabilities were added to the descriptions of the medical treatments for one of the groups. In line with the hypothesis, this reduced the prominence effect on the preference ratings observed for effectiveness. In Experiment 2, a matching task was used to demonstrate that probability was considered more important by a group of participating undergraduates than the value attributes. Furthermore, in both choices and preference ratings the expected prominence effect was found for probability. (shrink)

In humans, conscious perception and cognition depends upon the thalamocortical complex, which supports perception, explicit cognition, memory, language, planning, and strategic control. When parts of the T-C system are damaged or stimulated, corresponding effects are found on conscious contents and state, as assessed by reliable reports. In contrast, large regions like cerebellum and basal ganglia can be damaged without affecting conscious cognition directly. Functional brain recordings also show robust activity differences in cortex between experimentally matched conscious and unconscious events. This (...) basic anatomy and physiology is highly conserved in mammals and perhaps ancestral reptiles. While language is absent in other species, homologies in perception, memory, and motor cortex suggest that consciousness of one kind or another may be biologically fundamental and phylogenetically ancient. In humans we infer subjective experiences from behavioral and brain evidence. This evidence is quite similar in other mammals and perhaps some non-mammalian species. On the weight of the biological evidence, therefore, subjectivity may be conserved in species with human-like brains and behavior. (shrink)

Perceptual tasks such as object matching, mammogram interpretation, mental rotation, and satellite imagery change detection often require the assignment of correspondences to fuse information across views. We apply techniques developed for machine translation to the gaze data recorded from a complex perceptual matching task modeled after fingerprint examinations. The gaze data provide temporal sequences that the machine translation algorithm uses to estimate the subjects' assumptions of corresponding regions. Our results show that experts and novices have similar surface behavior, (...) such as the number of fixations made or the duration of fixations. However, the approach applied to data from experts is able to identify more corresponding areas between two prints. The fixations that are associated with clusters that map with high probability to corresponding locations on the other print are likely to have greater utility in a visual matching task. These techniques address a fundamental problem in eye tracking research with perceptual matching tasks: Given that the eyes always point somewhere, which fixations are the most informative and therefore are likely to be relevant for the comparison task? (shrink)

The aim of this study was to explore the effect of scoring first on match outcomes in the Chinese Football Super League. A total of 1,116 matches in which at least one goal was scored from the 2014 to 2018 seasons were collected. Match outcomes, absolute goal differences, the minute of the first goal, match locations, and teams’ budgets were analyzed. A team’s budget was measured in terms of a team’s value at the beginning of the season, and teams were (...) clustered into two groups. A descriptive analysis was conducted, and two generalized linear models were applied. The results showed a favorable outcome for the team that scored first both in match outcome and goal difference. Regarding the teams that scored first, 66.31% won their matches, 20.70% achieved a draw, and 12.99% lost. Specifically, home teams were more likely to win and less likely to lose or draw than away teams. Home teams also had a higher likelihood of obtaining a larger goal difference. Higher budget teams were more likely to win and less likely to lose or draw than low-budget teams. Additionally, for each minute, the team scores closer to the end of the match, and the average probability of winning increased by 0.0028. These findings can guide the strategies of coaches in different match scenarios according to the match location and the opponent’s quality. (shrink)

Quantum probability (QP) theory can be seen as a type of vector symbolic architecture (VSA): mental states are vectors storing structured information and manipulated using algebraic operations. Furthermore, the operations needed by QP match those in other VSAs. This allows existing biologically realistic neural models to be adapted to provide a mechanistic explanation of the cognitive phenomena described in the target article by Pothos & Busemeyer (P&B).

The main objective of this study was to analyze the influence of tactical and situational variables on offensive sequences during elite European handball matches. A sample of 55 games and 5.857 offensive sequences from the European Handball Federation Champions League, the selected teams were classified as the top eight teams in the league, were analyzed using X2 and logistic regression analyses. Results indicated that positional attacks [odds ratio = 0.34; 95% CI: 0.28–0.42; p < 0.001] and fast attacks decreased the (...) probability of success for an offensive sequence by 66% and 54% when compared with counterattacks. Offensive sequences that start in the attacking zone seem to be less effective than those that start from a situation of “ball in center.” Additionally, offensive sequences that finished in the defensive zone of the observed team were 3.19 times more effective than those that ended before the 9 m zone. We concluded that compared with offensive sequences where the shot is performed from the 9 m zone, the chances of an offensive sequence ending successfully are 3.65, 3.60, and 2.21 times higher, for offensive sequences where the shot is performed from 9 m, 6 m, and the defensive zone, respectively. On the other hand, many variables seem to impact the performance of handball teams. Nevertheless, a significant challenge remains, and more research needs to be conducted to analyze the obstacles that teams need to overcome while attacking in the most effective way possible. (shrink)

