scholarly journals Gradient formulae for probability functions depending on a heterogenous family of constraints

2021 ◽  
Vol 2 ◽  
pp. 1-29
Author(s):  
Wim van Ackooij ◽  
Pedro Pérez-Aros
Keyword(s):  
Probability Functions

An Introduction to Uncertain Futures

2018 ◽  
Author(s):  
Jens Beckert ◽  
Richard Bronk
Keyword(s):  
Optimal Strategies ◽  
Theoretical Framework ◽  
Objective Probability ◽  
Political Debate ◽  
Probability Functions ◽  
Market Economies ◽  
Socially Constructed ◽  
The Future ◽  
Radical Uncertainty ◽  
Calculative Practices

This chapter provides a theoretical framework for considering how imaginaries and narratives interact with calculative devices to structure expectations and beliefs in the economy. It analyses the nature of uncertainty in innovative market economies and examines how economic actors use imaginaries, narratives, models, and calculative practices to coordinate and legitimize action, determine value, and establish sufficient conviction to act despite the uncertainty they face. Placing the themes of the volume in the context of broader trends in economics and sociology, the chapter argues that, in conditions of widespread radical uncertainty, there is no uniquely rational set of expectations, and there are no optimal strategies or objective probability functions; instead, expectations are often structured by contingent narratives or socially constructed imaginaries. Moreover, since expectations are not anchored in a pre-existing future reality but have an important role in creating the future, they become legitimate objects of political debate and crucial instruments of power in markets and societies.

The calculation of single inclusion probability functions

1987 ◽  
Vol 86 (2) ◽  
pp. 1010-1019
Author(s):  
Gregory J. Gillette ◽  
John J. McCoy
Keyword(s):  
Inclusion Probability ◽  
Probability Functions ◽  
Single Inclusion

scholarly journals THE THEORY OF SPECTRUM EXCHANGEABILITY

2014 ◽  
Vol 8 (1) ◽  
pp. 108-130
Author(s):  
E. HOWARTH ◽  
J. B. PARIS
Keyword(s):  
Probability Function ◽  
Inductive Logic ◽  
Probability Functions ◽  
Homogeneous Functions ◽  
Finite Structures ◽  
Spectrum Exchangeability

AbstractSpectrum Exchangeability, Sx, is an irrelevance principle of Pure Inductive Logic, and arguably the most natural (but not the only) extension of Atom Exchangeability to polyadic languages. It has been shown1 that all probability functions which satisfy Sx are comprised of a mixture of two essential types of probability functions; heterogeneous and homogeneous functions. We determine the theory of Spectrum Exchangeability, which for a fixed language L is the set of sentences of L which must be assigned probability 1 by every probability function satisfying Sx, by examining separately the theories of heterogeneity and homogeneity. We find that the theory of Sx is equal to the theory of finite structures, i.e., those sentences true in all finite structures for L, and it emerges that Sx is inconsistent with the principle of Super-Regularity (Universal Certainty). As a further consequence we are able to characterize those probability functions which satisfy Sx and the Finite Values Property.

A Modified Supervaluationist Framework for Decision-Making

2021 ◽  
Vol 12 (2) ◽  
pp. 175-191
Author(s):  
Jonas Karge ◽  
Keyword(s):  
Decision Making ◽  
Probability Function ◽  
Imprecise Probabilities ◽  
Adequate Account ◽  
Alternative Account ◽  
Semantic Approach ◽  
Probability Functions ◽  
Degree Of Belief ◽  
The Way

How strongly an agent beliefs in a proposition can be represented by her degree of belief in that proposition. According to the orthodox Bayesian picture, an agent's degree of belief is best represented by a single probability function. On an alternative account, an agent’s beliefs are modeled based on a set of probability functions, called imprecise probabilities. Recently, however, imprecise probabilities have come under attack. Adam Elga claims that there is no adequate account of the way they can be manifested in decision-making. In response to Elga, more elaborate accounts of the imprecise framework have been developed. One of them is based on supervaluationism, originally, a semantic approach to vague predicates. Still, Seamus Bradley shows that some of those accounts that solve Elga’s problem, have a more severe defect: they undermine a central motivation for introducing imprecise probabilities in the first place. In this paper, I modify the supervaluationist approach in such a way that it accounts for both Elga’s and Bradley’s challenges to the imprecise framework.

scholarly journals Optimal utility and probability functions for agents with finite computational precision

2020 ◽  
Author(s):  
Keno Juechems ◽  
Jan Balaguer ◽  
Bernhard Spitzer ◽  
Christopher Summerfield
Keyword(s):  
Selective Pressure ◽  
Empirical Studies ◽  
Internal Representation ◽  
Simple Assumption ◽  
Probability Functions ◽  
True Value ◽  
The Face ◽  
Economic Choices ◽  
As If

When making economic choices, such as those between goods or gambles, humans act as if their internal representation of the value and probability of a prospect is distorted away from its true value. These distortions give rise to decisions which apparently fail to maximise reward, and preferences that reverse without reason. Why would humans have evolved to encode value and probability in a distorted fashion, in the face of selective pressure for reward-maximising choices? Here, we show that under the simple assumption that humans make decisions with finite computational precision – in other words, that decisions are irreducibly corrupted by noise – the distortions of value and probability displayed by humans are approximately optimal in that they maximise reward and minimise uncertainty. In two empirical studies, we manipulate factors that change the reward-maximising form of distortion, and find that in each case, humans adapt optimally to the manipulation. This work suggests an answer to the longstanding question of why humans make “irrational” economic choices.

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