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Redundant or excessive information can sometimes lead people to lean on it unnecessarily. Certain experimental designs can sometimes bias results in the researcher's favor. And, sometimes, interesting effects are too small to be studied, practically, or are simply zero. We believe a confluence of these factors led to a recent paper (Isaac & Brough, 2014, JCR). This initial paper proposed a new means by which probability judgments can be led astray: the category size bias, by which an individual event coming from a large category is judged more likely to occur than an event coming from a small one. Our work shows that this effect may be due to instructional and mechanical confounds, rather than interesting psychology. We present eleven studies with over ten times the sample size of the original in support of our conclusion: We replicate three of the five original studies and reduce or eliminate the effect by resolving these methodological issues, even significantly reversing the bias in one case (Study 6). Studies 7-8c suggest the remaining two studies are false positives. We conclude with a discussion of the subtleties of instruction wording, the difficulties of correcting the record, and the importance of replication and open science. [ABSTRACT FROM AUTHOR]

This paper presents the results of a study that sheds new light on the shape of indifference curves in the Marschak-Machina triangle. The most important observation, obtained non-parametrically, concerns jumps in indifference curves at the triangle legs towards the triangle origin. These jumps, however, do not appear at the hypotenuse. The pattern observed suggests discontinuity in lottery valuation when the range of lottery outcomes changes and is best explained by decision-making models based on the psychological phenomenon of range dependence (Parducci, 1965; Cohen, 1992; Kontek & Lewandowski, 2018). Models founded on other psychological phenomena, e.g., discontinuity in decision weights (Kahneman & Tversky, 1979), cumulative probability weighting (Tversky & Kahneman, 1992), attention shifting (Birnbaum, 2008), overweighting of salient payoffs (Bordallo, Gennaioli & Shefrin, 2012), and treating stated probabilities as imperfect information (Viscusi, 1989), predict indifference curve shapes that differ from the one obtained in this study. [ABSTRACT FROM AUTHOR]

This paper explored how frames influence people's evaluation of others' probabilistic predictions in light of the outcomes of binary events. Most probabilistic predictions (e.g., "there is a 75% chance that Denver will win the Super Bowl") can be partitioned into two components: A qualitative component that describes the predicted outcome ("Denver will win the Super Bowl"), and a quantitative component that represents the chance of the outcome occurring ("75% chance"). Various logically equivalent variations of a single prediction can be created through different combinations of these components and their logical or numerical complements (e.g., "25% chance that Denver will lose the Super Bowl", "75% chance that Seattle will lose the Super Bowl"). Based on the outcome of the predicted event, these logically equivalent predictions can be categorized into two classes: Congruently framed predictions, in which the qualitative component matches the outcome, and incongruently framed predictions, in which it does not. Although the two classes of predictions are logically equivalent, we hypothesize that people would judge congruently framed predictions to be more accurate. The paper tested this hypothesis in seven experiments and found supporting evidence across a number of domains and experimental manipulations, and even when the congruently framed prediction was logically inferior. It also found that this effect held even for subjects who saw both congruently framed and incongruently framed versions of a prediction and judged the two to be logically equivalent. [ABSTRACT FROM AUTHOR]

Stastny and Lehner (2018) compared the accuracy of forecasts in an intelligence community predictionmarket to comparable forecasts in analysis reports prepared by groups of professional intelligence analysts. To obtain quantitative probabilities from the analysis reports experienced analysts were asked to read the reports and state what probability they thought the reports implied for each forecast question. These were called imputed probabilities. Stastny and Lehner found that the prediction market was more accurate than the imputed probabilities and concluded that this was evidence that the prediction market was more accurate than the analysis reports. In a commentary, Mandel (2019) took exception to this interpretation. In a re-analysis of the data, Mandel found a very strong correlation between readers' personal and imputed probabilities. From this Mandel builds a case that the imputed probabilities are little more than a reflection of the readers' personal views; that they do not fairly reflect the contents of the analysis reports; and therefore, any accuracy results are spurious. This paper argues two points. First, the high correlation between imputed and personal probabilities was not evidence of substantial imputation bias. Rather it was the natural by-product of the fact that the imputed and personal probabilities were both forecasts of the same events. An additional analysis shows a much lower level of imputation bias that is consistent with the original results and interpretation. Second, the focus of Stastny and Lehner (2018) was on the reports as understood by readers. In this context, even if there was substantial imputation bias it would not invalidate accuracy results; it would instead provide a possible causal explanation of those results. [ABSTRACT FROM AUTHOR]

