“Memory of Water” Without Water: Modeling of Benveniste’s Experiments with a Personalist Interpretation of Probability

Benveniste’s experiments were at the origin of a scientific controversy that has never been satisfactorily resolved. Hypotheses based on modifications of water structure that were proposed to explain these experiments (“memory of water”) were generally considered as quite improbable. In the present paper, we show that Benveniste’s experiments violated the law of total probability, one of the pillars of classical probability theory. Although this could suggest that quantum logic was at work, the decoherence process is however at first sight an obstacle to describe this macroscopic experimental situation. Based on the principles of a personalist view of probability (quantum Bayesianism or QBism), a modeling could nevertheless be built that fitted the outcomes reported in Benveniste’s experiments. Indeed, in QBism, there is no split between microscopic and macroscopic, but between the world where an agent lives and his internal experience of that world. The outcome of an experiment is thus displaced from the object to its perception by an agent. By taking into account both the personalist view of probability and measurement fluctuations, all characteristics of Benveniste’s experiments could be described in a simple modeling: change of the biological system from resting state to “activated” state, concordance of “expected” and observed outcomes and apparent “jumping” of “biological activities” from sample to sample. No hypothesis on change of water structure was necessary. In conclusion, a modeling of Benveniste’s experiments based on a personalist view of probability offers for the first time a logical framework for these experiments that have remained controversial and paradoxical till date.     

A Categorical Approach to Probability Theory

First, we discuss basic probability notions from the viewpoint of category theory. Our approach is based on the following four “sine quibus non” conditions: 1. (elementary) category theory is efficient (and suffices); 2. random variables, observables, probability measures, and states are morphisms; 3. classical probability theory and fuzzy probability theory in the sense of S. Gudder and S. Bugajski are special cases of a more general model; 4. a good model allows natural modifications. Second, we show that the category ID of D-posets of fuzzy sets and sequentially continuous D-homomorphisms allows to characterize the passage from classical to fuzzy events as the minimal generalization having nontrivial quantum character: a degenerated state can be transported to a nondegenerated one. Third, we describe a general model of probability theory based on the category ID so that the classical and fuzzy probability theories become special cases and the model allows natural modifications. Finally, we present a modification in which the closed unit interval [0,1] as the domain of traditional states is replaced by a suitable simplex.     

Does probability weighting matter in probability elicitation?

One of the most widely used methods for probability encoding in decision analysis uses binary comparisons (choices) between two lotteries: one that depends on the values of the random variable of interest and another that is contingent on an external reference chance device (typically a probability wheel). This note investigates the degree to which differences in probability weighting functions between the two types of events could affect the practice of subjective probability encoding. We develop a general methodology to investigate this question and illustrate it with two popular probability weighting functions over the range of parameters reported in the literature. We use this methodology to (a) alert decision analysts and researchers to the possibility of reversals, (b) identify the circumstances under which overt preferences for one lottery over the other are not affected by the weighting function, (c) document the magnitude of the differences between choices based on probabilities and their corresponding weighting functions, and (d) offer practical recommendations for probability elicitation.     

On appropriate procedures for combining probability distributions within the same family

This article considers procedures for combining individual probability distributions that belong to some “family” into a “group” probability distribution that belongs to the same family. The procedures considered are Vincentizing, in which quantiles are averaged across distributions; generalized Vincentizing, in which the quantiles are transformed before averaging; and pooling based on the distribution function or the probability density function. Some of these results are applied to models of reaction time in psychological experiments.     

Iterative Probability Kinematics

Following the pioneer work of Bruno De Finetti [12], conditional probability spaces (allowing for conditioning with events of measure zero) have been studied since (at least) the 1950's. Perhaps the most salient axiomatizations are Karl Popper's in [31], and Alfred Renyi's in [33]. Nonstandard probability spaces [34] are a well know alternative to this approach. Vann McGee proposed in [30] a result relating both approaches by showing that the standard values of infinitesimal probability functions are representable as Popper functions, and that every Popper function is representable in terms of the standard real values of some infinitesimal measure.Our main goal in this article is to study the constraints on (qualitative and probabilistic) change imposed by an extended version of McGee's result. We focus on an extension capable of allowing for iterated changes of view. Such extension, we argue, seems to be needed in almost all considered applications. Since most of the available axiomatizations stipulate (definitionally) important constraints on iterated change, we propose a non-question-begging framework, Iterative Probability Systems (IPS) and we show that every Popper function can be regarded as a Bayesian IPS. A generalized version of McGee's result is then proved and several of its consequences considered. In particular we note that our proof requires the imposition of Cumulativity, i.e. the principle that a proposition that is accepted at any stage of an iterative process of acceptance will continue to be accepted at any later stage. The plausibility and range of applicability of Cumulativity is then studied. In particular we appeal to a method for defining belief from conditional probability (first proposed in [42] and then slightly modified in [6] and [3]) in order to characterize the notion of qualitative change induced by Cumulative models of probability kinematics. The resulting cumulative notion is then compared with existing axiomatizations of belief change and probabilistic supposition. We also consider applications in the probabilistic accounts of conditionals [1] and [30].     