The history of the mathematical probability includes two phases: 1) From Pascal and Fermat to Laplace, the theory gained in application fields; 2) In the first half of the 20th Century, two competing axiomatic systems were respectively proposed by von Mises in 1919 and Kolmogorov in 1933. This paper places this historical sketch in the context of the philosophical complexity of the probability concept and explains the resounding success of Kolmogorov’s theory through its ability to avoid direct interpretation. (...) Indeed, unlike experimental sciences, and despite its numerous applications, probability theory cannot be tested per se. Rather it relates to practical matters by means of transition hypotheses or bridging principles that match the structure of practical problems with abstract theory. In this respect probability theory has a very special status among scientific disciplines. (shrink)

Empirical work has lately confirmed what many philosophers have taken to be true: people are ‘biased toward the future’. All else being equal, we usually prefer to have positive experiences in the future, and negative experiences in the past. According to one hypothesis, the temporal metaphysics hypothesis, future-bias is explained either by our beliefs about temporal metaphysics—the temporal belief hypothesis—or alternatively by our temporal phenomenology—the temporal phenomenology hypothesis. We empirically investigate a particular version of the temporal belief hypothesis according to (...) which future-bias is explained by the belief that time robustly passes. Our results do not match the apparent predictions of this hypothesis, and so provide evidence against it. But we also find that people give more future-biased responses when asked to simulate a belief in robust passage. We take this to suggest that the phenomenology that attends simulation of that belief may be partially responsible for future-bias, and we examine the implications of these results for debates about the rationality of future-bias. (shrink)

Occasionally, people are called upon to estimate probabilities after an event has occurred. In hindsight, was this an outcome we could have expected? Could things easily have turned out differently? One strategy for performing post hoc probability judgements would be to mentally turn the clock back and reconstruct one's expectations before the event. But if asked about the probability of an alternative, counterfactual outcome, a simpler strategy is available, based on this outcome's perceived closeness to what actually happened. (...) The article presents five studies exploring the relationship between counterfactual closeness and counterfactual probability. The first study indicates that post hoc probabilities typically refer to the counterfactual rather than the factual outcome. Studies 2-5 show that physical, temporal, or conceptual proximity play a decisive role for post hoc probability assessments of counterfactual events. When margins are narrow, the probabilities of, for instance, winning a match (when losing), and of losing (when actually winning) may even be rated higher than the corresponding probabilities of what really happened. Closeness is also more often referred to, and rated to be a better reason for believing there is a ''good chance" of the counterfactual rather than of the factual result occurring. Finally, the closeness of the alternative outcome in success and failure stories is shown to be significantly correlated to its rated probability. (shrink)

In Pelota matches, bets are made between viewers through a middleman who receives 16% of the finally paid amount. In this paper, a description of the way bets are made and an explanation of the existence of those markets are presented. Taking betting markets as a simplified analogy for financial markets we have searched for the explanation in a world where both sides of the market are not different in believes and preferences. We find that for a bet to exist (...) when bettors are rank dependent expected utility maximizers, they have to be optimistic. Taking observations from actually made bets a preliminary analysis about the biases of those markets is presented. (shrink)

We use probability-matching variations on Ellsberg’s single-urn experiment to assess three questions: (1) How sensitive are ambiguity attitudes to changes from a gain to a loss frame? (2) How sensitive are ambiguity attitudes to making ambiguity easier to recognize? (3) What is the relation between subjects’ consistency of choice and the ambiguity attitudes their choices display? Contrary to most other studies, we find that a switch from a gain to a loss frame does not lead to a switch (...) from ambiguity aversion to ambiguity neutrality and/or ambiguity seeking. We also find that making ambiguity easier to recognize has little effect. Finally, we find that while ambiguity aversion does not depend on consistency, other attitudes do: consistent choosers are much more likely to be ambiguity neutral, while ambiguity seeking is much more frequent among highly inconsistent choosers. (shrink)

According to the concept of direct parameter specification, nonconsciously registered information can be processed to the extent that it matches currently active intentions of a person. This prediction was tested and confirmed in the current study. Masked visual information provided by peripheral cues led to reaction time effects only if the information specified one of the required responses . Information delivered by the same masked cues that did not match the intentions was not used. However, the same information influenced RT (...) if it was provided by visible cues . The results suggest that the processing of nonconsciously registered information is flexible because it is susceptible to the changing intentions of a person. Yet, these processes are apparently restricted, as nonconsciously registered information cannot be used as easily for purposes not corresponding to the currently active intentions as better visible information. (shrink)

In many learning or inference tasks human behavior approximates that of a Bayesian ideal observer, suggesting that, at some level, cognition can be described as Bayesian inference. However, a number of findings have highlighted an intriguing mismatch between human behavior and standard assumptions about optimality: People often appear to make decisions based on just one or a few samples from the appropriate posterior probability distribution, rather than using the full distribution. Although sampling-based approximations are a common way to implement (...) Bayesian inference, the very limited numbers of samples often used by humans seem insufficient to approximate the required probability distributions very accurately. Here, we consider this discrepancy in the broader framework of statistical decision theory, and ask: If people are making decisions based on samples—but as samples are costly—how many samples should people use to optimize their total expected or worst-case reward over a large number of decisions? We find that under reasonable assumptions about the time costs of sampling, making many quick but locally suboptimal decisions based on very few samples may be the globally optimal strategy over long periods. These results help to reconcile a large body of work showing sampling-based or probability matching behavior with the hypothesis that human cognition can be understood in Bayesian terms, and they suggest promising future directions for studies of resource-constrained cognition. (shrink)