Recent years have seen a large increase in the popularity of Texas hold ’em poker. It is now the most commonly played variant of the game, both in casinos and through online platforms. In this paper, we present a simulation study for games of Texas hold ’em with between two and 23 players. From these simulations, we estimate the probabilities of each player having been dealt the winning hand. These probabilities are calculated conditional on both partial information (that is, the player only having knowledge of his/her cards) and also on fuller information (that is, the true probabilities of each player winning given knowledge of the cards dealt to each player). Where possible, our estimates are compared to exact analytic results and are shown to have converged to three significant figures. With these results, we assess the poker strategies described in two recent pieces of popular culture. In comparing the ideas expressed in Taylor Swift’s song, New Romantics , and the betting patterns employed by James Bond in the 2006 film, Casino Royale , we conclude that Ms Swift demonstrates a greater understanding of the true probabilities of winning a game of Texas hold ’em poker. [ABSTRACT FROM AUTHOR]

This paper summarizes an empirical comparison of the accuracy of forecasts included in analysis reports developed by professional intelligence analysts to comparable forecasts in a prediction market that has broad participation from across an intelligence community. To compare forecast accuracy, 99 event forecasts were extracted from qualitative descriptions found in 41 analysis reports and posted on the prediction market. Quantitative probabilities were imputed from the qualitative forecasts by asking seasoned professional analysts, who did not participate in the prediction market, to read the reports and to infer a quantitative probability based on what was written. These readers were also asked to provide their personal probabilities before and after reading the reports. There were two statistically significant results of particular interest. First, the primary result is that the prediction market forecasts were more accurate than the analysis reports. On average prediction market probabilities were 0.114 closer to ground truth than the analysis report probabilities. Second, in cases where analysts (readers) updated their personal probabilities in a direction opposite to what the reports implied, analysts tended to update their probabilities in the correct direction. This occurred even though, on average, reading the reports did not make readers more accurate. [ABSTRACT FROM AUTHOR]

Brier score decompositions, including those attributed to Murphy and to Yates, provide popular metrics for estimating forecast performance attributes like calibration and discrimination. However, the decompositions are generally limited to situations where forecasters make successive forecast judgments against the same class of substantive event (e.g., rain vs. no rain). They do not readily translate to common situations where: forecasts are weighted unequally; forecasts can be made against a range of heterogeneous topics and events over varying time horizons; forecasts can be updated over time until an event occurs or an event deadline is reached; or outcome alternatives can vary in number and nature (e.g., ordered vs. unordered outcomes) across forecast questions. In this paper, we propose extensions of the Murphy and Yates decompositions to address these features. The extensions involve new analytic expressions for the decompositions of weighted Brier scores, along with proposed resampling methods. We use data from a recent forecasting tournament to illustrate the methods. [ABSTRACT FROM AUTHOR]

When decisions involve opting in or out of competition many decision makers will opt-in even when doing so leads to losses on average. In the current paper, we examine the generality of this effect in risky choices not involving competition. We found that re-framing a sure (certain) zero option as an option to observe the results of the other options without choosing would lead to increased consequential choice (i.e., increased selection of risky options rather than the zero option). Specifically, in two studies we compared the rate of consequential choice in a novel paradigm where decision makers decide to observe or to choose with consequence from a set of risky options (decisions-to-engage) to a full-feedback decisions-from-feedback paradigm where the choice set included a labeled sure zero option. Compared to decisions-from-feedback, participants were more likely to choose from mixed (risky) gambles with consequence (over a zero outcome) in decisions-to-engage. This occurred irrespective of whether doing so was advantageous (i.e., when choice led to monetary gains on average) or disadvantageous (i.e., when choice led to monetary losses on average), and when descriptions of the options outcomes and probabilities were provided (Study 2). These findings provide an important boundary condition for the positive effects of experience on the quality of choice, and suggest that decision makers' preference for agency can sometimes induce poorer choices. [ABSTRACT FROM AUTHOR]

Recently Houdayer and Isono have proved, among other things, that every biexact group $\unicode[STIX]{x1D6E4}$ has the property that for any non-singular strongly ergodic essentially free action $\unicode[STIX]{x1D6E4}\curvearrowright (X,\unicode[STIX]{x1D707})$ on a standard measure space, the group measure space von Neumann algebra $\unicode[STIX]{x1D6E4}\ltimes L^{\infty }(X)$ is full. In this paper, we prove the same property for a wider class of groups, notably including $\text{SL}(3,\mathbb{Z})$. We also prove that for any connected simple Lie group $G$ with finite center, any lattice $\unicode[STIX]{x1D6E4}\leqslant G$, and any closed non-amenable subgroup $H\leqslant G$, the non-singular action $\unicode[STIX]{x1D6E4}\curvearrowright G/H$ is strongly ergodic and the von Neumann factor $\unicode[STIX]{x1D6E4}\ltimes L^{\infty }(G/H)$ is full. [ABSTRACT FROM AUTHOR]

The front and back cover matter of the periodical is presented which includes information on submission of research papers in all areas of mathematics such as probability and mathematical physics; and the table of contents for the April 2016 issue.