Related papers: Probability Reversal and the Disjunction Effect in…
The disjunction effect in human decision making is often taken to show that the classical law of total probability is violated, motivating quantum-like models. We re-examine this claim for the Prisoner's Dilemma disjunction effect. Under…
The primary objective of this paper is to revisit Simpson's paradox using a statistical misspecification perspective. It is argued that the reversal of statistical associations is sometimes spurious, stemming from invalid probabilistic…
Given two sets of data which lead to a similar statistical conclusion, the Simpson Paradox describes the tactic of combining these two sets and achieving the opposite conclusion. Depending upon the given data, this may or may not succeed.…
Scepticism towards childhood vaccines and genetically modified food has grown despite scientific evidence of their safety. Beliefs about scientific issues are difficult to change because they are entrenched within many related moral…
When a linear model is adjusted to control for additional explanatory variables the sign of a fitted coefficient may reverse. Here these reversals are studied using coefficients of determination. The resulting theory can be used to…
Simpson's paradox, a long-standing statistical phenomenon, describes the reversal of an observed association when data are disaggregated into sub-populations. It has critical implications across statistics, epidemiology, economics, and…
Algorithmic recourse aims to provide actionable recommendations to individuals to obtain a more favourable outcome from an automated decision-making system. As it involves reasoning about interventions performed in the physical world,…
Many models of economics assume that individuals distort objective probabilities. We propose a simple consistency condition on distortion functions, which we term distortion coherence, that ensures that the function commutes with…
We prove a theorem which shows that a collection of experimental data of probabilistic weights related to decisions with respect to situations and their disjunction cannot be modeled within a classical probabilistic weight structure in case…
A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…
We present examples where the use of belief functions provided sound and elegant solutions to real life problems. These are essentially characterized by ?missing' information. The examples deal with 1) discriminant analysis using a learning…
Simpson's paradox and collapsibility are two closely related concepts in the context of data analysis. While the knowledge about the occurrence of Simpson's paradox helps a statistician to draw correct and meaningful conclusions, the…
Understanding how humans revise their beliefs in light of new information is crucial for developing AI systems which can effectively model, and thus align with, human reasoning. While theoretical belief revision frameworks rely on a set of…
In observational studies, the causal effect of a treatment may be confounded with variables that are related to both the treatment and the outcome of interest. In order to identify a causal effect, such studies often rely on the…
Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities---this is the conjunction fallacy. One of the most discussed accounts of this…
Belief fusion is the principle of combining separate beliefs or bodies of evidence originating from different sources. Depending on the situation to be modelled, different belief fusion methods can be applied. Cumulative and averaging…
Simpson's Paradox is a well-known phenomenon in statistical science, where the relationship between the response variable $X$ and a certain explanatory factor of interest $A$ reverses when an additional factor $B_1$ is considered. This…
Background: Confirmation bias is the tendency to acquire or evaluate new information in a way that is consistent with one's preexisting beliefs. It is omnipresent in psychology, economics, and even scientific practices. Prior theoretical…
We perform new experiment using almost the same sample size considered by Tversky and Shafir to test the validity of classical probability theory in decision making. The results clearly indicate that the disjunction effect depends also on…
While belief functions may be seen formally as a generalization of probabilistic distributions, the question of the interactions between belief functions and probability is still an issue in practice. This question is difficult, since the…