Bayesian probability has recently been proposed as a normative theory of argumentation. In this article, we provide a Bayesian formalisation of the ad Hitlerum argument, as a special case of the ad hominem argument. Across three experiments, we demonstrate that people's evaluation of the argument is sensitive to probabilistic factors deemed relevant on a Bayesian formalisation. Moreover, we provide the first parameter-free quantitative evidence in favour of the Bayesian approach to argumentation. Quantitative Bayesian prescriptions were derived from participants' stated (...) subjective probabilities (Experiments 1 and 2), as well as from frequency information explicitly provided in the experiment (Experiment 3). Participants' stated evaluations of the convincingness of the argument were well matched to these prescriptions. (shrink)

This paper describes a simple, causally deterministic model of quantum measurement based on an amplitude threshold detection scheme. Surprisingly, it is found to reproduce many phenomena normally thought to be uniquely quantum in nature. To model an \(N\) -dimensional pure state, the model uses \(N\) complex random variables given by a scaled version of the wave vector with additive complex noise. Measurements are defined by threshold crossings of the individual components, conditioned on single-component threshold crossings. The resulting detection probabilities match (...) or approximate those predicted by quantum mechanics according to the Born rule. Nevertheless, quantum phenomena such as entanglement, contextuality, and violations of Bell’s inequality under local measurements are all shown to be exhibited by the model, thereby demonstrating that such phenomena are not without classical analogs. (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)

Bayesian models of human learning are becoming increasingly popular in cognitive science. We argue that their purported confirmation largely relies on a methodology that depends on premises that are inconsistent with the claim that people are Bayesian about learning and inference. Bayesian models in cognitive science derive their appeal from their normative claim that the modeled inference is in some sense rational. Standard accounts of the rationality of Bayesian inference imply predictions that an agent selects the option that maximizes the (...) posterior expected utility. Experimental confirmation of the models, however, has been claimed because of groups of agents that probability match the posterior. Probability matching only constitutes support for the Bayesian claim if additional unobvious and untested (but testable) assumptions are invoked. The alternative strategy of weakening the underlying notion of rationality no longer distinguishes the Bayesian model uniquely. A new account of rationality—either for inference or for decision-making—is required to successfully confirm Bayesian models in cognitive science. (shrink)

This study examined students' reasoning about simple repeated choices. Each choice involved ''betting'' on two events, differing in probability. We asked subjects to generate or evaluate alternative strategies such as betting on the most likely event on every trial, betting on it on almost every trial, or employing a ''probability matching'' strategy. Almost half of the college students did not generate or rank strategies according to their expected value, but few subjects preferred a strategy of strict (...) class='Hi'>probability matching. High-school students showed greater deviations from expected value than college students. Similar misunderstandings were observed in a choice task involving real (not hypothetical) repeated trials. Large gender differences in prediction strategies and in related computational skills were observed. Subjects who understand the optimal strategy usually do so in terms of independence of successive trials rather than calculation. Some subjects understand the concept of independence but fail to bring it to bear, thinking it can be overridden by intuition or local balancing (representativeness). (shrink)

Memory exhibits episodic superposition, an analog of the quantum superposition of physical states: Before a cue for a presented or unpresented item is administered on a memory test, the item has the simultaneous potential to occupy all members of a mutually exclusive set of episodic states, though it occupies only one of those states after the cue is administered. This phenomenon can be modeled with a nonadditive probability model called overdistribution (OD), which implements fuzzy-trace theory's distinction between verbatim and (...) gist representations. We show that it can also be modeled based on quantum probability theory. A quantum episodic memory (QEM) model is developed, which is derived from quantum probability theory but also implements the process conceptions of global matching memory models. OD and QEM have different strengths, and the current challenge is to identify contrasting empirical predictions that can be used to pit them against each other. (shrink)

This paper models knowledge in cases where an agent has multiple experiences over time. Using this model, we introduce a series of observations that undermine the pretheoretic idea that the evidential significance of experience depends on the extent to which that experience matches the world. On the basis of these observations, we model knowledge in terms of what is likely given the agent’s experience. An agent knows p when p is implied by her epistemic possibilities. A world is epistemically possible (...) when its probability given the agent’s experiences is not significantly lower than the probability of the actual world given that experience. (shrink)

The matching law accounts for both addictive behavior and the usefulness of a person's evaluating choices in overall categories. To explain why overall bookkeeping, once learned, does not easily win out over local bookkeeping, another implication of matching is needed: intertemporal bargaining. The role of melioration, though probably important for new addiction is separate.