Numerical Probability

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Li-lin Rao - One of the best experts on this subject based on the ideXlab platform.

  • ERP correlates of verbal and Numerical probabilities in risky choices: A two-stage Probability processing view
    Frontiers in human neuroscience, 2016
    Co-Authors: Yan-hua Xuan, Yun Wang, Li-lin Rao
    Abstract:

    Two kinds of Probability expressions, verbal and Numerical, have been used to characterize the uncertainty that people face. However, the question of whether verbal and Numerical probabilities are cognitively processed in a similar manner remains unresolved. From a levels-of-processing perspective, verbal and Numerical probabilities may be processed differently during early sensory processing but similarly in later semantic-associated operations. This event-related potential (ERP) study investigated the neural processing of verbal and Numerical probabilities in risky choices. The results showed that verbal Probability and Numerical Probability elicited different N1 amplitudes but that verbal and Numerical probabilities elicited similar N2 and P3 waveforms in response to different levels of Probability (high to low). These results were consistent with a levels-of-processing framework and suggest some internal consistency between the cognitive processing of verbal and Numerical probabilities in risky choices. Our findings shed light on possible mechanism underlying Probability expression and may provide the neural evidence to support the translation of verbal to Numerical probabilities (or vice versa).

  • Probability expression for changeable and changeless uncertainties: an implicit test
    Frontiers in psychology, 2014
    Co-Authors: Yun Wang, Li-lin Rao
    Abstract:

    ‘Everything changes and nothing remains still.’ We designed three implicit studies to understand how people react or adapt to a rapidly changing world by testing whether verbal Probability is better in expressing changeable uncertainty while Numerical Probability is better in expressing unchangeable uncertainty. We found that the ‘verbal-changeable’ combination in implicit tasks was more compatible than the ‘Numerical-changeable’ combination. Furthermore, the ‘Numerical-changeless’ combination was more compatible than the ‘verbal-changeless’ combination. Thus, a novel feature called ‘changeability’ was proposed to describe the changeable nature of verbal Probability. However, Numerical Probability is a better carrier of changeless uncertainty than verbal Probability. These results extend the domain of Probability predictions and enrich our general understanding of communication with verbal and Numerical probabilities. Given that the world around us is constantly changing, this ‘changeability’ feature may play a major role in preparing for uncertainty.

Yun Wang - One of the best experts on this subject based on the ideXlab platform.

  • ERP correlates of verbal and Numerical probabilities in risky choices: A two-stage Probability processing view
    Frontiers in human neuroscience, 2016
    Co-Authors: Yan-hua Xuan, Yun Wang, Li-lin Rao
    Abstract:

    Two kinds of Probability expressions, verbal and Numerical, have been used to characterize the uncertainty that people face. However, the question of whether verbal and Numerical probabilities are cognitively processed in a similar manner remains unresolved. From a levels-of-processing perspective, verbal and Numerical probabilities may be processed differently during early sensory processing but similarly in later semantic-associated operations. This event-related potential (ERP) study investigated the neural processing of verbal and Numerical probabilities in risky choices. The results showed that verbal Probability and Numerical Probability elicited different N1 amplitudes but that verbal and Numerical probabilities elicited similar N2 and P3 waveforms in response to different levels of Probability (high to low). These results were consistent with a levels-of-processing framework and suggest some internal consistency between the cognitive processing of verbal and Numerical probabilities in risky choices. Our findings shed light on possible mechanism underlying Probability expression and may provide the neural evidence to support the translation of verbal to Numerical probabilities (or vice versa).

  • Probability expression for changeable and changeless uncertainties: an implicit test
    Frontiers in psychology, 2014
    Co-Authors: Yun Wang, Li-lin Rao
    Abstract:

    ‘Everything changes and nothing remains still.’ We designed three implicit studies to understand how people react or adapt to a rapidly changing world by testing whether verbal Probability is better in expressing changeable uncertainty while Numerical Probability is better in expressing unchangeable uncertainty. We found that the ‘verbal-changeable’ combination in implicit tasks was more compatible than the ‘Numerical-changeable’ combination. Furthermore, the ‘Numerical-changeless’ combination was more compatible than the ‘verbal-changeless’ combination. Thus, a novel feature called ‘changeability’ was proposed to describe the changeable nature of verbal Probability. However, Numerical Probability is a better carrier of changeless uncertainty than verbal Probability. These results extend the domain of Probability predictions and enrich our general understanding of communication with verbal and Numerical probabilities. Given that the world around us is constantly changing, this ‘changeability’ feature may play a major role in preparing for uncertainty.

Thomas S. Wallsten - One of the best experts on this subject based on the ideXlab platform.

