Instability Of Ex Post Aggregation In The Bolker–Jeffrey Framework And Related Instability Phenomena

Suppose n Bayesian agents need to make a decision as a group. The groupas a whole is also supposed to be a Bayesian agent whose probabilities andutilities are derived or aggregated in reasonable ways from the probabilitiesand utilities of the group members. The aggregation could beex ante, i.e., interms of expected utilities, or it could be ex post, i.e., in terms of utilitiesonly, or in terms of utilities and probabilities separately. This study exploresthe ex post approach. Using the Bolker/Jeffrey framework, we show thatex post aggregation is subject to an instability phenomenon. That is, it mayhappen that the group preference between actions ``flips back and forth' dependingon the level of detail in which the decision problem is described. Structurally verysimilar phenomena also occur elsewhere in social choice theory, in statistics (Simpson'sParadox), and in voting theory (Ostrogorski's Paradox).     

A Theory of Bayesian Groups

A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non‐public or even private information (learnt by not all or just one individual), or to non‐representable information (not representable by any event in the domain where credences are held). I propose a taxonomy of six types of ‘group Bayesianism’. They differ in the information for which Bayesian revision of group credences is required: public representable information, private representable information, public non‐representable information, etc. Six corresponding theorems establish how individual credences must (not) be aggregated to ensure group Bayesianism of any type, respectively. Aggregating through standard averaging is never permitted; instead, different forms of geometric averaging must be used. One theorem—that for public representable information—is essentially Russell et al.'s central result (with minor corrections). Another theorem—that for public non‐representable information—fills a gap in the theory of externally Bayesian opinion pooling.     

Posterior predictive checks can and should be Bayesian: Comment on Gelman and Shalizi, ‘Philosophy and the practice of Bayesian statistics’

Bayesian inference is conditional on the space of models assumed by the analyst. The posterior distribution indicates only which of the available parameter values are less bad than the others, without indicating whether the best available parameter values really fit the data well. A posterior predictive check is important to assess whether the posterior predictions of the least bad parameters are discrepant from the actual data in systematic ways. Gelman and Shalizi (2012a) assert that the posterior predictive check, whether done qualitatively or quantitatively, is non‐Bayesian. I suggest that the qualitative posterior predictive check might be Bayesian, and the quantitative posterior predictive check should be Bayesian. In particular, I show that the ‘Bayesian p‐value’, from which an analyst attempts to reject a model without recourse to an alternative model, is ambiguous and inconclusive. Instead, the posterior predictive check, whether qualitative or quantitative, should be consummated with Bayesian estimation of an expanded model. The conclusion agrees with Gelman and Shalizi regarding the importance of the posterior predictive check for breaking out of an initially assumed space of models. Philosophically, the conclusion allows the liberation to be completely Bayesian instead of relying on a non‐Bayesian deus ex machina. Practically, the conclusion cautions against use of the Bayesian p‐value in favour of direct model expansion and Bayesian evaluation.     

We are All Bayesian,Everyone is Not a Bayesian

Medical research makes intensive use of statistics in order to support its claims. In this paper we make explicit an epistemological tension between the conduct of clinical trials and their interpretation: statistical evidence is sometimes discarded on the basis of an (often) underlined Bayesian reasoning. We suggest that acknowledging the potentiality of Bayesian statistics might contribute to clarify and improve comprehension of medical research. Nevertheless, despite Bayesianism may provide a better account for scientific inference with respect to the standard frequentist approach, Bayesian statistics is rarely adopted in clinical research. The main reason lies in the supposed subjective elements characterizing this perspective. Hence, we discuss this objection presenting the so-called Reference analysis, a formal method which has been developed in the context of objective Bayesian statistics in order to define priors which have a minimal or null impact on posterior probabilities. Furthermore, according to this method only available data are relevant sources of information, so that it resists the most common criticisms against Bayesianism.

     

Naive Probability: Model‐Based Estimates of Unique Events

We describe a dual‐process theory of how individuals estimate the probabilities of unique events, such as Hillary Clinton becoming U.S. President. It postulates that uncertainty is a guide to improbability. In its computer implementation, an intuitive system 1 simulates evidence in mental models and forms analog non‐numerical representations of the magnitude of degrees of belief. This system has minimal computational power and combines evidence using a small repertoire of primitive operations. It resolves the uncertainty of divergent evidence for single events, for conjunctions of events, and for inclusive disjunctions of events, by taking a primitive average of non‐numerical probabilities. It computes conditional probabilities in a tractable way, treating the given event as evidence that may be relevant to the probability of the dependent event. A deliberative system 2 maps the resulting representations into numerical probabilities. With access to working memory, it carries out arithmetical operations in combining numerical estimates. Experiments corroborated the theory's predictions. Participants concurred in estimates of real possibilities. They violated the complete joint probability distribution in the predicted ways, when they made estimates about conjunctions: P(A), P(B), P(A and B), disjunctions: P(A), P(B), P(A or B or both), and conditional probabilities P(A), P(B), P(B|A). They were faster to estimate the probabilities of compound propositions when they had already estimated the probabilities of each of their components. We discuss the implications of these results for theories of probabilistic reasoning.     

