The algebraic versus the topological approach to additive representations

DOI10.1016/0022-2496(88)90021-1zbMath0663.92024OpenAlexW2123830052MaRDI QIDQ1115377

Peter P. Wakker

Publication date: 1988

Published in: Journal of Mathematical Psychology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-2496(88)90021-1

zbMATH Keywords

continuitybinary relationadditive functionmeasurement theorypreference functionproduct topologyadditive conjoint measurementconnected topological spacesessential coordinates

Mathematics Subject Classification ID

Partial orders, general (06A06) Connections of general topology with other structures, applications (54H99) Mathematical psychology (91E99)

Related Items (51)

Introduction to the special issue in honor of Peter Wakker ⋮ Preferences over rich sets of random variables: on the incompatibility of convexity and semicontinuity in measure ⋮ A note on Wakker's cardinal coordinate independence ⋮ Fechner's strong utility model for choice among \(n > 2\) alternatives: risky lotteries, savage acts, and intertemporal payoffs ⋮ Probability weighting and L-moments ⋮ A monotone model of intertemporal choice ⋮ On the psychophysics of binocular space perception ⋮ The continuity postulate in economic theory: a deconstruction and an integration ⋮ Subjective probability under additive aggregation of conditional preferences ⋮ Subjective expected utility with imperfect perception ⋮ Probabilistic intertemporal choice ⋮ An axiomatization of continuous quasilinear utility ⋮ Preference for knowledge ⋮ Theory of decisions by intra-dimensional comparisons ⋮ A bi-preference interplay between transitivity and completeness: reformulating and extending Schmeidler's theorem ⋮ A simple and general axiomatization of average utility maximization for infinite streams ⋮ Intertemporal choice with savoring of yesterday ⋮ Uniform expected utility criteria for decision making under ignorance or objective ambiguity ⋮ Multiutility representations for incomplete difference preorders ⋮ Axiomatization of weighted (separable) utility ⋮ Subjective expected utility without preferences ⋮ Nontransitive additive conjoint measurement ⋮ Additive representations on rank-ordered sets. I: The algebraic approach ⋮ Concave/convex weighting and utility functions for risk: a new light on classical theorems ⋮ A theory of (relative) discounting ⋮ How to measure the average rate of change? ⋮ What do numbers measure? A new approach to fundamental measurement ⋮ Combining additive representations on subsets into an overall representation ⋮ Rank-additive population ethics ⋮ On the characterization of linear habit formation ⋮ Additive representations on rank-ordered sets. II: The topological approach ⋮ Reference-dependent expected utility with incomplete preferences ⋮ Intertemporal Choice with Continuity Constraints ⋮ Conditional expected utility criteria for decision making under ignorance or objective ambiguity ⋮ Ordered categories and additive conjoint measurement on connected sets ⋮ The sure-thing principle and the comonotonic sure-thing principle: An axiomatic analysis ⋮ Topological connectedness and behavioral assumptions on preferences: a two-way relationship ⋮ The hexagon condition and additive representation for two dimensions: an algebraic approach ⋮ A qualitative characterization of the exponential distribution ⋮ An axiom for concavifiable preferences in view of Alt's theory ⋮ A theory of time preferences over risky outcomes ⋮ Two factor additive conjoint measurement with one solvable component ⋮ Representations of preferences with pseudolinear utility functions ⋮ Completeness and transitivity of preferences on mixture sets ⋮ The intermediate value theorem and decision-making in psychology and economics: an expositional consolidation ⋮ Additive representations on a simplex ⋮ Scale type \((N,N)\) and an order-based topology induced on the automorphism group ⋮ Separating marginal utility and probabilistic risk aversion ⋮ Additive representation for equally spaced structures ⋮ From local to global additive representation ⋮ Additive utilities on densely ordered sets.

Cites Work

• Cardinal coordinate independence for expected utility
• On the extension of additive utilities to infinite sets
• Measurement structures and linear inequalities
• Two extensions of conjoint measurement
• Additivity, utility, and subjective probability
• On the empirical status of axioms in theories of fundamental measurement
• Continuous and Semi-Continuous Utility
• A Note on Weak Separability
• Determinateness of the Utility Function: Revisiting a Controversy of the Thirties
• A Note on "A Four-Flagged Lemma"
• Existence of a Continuous Utility Function: An Elementary Proof
• A Four-Flagged Lemma
• Risk Aversion in the Small and in the Large
• Continuity Properties of Paretian Utility
• Weak Convergence Results for a Class of Multivariate Markov Processes
• The Structure of Utility Functions
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