  • comparing the calibration and coherence of Numerical and verbal Probability judgments
    Management Science, 1993
    Co-Authors: Thomas S. Wallsten, David V Budescu, Rami Zwick
    Abstract:

    Despite the common reliance on Numerical Probability estimates in decision research and decision analysis, there is considerable interest in the use of verbal Probability expressions to communicate opinion. A method is proposed for obtaining and quantitatively evaluating verbal judgments in which each analyst uses a limited vocabulary that he or she has individually selected and scaled. An experiment compared this method to standard Numerical responding under three different payoff conditions. Response mode and payoff never interacted. Probability scores and their components were virtually identical for the two response modes and for all payoff groups. Also, judgments of complementary events were essentially additive under all conditions. The two response modes differed in that the central response category was used more frequently in the Numerical than the verbal case, while overconfidence was greater verbally than Numerically. Response distributions and degrees of overconfidence were also affected by payoffs. Practical and theoretical implications are discussed.

  • The Negative Effect of Probability Assessments on Decision Quality
    Organizational Behavior and Human Decision Processes, 1993
    Co-Authors: Ido Erev, Gary Bornstein, Thomas S. Wallsten
    Abstract:

    Abstract It is commonly assumed that uncertain information can be reduced to Numerical probabilities without biasing preferences. It is also implicitly assumed in much research and many applications that people can express these probabilities. In contradiction to these assumptions Experiment 1 shows that the production of Probability assessments biases decisions in an n-person game. Experiment 2 shows that the explicit assessment of Numerical probabilities renders choices between gambles concerning future basketball events less optimal. These findings seem to be a result of overweighting the Probability dimension relative to the payoff dimension given Numerical judgments. Experiment 2 also suggests that without explicit Numerical Probability judgments subjects are less likely to violate the dominance principle. The theoretical and practical implications of the results are discussed.

Terrence L. Fine - One of the best experts on this subject based on the ideXlab platform.

  • Unstable Collectives and Envelopes of Probability Measures
    The Annals of Probability, 1991
    Co-Authors: Adrian Papamarcou, Terrence L. Fine
    Abstract:

    We discuss issues of existence and stochastic modeling in regard to sequences that exhibit combined features of independence and instability of relative frequencies of marginal events. The concept of independence used here is borrowed from the frequentist account of Numerical Probability advanced by von Mises: A sequence is independent if certain salient asymptotic properties are invariant under the causal selection of subsequences. We show that independence (in the above sense) and instability of relative frequency are indeed compatible and that sequences with such features support stochastic models expressed in terms of envelopes of Probability measures.

  • Stationarity and almost sure divergence of time averages in interval-valued Probability
    Journal of Theoretical Probability, 1991
    Co-Authors: Adrian Papamarcou, Terrence L. Fine
    Abstract:

    Our work is motivated by the study of empirical processes (such as flicker noise) that occur in stable systems yet give rise to observations with seemingly divergent time averages. Stationary models for such processes do not exist in the domain of Numerical Probability, as the ergodic theorems dictate the convergence of time averages of stationary and bounded processes. This has led us to investigate such models in the wider framework of interval-valued Probability. In this paper we construct interval-valued probabilities on the space of infinite binary sequences that combine properties of (i) strict stationarity, (ii) unicity of extension from the algebra of cylinder sets to a wider collection containing salient asymptotic events, and (iii) almost sure support of divergence of time averages. These properties are not shared by conventional stochastic models.

David M Piercey - One of the best experts on this subject based on the ideXlab platform.

  • motivated reasoning and verbal vs Numerical Probability assessment evidence from an accounting context
    Organizational Behavior and Human Decision Processes, 2009
    Co-Authors: David M Piercey
    Abstract:

    A perplexing yet persistent empirical finding is that individuals assess probabilities in words and in numbers nearly equivalently, and theorists have called for future research to search for factors that cause differences. This study uses an accounting context in which individuals are commonly motivated to reach preferred (rather than accurate) conclusions. Within this context, I predict new differences between verbal and Numerical Probability assessments, as follows: first, individuals will justify an optimistic verbal assessment (e.g., somewhat possible) by retaining the option of re-defining it, in case of negative outcomes, as though the phrase really means something different, and, for that matter, means more things. This re-definition will maintain some connection to the original meaning of the phrase, but de-emphasized relative to the new meaning. Second, based on this behavior, I also predict individuals' verbal Probability assessments to be (1) more biased and yet (2) perceived as more justifiable than their Numerical assessments. I find supportive evidence in an experiment designed to test the hypotheses. This study contributes to motivated reasoning and Probability assessment theories (1) with new evidence of how individuals can word-smith in multiple attributes of a phrase to justify reaching a preferred conclusion, and (2) with new, reliable differences between verbal and Numerical Probability assessments. This study has important theoretical and practical implications relevant to organizational contexts in which people assess the likelihoods of uncertainties in words or numbers, and with motivations to reach a preferred conclusion.