Testing Credit and Blame Attributions as Explanation for Choices under Ambiguity

People make decisions every day based on their estimates of the chances of various events occurring. By their very nature, these subjective estimates are less certain, and thus more ambiguous, than objective probabilities such as those associated with roulette wheels or lotteries. In two experimental studies, we investigate choices between bets on the decision maker′s knowledge versus bets on a lottery with the same chance of winning. In Study 1, we partially replicate the Heath and Tversky (1991) finding that subjects have an increasing preference for betting on their own knowledge over the matched-chance lottery as probability increases. We also discover a significant minority of subjects who exhibit the opposite pattern and prefer the lottery as probability increases. In addition, we explicitly test the subjects′ attributions about the credit they would feel for a win and the blame they would feel for a loss, and these attributions do provide some explanation for their choice behavior. In Study 2, we manipulate knowledge and accountability, in an attempt to heighten the attributions of credit and blame, and we replicate the findings.     

归类不确定情景下特征推理的综合条件概率模型

用大学生被试,通过三个实验探讨在集中呈现类别成员样本信息的归类不确定情景下的特征推理。实验结果表明,单纯的归类确定性程度和靶类别靶特征的代表性并不直接影响被试的特征推理,而是预测特征相对于目标特征的综合条件概率直接影响被试的特征推理;特征推理不是基于类别中介的间接推理,而是基于特征关联综合条件概率的直接推理。实验结果支持作者提出的预测特征综合条件概率模型。     

旧证据问题：一种动态的消解方案

旧证据问题是指贝叶斯确证理论在讨论旧证据确证新理论（假说）的问题上将出现不合理的结果,它的消解是贝叶斯确证理论辩护的一个非常重要的环节。本文倡导一种基于Levi理论的动态方案来消解这一问题。在这种方案下,知识汇集的动态性使得旧证据在新理论引入前后的置信概率可能是不相同的,在此基础上我们证明,经新理论扩充后而得到的知识汇集无论是一致扩充还是不一致扩充,均存在一个旧证据E,它对该新理论具有确证作用。     

Inference to the best explanation: does it track truth?

In the form of inference known as inference to the best explanation there are various ways to characterise what is meant by the best explanation. This paper considers a number of such characterisations including several based on confirmation measures and several based on coherence measures. The goal is to find a measure which adequately captures what is meant by ‘best’ and which also yields the truth with a high degree of probability. Computer simulations are used to show that the overlap coherence measure achieves this goal, enabling the true explanation to be identified almost as often as an approach which simply selects the most probable explanation. Further advantages to this approach are also considered in the case where there is uncertainty in the prior probability distribution.     

Plea bargaining recommendations by criminal defense attorneys: evidence strength, potential sentence, and defendant preference

Although most criminal cases are disposed of through the process of plea bargaining, little research has focused on this process, and that research has focused on two variables: probability of conviction and potential sentence. This study examined the plea bargaining process from the perspective of the criminal defense attorney and expands prior research by including a third variable: defendant preference regarding plea. Attorney participants (N = 186) responded to a survey containing a vignette presented in a 2 x 2 x 2 between-subjects design, in which there was systematic manipulation of the following three variables in the context of criminal litigation: likelihood of conviction based on the strength of evidence, defendant preference regarding plea, and potential sentence if convicted. All of these variables were considered important to criminal defense attorneys, and how these variables significantly interacted with each other is explained. We discuss these findings in light of past research and theory that suggested attorneys make plea recommendations according only to probability of conviction and potential sentence, and we discuss implications and directions for future research.     

Mathematical logic in the soviet union, 1917–1980

This essay describes a variety of contributions which relate to the connection of probability with logic. Some are grand attempts at providing a logical foundation for probability and inductive inference. Others are concerned with probabilistic inference or, more generally, with the transmittance of probability through the structure (logical syntax) of language. In this latter context probability is considered as a semantic notion playing the same role as does truth value in conventional logic. At the conclusion of the essay two fully elaborated semantically based constructions of probability logic are presented.     

The reference class problem is your problem too

The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference class problem. Other versions of these interpretations apparently evade the problem. But I contend that they are all “no-theory” theories of probability - accounts that leave quite obscure why probability should function as a guide to life, a suitable basis for rational inference and action. The reference class problem besets those theories that are genuinely informative and that plausibly constrain our inductive reasonings and decisions. I distinguish a “metaphysical” and an “epistemological” reference class problem. I submit that we can dissolve the former problem by recognizing that probability is fundamentally a two-place notion: conditional probability is the proper primitive of probability theory. However, I concede that the epistemological problem remains.     

