How to confuse with statistics or: the use and misuse of conditional probabilities

The article shows by various examples how consumers of statistical information may be confused when this information is presented in terms of conditional probabilities. It also shows how this confusion helps others to lie with statistics, and it suggests how either confusion or lies can be avoided by using alternative modes of conveying statistical information. --

Peacemaking among inconsistent rationalities?

Kacelnik, Schuck-Paim and Pompilio (this volume, p. 377) show that rationality axioms from economics are neither necessary nor sufficient to guarantee that animal behavior is biologically adaptive. To illustrate that biological adaptiveness does not imply conformity with the consistency axioms of economics, Kacelnik et al describe animals that sensibly experiment with actions yielding sub-maximum levels of short-term energy intake to monitor their environments for change, leading to apparently intransitive patterns of choice that are nevertheless biologically adaptive. Invalidating the converse claim that economic rationality implies biological adaptiveness is Kacelnik et al’s example of female ruffs that are worse off when they conform to the constant-ratio rule, frequently interpreted as a normative consistency requirement of economic rationality. Together, the two examples demonstrate that axiomatic norms are both unnecessary and insufficient for determining whether a particular behavior is biologically adaptive. Additionally, Kacelnik et al call into question what has been reported in the animal behavior literature as preference reversals, such as risk attitudes among wild rufous hummingbirds or the food-hoarding propensities of grey jays. Kacelnik et al attribute apparent reversals to state-dependent fitness functions modulated by subtle differences in the training phase of animal experiments. For example, animals trained on menus that include a strictly dominated option will tend to have lower accumulated energy reserves and therefore exhibit systematically different patterns of choice––not because they fail to maximize, but because their training has induced systematically different nutritional states. Another possible explanation for preference reversals in animal studies with strictly dominated, or “decoy” options is that menus containing dominated items may convey valid information about future opportunities (Houston and McNamara, 1999). If menus are correlated through time, then menus with inferior options today predict scarcity in the future and imply a distinct optimal course of action, in violation of regularity assumptions that posit invariance with respect to the inclusion of strictly dominated alternatives. In environments with payoff structures that can be modeled as cooperative games, a family’s best response sometimes requires individual family members to behave suboptimally as part of a diversification strategy that reduces the risk of reproductive failure (Hutchinson, 1996). Futhermore, theoretical biologists have documented the fragility of expected fitness maximizing behaviour with respect to the assumption of stable environments. Once the model allows for shocks to the environment’s stochastic structure, simple behavior rules that are suboptimal (in terms of expected fitness) when viewed narrowly from the perspective of unchanging payoffs in a fixed environment may outperform rules based on maximazation within a static small world (Bookstaber and Langsam, 1985).Rationality, rationalities, irrationality, bounded rationality, biology, biological rationality

Does Consistency Predict Accuracy of Beliefs?: Economists Surveyed About PSA

Subjective beliefs and behavior regarding the Prostate Specific Antigen (PSA) test for prostate cancer were surveyed among attendees of the 2006 meeting of the American Economic Association. Logical inconsistency was measured in percentage deviations from a restriction imposed by Bayes’ Rule on pairs of conditional beliefs. Economists with inconsistent beliefs tended to be more accurate than average, and consistent Bayesians were substantially less accurate. Within a loss function framework, we look for and cannot find evidence that inconsistent beliefs cause economic losses. Subjective beliefs about cancer risks do not predict PSA testing decisions, but social influences do.logical consistency, predictive accuracy, elicitation, non-Bayesian, ecological rationality

Does consistency predict accuracy of beliefs?: Economists surveyed about PSA

Subjective beliefs and behavior regarding the Prostate Specific Antigen (PSA) test for prostate cancer were surveyed among attendees of the 2006 meeting of the American Economic Association. Logical inconsistency was measured in percentage deviations from a restriction imposed by Bayes’ Rule on pairs of conditional beliefs. Economists with inconsistent beliefs tended to be more accurate than average, and consistent Bayesians were substantially less accurate. Within a loss function framework, we look for and cannot find evidence that inconsistent beliefs cause economic losses. Subjective beliefs about cancer risks do not predict PSA testing decisions, but social influences do.logical consistency, predictive accuracy, elicitation, non-Bayesian, ecological rationality

Coping with uncertainty in public health: the use of heuristics

The observation that experts and lay people use cognitive shortcuts or heuristics to arrive at judgements about complex problems is certainly not new. But what is new is the finding that a group of reasoning strategies, which have been maligned by philosophers and logicians alike, have demonstrable value in helping members of the public come to a judgement about public health problems. These problems, which span food safety crises, immunization scares and risks associated with exposure to environmental toxins, presuppose knowledge and expertise which falls outside of the epistemic and technical competence of most members of the public. Notwithstanding the complexity of these problems, they are not perceived by lay people to be wholly unintelligible or incomprehensible. This short communication reports on the findings of a questionnaire-based investigation into the use of these reasoning strategies by 879 members of the public. The results reveal a rational competence on the part of lay people which has been hitherto unexamined, and which may be usefully exploited in all aspects of public health work

Why heuristics work

ABSTRACT—The adaptive toolbox is a Darwinian-inspired theory that conceives of the mind as a modular system that is composed of heuristics, their building blocks, and evolved capacities. The study of the adaptive toolbox is descriptive and analyzes the selection and structure of heuristics in social and physical environments. The study of ecological rationality is prescriptive and identifies the structure of environments in which specific heuristics either succeed or fail. Results have been used for designing heuristics and environments to improve professional decision making in the real world. Logic, probability, and heuristics are three central ideas in the intellectual history of the mind. For Aristotle, logic was a theory of ideal human reasoning and inference. Probability theory emerged only late in the mid-17th century, replacing logica