Probability Biases in Genetic Problem Solving: A Comparison of Undergraduates, Genetic Counseling Graduate Students, and Genetic Counselors

Heuristics are mental shortcuts that aid people in everyday problem-solving and decision-making. Although numerous studies have demonstrated their use in contexts ranging from consumers’ shopping decisions to experts’ estimations of experimental validity, virtually no published research has addressed heuristics use in problems involving genetic conditions and associated risk probabilities. The present research consists of two studies. In the first study, 220 undergraduates attempted to solve four genetic problems—two common heuristic problems modified to focus on genetic likelihood, and two created to study heuristics and probability rule application. Results revealed that the vast majority of undergraduates used heuristics and also demonstrated a complete misuse of probability rules. In the second study, 156 practicing genetic counselors and 89 genetic counseling students solved slightly modified versions of the genetic problems used in Study 1. Results indicated that a large percentage of both genetic counselors and students used heuristics, but the counselors demonstrated superior problem-solving performance compared to both the genetic counseling students and the undergraduates from Study 1. Research, training, and practice recommendations are presented.     

主观概率判断中次可加性的三因素实验研究

采用三因素完全随机实验探究主观概率判断是否满足次可加性规律,结果表明:(1)分解方式、分解数量和分解事例的典型性等三个因素对主观概率判断均有显著的影响。(2)次可加性不是一种普遍现象,主观概率判断中也会出现可加性和超可加性:把事件隐分为非典型事例时会出现超可加性,把事件隐分为典型或者典型加非典型性的事例时会出现可加性,而把事件显分时会一致出现次可加性。     

等级效标分数的概率神经网络预测方法研究

针对基于统计学的等级效标分数预测存在的问题,提出了运用概率神经网络进行等级效标分数预测的方法。在20种条件下进行了计算机模拟实验,包括测验分数为单变量和多变量,以及各种水平的白噪声干扰条件,结果表明在测验分数为多变量的情况下,或者在有白噪声干扰的条件下,运用概率神经网络方法可以比统计学方法更好地对等级效标分数进行预测。     

Dissimilarity cumulation theory and subjective metrics

We present a new mathematical notion, dissimilarity function, and based on it, a radical extension of Fechnerian Scaling, a theory dealing with the computation of subjective distances from pairwise discrimination probabilities. The new theory is applicable to all possible stimulus spaces subject to the following two assumptions: (A) that discrimination probabilities satisfy the Regular Minimality law and (B) that the canonical psychometric increments of the first and second kind are dissimilarity functions. A dissimilarity function Dab for pairs of stimuli in a canonical representation is defined by the following properties: (1) a≠b?Dab>0; (2) Daa=0; (3) If and , then ; and (4) for any sequence {a_nX_nb_n}_n∈N, where X_n is a chain of stimuli, Da_nX_nb_n→0?Da_nb_n→0. The expression DaXb refers to the dissimilarity value cumulated along successive links of the chain aXb. The subjective (Fechnerian) distance between a and b is defined as the infimum of DaXb+DbYa across all possible chains X and Y inserted between a and b.     

The origins of probabilistic inference in human infants

Reasoning under uncertainty is the bread and butter of everyday life. Many areas of psychology, from cognitive, developmental, social, to clinical, are interested in how individuals make inferences and decisions with incomplete information. The ability to reason under uncertainty necessarily involves probability computations, be they exact calculations or estimations. What are the developmental origins of probabilistic reasoning? Recent work has begun to examine whether infants and toddlers can compute probabilities; however, previous experiments have confounded quantity and probability—in most cases young human learners could have relied on simple comparisons of absolute quantities, as opposed to proportions, to succeed in these tasks. We present four experiments providing evidence that infants younger than 12 months show sensitivity to probabilities based on proportions. Furthermore, infants use this sensitivity to make predictions and fulfill their own desires, providing the first demonstration that even preverbal learners use probabilistic information to navigate the world. These results provide strong evidence for a rich quantitative and statistical reasoning system in infants.     