预测特征竞争范式下的特征推理方式

当面临归类不确定的情景时,人们的特征推理是基于类别进行,还是基于特征联结进行,一直是类别研究中的重要内容。本研究采用预测特征竞争范式对这一问题进行了探究。共两个实验：实验1采用预测特征竞争范式探讨推理前预先归类时,人们的推理方式是基于类别还是基于特征联结。实验2采用预测特征竞争范式探讨推理前不预先归类时,人们的推理是基于类别还是基于特征联结。实验结果表明,推理前预先归类时,被试倾向于基于类别进行推理。推理前不预先归类时,被试倾向于根据特征联结进行推理。     

The relationship between reward and probability: Evidence that exploration may be intrinsically rewarding

ABSTRACT

The probability of an event occurring and the reward associated with the event can both modulate behaviour. Response times are decreased to stimuli that are either more rewarding or more likely. These two factors can be combined to give an Expected Value (EV) associated with the event (i.e., probability of the event x reward magnitude). In four experiments we investigate the effect of reward and probability on both saccadic and manual responses. When tested separately we find evidence for both a reward and probability effect across response types. When manipulations of reward magnitude and probability of the event were combined, the probability modulations dominated and these data were not well accounted for by the EV. However, a post-hoc model that included an additional intrinsic reward associated with responding provided an excellent account for the data. We argue that reward consists of both an explicit and intrinsic component. In our task, the saccadic and manual responses are linked to the information provided by the targets and the goals of the task, and successful completion of these is in itself rewarding. As a result, targets associated with a higher probability of being presented have a higher intrinsic reward.     

Estimating the probability of negative events

How well we are attuned to the statistics of our environment is a fundamental question in understanding human behaviour. It seems particularly important to be able to provide accurate assessments of the probability with which negative events occur so as to guide rational choice of preventative actions. One question that arises here is whether or not our probability estimates for negative events are systematically biased by their severity. In a minimal experimental context involving an unambiguous, objective representation of probability, we found that participants judged a controllable event as more likely to occur when its utility was extremely negative than when it was more neutral. A decision-theoretic explanation based on loss function asymmetries is advanced which supports the claim that probability estimates are not intrinsically biased by utilities.     

Implicit attentional orienting in a target detection task with central cues

Studies using Posner’s spatial cueing paradigm have demonstrated that participants can allocate their attention to specific target locations based on the predictiveness of preceding cues. Four experiments were conducted to investigate attentional orienting processes operating in a high probability condition (cues 75% predictive) as compared to a low probability condition (cues 50% predictive) using various types of centrally-presented cues. Spatially-informative cues (arrows and circles with gaps) resulted in cueing effects (CEs) for both probability conditions, with significantly larger CEs in the high probability conditions than the low probability conditions. Participants in the high probability conditions reported little or no awareness of cue–target probabilities after task completion. Our results provide support for an implicit learning account of the proportion valid effect under experimental conditions involving spatially-informative central cues and relatively short stimulus onset asynchronies (SOAs).     

What shapes the probability weighting function? Influence of affect,numeric competencies,and information formats

Research suggests that people are less sensitive to variations in probability in affect‐rich compared with affect‐poor risky choices. This effect is modeled by a more curved probability weighting function (PWF). We investigated the role of different numeric competencies and the effectiveness of several intervention strategies to decrease this affect‐laden probability distortion. In two experiments, we manipulated the affect‐richness of a risky prospect. In Experiment 1 (N = 467), we measured numeracy and symbolic‐number mapping (i.e., the ability to accurately map numbers onto their underlying magnitudes). The affect‐based manipulations showed the expected effects only in participants with more accurate symbolic‐number mapping, who also reported more differentiated emotional reactions to the various probabilities and displayed more linear PWFs. Instructions to focus on the probability information decreased probability distortion and revealed differences in the use of probability information on the basis of symbolic‐number mapping ability. In Experiment 2 (N = 417), we manipulated the format in which the probability information was presented: using visual aids versus no visual aids and a positive frame (e.g., one person wins) versus combined frame (e.g., one person wins and 99 persons do not win). The affect‐based manipulations had no effect but both the visual aids and combined frame decreased probability distortion. Whereas affect‐richness manipulations require further research, results suggest that probability weighting is at least partially driven by the inability to translate numerical information into meaningful and well‐calibrated affective intuitions. Visual aids and simple framing manipulations designed to calibrate these intuitions can help decision makers extract the gist and increase sensitivity to probabilities.     

睾酮对价值加工的影响——基于“累积前景”理论框架的决策行为研究

较多研究支持睾酮和决策中的风险寻求行为呈正相关,但是也有其他的研究未能发现这种关系。基于决策的累计前景理论,本研究使用动态估计参数估计任务(DEEP),结合计算模型的方法,对120名双盲给药、有安慰剂对照的被试进行睾酮对价值加工过程作用的探究。结果显示,睾酮减少了个体的概率扭曲以及增加了损失规避,但是没有引发明显的风险寻求行为,研究结果表明睾酮对个体的价值加工过程产生了影响,使个体对概率的感知更接近于客观值并且增加了对损失的敏感性。