Determinants of confirmation

Epistemologists often suppose that the extent to which evidencee confirms hypothesisH depends on probabilities involvinge andH, and nothing more. We show experimentally that human reasoners sometimes violate this assumption.     

Creativity,Problem Solving,and Solution Set Sightedness: Radically Reformulating BVSR

Too often, psychological debates become polarized into dichotomous positions. Such polarization may have occurred with respect to Campbell's (1960) blind variation and selective retention (BVSR) theory of creativity. To resolve this unnecessary controversy, BVSR was radically reformulated with respect to creative problem solving. The reformulation began by defining (a) potential solution sets consisting of k possible solutions each described by their respective probability and utility values, (b) a set sightedness metric that gauges the extent to which the probabilities correspond to the utilities, and (c) a solution creativity index based on the joint improbability and utility of each solution. These definitions are then applied to representative cases in which simultaneous or sequential generate‐and‐test procedures scrutinize solution sets of variable size and with representative patterns of probabilities and utilities. The principal features of BVSR theory were then derived, including the implications of superfluity and backtracking. Critically, it was formally demonstrated that the most creative solutions must emerge from solution sets that score extremely low in sightedness. Although this preliminary revision has ample room for further development, the demonstration proves that BVSR's explanatory value does not depend on any specious association with Darwin's theory of evolution.     

Developments in Psychoanalysis by Leon Salzman

This paper examines the evolution of contemporary psychoanalytic group theory and practice in the United States. There is a brief survey of the evolution of American group treatment, which acknowledges the work of early pioneers and the influence of theorists from other countries.

Over the years, divergent views have emerged regarding the value of focusing on group dynamics and interpretations versus individual dynamics in a group setting. Some of these views are explored.

The balance of the paper is devoted to summarizing the concepts of influential, contemporary American theorists who stress the unique opportunity and the theoretical base afforded by the group milieu in applying psychoanalytic understanding and working through individual and group dynamics therapeutically.     

The Modal Logic of Bayesian Belief Revision

In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using Bayes’ rule. We define a hierarchy of modal logics that capture the logical features of Bayesian belief revision. Elements in the hierarchy are distinguished by the cardinality of the set of elementary propositions on which the agent’s prior is defined. Inclusions among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to the strongest modal companion of Medvedev’s logic of finite problems it is shown that the modal logic of belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable.

     

Robust interactive decision-analysis (RID): Behavioral results and implications

We have proposed a novel interactive procedure for performing decision analysis, called Robust Interactive Decision Analysis (RID), which permits a decision maker (DM) to voluntarily and interactively express strong (viz, sure) binary preferences for actions, partial decision functions, and full decision functions, and only imprecise probability and utility function assessments. These serve as INPUTS TO operators to prune the state probability space and decision space until an optimal choice strategy is obtained. The viability of the RID approach depends on a DM's ability to provide such information consistently and meaningfully. On a limited scale we experimentally investigate the behavioral implications of the RID method in order to ascertain its potential operational feasibility and viability. More specifically, we examine whether a DM can (1) express strong preferences between pairs of vectors of unconditional and conditional payoffs or utilities consistently; (2) provide imprecise (ordinal and interval) state probabilities that are individually as well as mutually consistent with the state probabilities imputed from the expressed strong preferences. The results show that a DM can provide strong individually and mutually consistent preference and ordinal probability information. Moreover, most individuals also appear to be able to provide interval probabilities that are individually and mutually consistent with their strong preference inputs. However, the several violations observed, our small sample size, and the limited scope of our investigation suggest that further experimentation is needed to determine whether and/or how such inputs should be elicited. Overall, the results indicate that the RID method is behaviorally viable.     

Little Bayesians or little Einsteins? Probability and explanatory virtue in children's inferences

Like scientists, children seek ways to explain causal systems in the world. But are children scientists in the strict Bayesian tradition of maximizing posterior probability? Or do they attend to other explanatory considerations, as laypeople and scientists – such as Einstein – do? Four experiments support the latter possibility. In particular, we demonstrate in four experiments that 4‐ to 8‐year‐old children, like adults, have a robust latent scope bias that leads to inferences that do not maximize posterior probability. When faced with two explanations equally consistent with observed data, where one explanation makes an unverified prediction, children consistently preferred the explanation that does not make this prediction (Experiment 1), even if the prior probabilities are identical (Experiment 3). Additional evidence suggests that this latent scope bias may result from the same explanatory strategies used by adults (Experiments 1 and 2), and can be attenuated by strong prior odds (Experiment 4). We argue that children, like adults, rely on ‘explanatory virtues’ in inference – a strategy that often leads to normative responses, but can also lead to systematic error.     