Ownership Status and the Representation of Assets of Uncertain Value: The Balloon Endowment Risk Task (BERT)

Owners tend to overvalue possessions relative to non‐owners: a phenomenon known as the endowment effect. In three experiments, using markets for goods of uncertain value, we investigated whether this can be partly attributed to misperceiving an asset's profitability or to uncertainty about a good's utility. To test our hypotheses, we devised the Balloon Endowment Risk Task, in which participants can sell or buy their right to participate in the Balloon Analogue Risk Task. Once purchased/retained, a virtual balloon is pumped to accrue money, which is lost if the balloon bursts. Participants first learn about the risky asset (balloon) by observing others playing the Balloon Analogue Risk Task before they enter the market. In Experiment 1, we replicated the endowment effect; yet, owners and non‐owners predicted pumping the same number of times and subsequently did so when given that opportunity. In Experiments 2 and 3, the level of uncertainty about the balloon's profitability was manipulated by modifying the number of bursts that participants viewed in the initial learning stage. When more diagnostic information was provided, making the average burst point easier to estimate and reducing value uncertainty and increasing confidence in valuation, the endowment effect diminished although mean estimates of the average burst point did not differ between owners and non‐owners. Thus, endowment effects were partly attributable to value uncertainty but could not be explained by owners and non‐owners having divergent perceptions of the asset's payoff distribution. Copyright © 2014 John Wiley & Sons, Ltd.     

Relational semantics for full linear logic

Relational semantics, given by Kripke frames, play an essential role in the study of modal and intuitionistic logic. In [4] it is shown that the theory of relational semantics is also available in the more general setting of substructural logic, at least in an algebraic guise. Building on these ideas, in [5] a type of frames is described which generalise Kripke frames and provide semantics for substructural logics in a purely relational form.In this paper we study full linear logic from an algebraic point of view. The main additional hurdle is the exponential. We analyse this operation algebraically and use canonical extensions to obtain relational semantics. Thus, we extend the work in [4], [5] and use their approach to obtain relational semantics for full linear logic. Hereby we illustrate the strength of using canonical extension to retrieve relational semantics: it allows a modular and uniform treatment of additional operations and axioms.Traditionally, so-called phase semantics are used as models for (provability in) linear logic [8]. These have the drawback that, contrary to our approach, they do not allow a modular treatment of additional axioms. However, the two approaches are related, as we will explain.     

The Equiprobability Bias from a Mathematical and Psychological Perspective

The equiprobability bias (EB) is a tendency to believe that every process in which randomness is involved corresponds to a fair distribution, with equal probabilities for any possible outcome. The EB is known to affect both children and adults, and to increase with probability education. Because it results in probability errors resistant to pedagogical interventions, it has been described as a deep misconception about randomness: the erroneous belief that randomness implies uniformity. In the present paper, we show that the EB is actually not the result of a conceptual error about the definition of randomness. On the contrary, the mathematical theory of randomness does imply uniformity. However, the EB is still a bias, because people tend to assume uniformity even in the case of events that are not random. The pervasiveness of the EB reveals a paradox: The combination of random processes is not necessarily random. The link between the EB and this paradox is discussed, and suggestions are made regarding educational design to overcome difficulties encountered by students as a consequence of the EB.     

Waiting When Both Certainty and Magnitude Are Increasing: Certainty Overshadows Magnitude

In everyday decision making, people often face decisions with outcomes that differ on multiple dimensions. The trade‐off in preferences between magnitude, temporal proximity, and probability of an outcome is a fundamental concern in the decision‐making literature. Yet, their joint effects on behavior in an experience‐based decision‐making task are understudied. Two experiments examined the relative influences of the magnitude and probability of an outcome when both were increasing over a 10‐second delay. A first‐person shooter video game was adapted for this purpose. Experiment 1 showed that participants waited longer to ensure a higher probability of the outcome than to ensure a greater magnitude when experienced separately and together. Experiment 2 provided a precise method of comparing their relative control on waiting by having each increase at different rates. Both experiments revealed a stronger influence of increasing probability than increasing magnitude. The results were more consistent with hyperbolic discounting of probability than with cumulative prospect theory's decision weight function. Copyright © 2014 John Wiley & Sons, Ltd.