Reasonology and False Beliefs

Abstract

Whereas some philosophers view all reasons for action as psychological states of agents, others—objective favourers theorists—locate the overwhelming majority of reasons for action outside the agent, in items that objectively favour courses of action. (The latter may count such psychological states as a person's belief that demons dance in his kitchen as a reason for him to seek psychiatric help.) This article explores options that objective favourers theorists have regarding cases in which, owing significantly to a false belief, an agent performs an action for which there is no objective favourer. Topics addressed include whether such theorists, including Jonathan Dancy himself, should accept Dancy's thesis that ‘intentional, deliberate, purposeful action is always done for a reason’ and whether there are two different concepts of reasons for action, one geared to action-evaluation and the other to action-explanation.     

NEUTRALITY IN THE FIELD: ALPHA‐FUNCTION AND THE DREAMING DYAD IN PSYCHOANALYTIC PROCESS

Analysts have interpreted the concept of neutrality in a variety of ways, beginning with Strachey's use of that word to translate Freud's (1915) term, Indifferenz. In this paper, neutrality is linked to Freud's notions of free association and evenly suspended attention. A history of psychoanalytic attempts to clarify the concept are presented, with special attention to issues of ambiguity and the patient's role in the determination of neutrality. Neutrality is further elaborated in relation to the bipersonal field as described by the Barangers and contemporary field theorists. Understood in terms of the field, neutrality becomes a transpersonal concept, here conceived in terms of alpha‐function and a dreaming dyad. Two clinical examples cast in the light of a Bionian perspective are discussed to suggest an alternative understanding of analytic impasses and their relation to alpha‐function and neutrality.     

L'état c'est moi — Except When I Am Not: Commentary on Paper by Orna Guranlik and Daphne Simeon

In this discussion, I situate Guralnik and Simeon's argument about depersonalization and interpellation among ways that different psychoanalytic theorists have understood the interaction of the psychic and social domains. I elaborate on what Guralnik and Simeon mean when they refer to the role of “the State” in dissociation, interpellation, and depersonalization. Upon showing how self-states simultaneously incorporate and resist the State, Guralnik and Simeon provide a clinical rationale to confront interpellation's “discursive instructions.” This leads me to explore the curious status of the term state in psychoanalytic theory and practice.     

EXPLAINING THE LIMITS OF OLSSON'S IMPOSSIBILITY RESULT

In his groundbreaking book, Against Coherence (2005), Erik Olsson presents an ingenious impossibility theorem that appears to show that there is no informative relationship between probabilistic measures of coherence and higher likelihood of truth. Although Olsson's result provides an important insight into probabilistic models of epistemological coherence, the scope of his negative result is more limited than generally appreciated. The key issue is the role conditional independence conditions play within the witness testimony model Olsson uses to establish his result. Olsson maintains that his witness model yields charitable ceteris paribus conditions for any theory of probabilistic coherence. Not so. In fact, Olsson's model, like Bayesian witness models in general, selects a peculiar class of models that are in no way representative of the range of options available to coherence theorists. Recent positive results suggest that there is a way to develop a formal theory of coherence after all. Further, although Bayesian witness models are not conducive to the truth, they are conducive to reliability.     

What Are the “True” Statistics of the Environment?

A widespread assumption in the contemporary discussion of probabilistic models of cognition, often attributed to the Bayesian program, is that inference is optimal when the observer's priors match the true priors in the world—the actual “statistics of the environment.” But in fact the idea of a “true” prior plays no role in traditional Bayesian philosophy, which regards probability as a quantification of belief, not an objective characteristic of the world. In this paper I discuss the significance of the traditional Bayesian epistemic view of probability and its mismatch with the more objectivist assumptions about probability that are widely held in contemporary cognitive science. I then introduce a novel mathematical framework, the observer lattice, that aims to clarify this issue while avoiding philosophically tendentious assumptions. The mathematical argument shows that even if we assume that “ground truth” probabilities actually do exist, there is no objective way to tell what they are. Different observers, conditioning on different information, will inevitably have different probability estimates, and there is no general procedure to determine which one is right. The argument sheds light on the use of probabilistic models in cognitive science, and in particular on what exactly it means for the mind to be “tuned” to its environment.     

Ethics and practices of re‐presentation: Witnessing self and other

Context: The challenge of producing ethical representational practices is of critical interest to both practitioner‐researchers and research theorists. For practitioners becoming researchers a central ethical question may be how to manage a relational presence in writing their research, in ways that acknowledge participants, the research relationship, and a researcher's own subjectivity. Focus: The article offers examples from practitioner research to illustrate and theorise how researcher subjectivity is managed through the use of witnessing practices as a representational strategy. Witnessing practices – translated into counselling research from narrative therapy – offer researchers a strategy to take up a reflexive, relational presence in research reports. Discussion: Researcher witnessing honours the contributions of research participants as well as making visible the shaping effects of the research on a researcher's life. Through witnessing self and other, and thus declaring presence, privilege and partiality, re‐presentational ethics are made transparent.