Capacities satisfying the buoyancy property on average Capacities satisfying the buoyancy property on average

Buoyancy and its dual property antibuoyancy relate to the Pigou-Dalton principal of progressive transfers. When capacities satisfying the antibuoyancy property are used in Choquet integration, the effective weights applied are decreasing with respect to the inputs when arranged in increasing order....

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Bibliographic Details
Published in:Theory and decision Vol. 99; no. 1-2; pp. 13 - 36
Main Authors: Beliakov, Gleb, James, Simon, Wu, Jian-Zhang
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2025
Springer Nature B.V
Subjects:
Averages
Behavioral/Experimental Economics
Buoyancy
Cardinality
Decision making
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Experiments
Finance
Game Theory
Indexes
Insurance
Integer programming
Linear programming
Management
Operations Research/Decision Theory
Property
Social and Behav. Sciences
Statistics for Business
Usefulness
Variables
Welfare
Choquet integral
Capacity
Antibuoyant fuzzy measures
Shapley indices
ISSN:0040-5833, 1573-7187
Online Access:Get full text
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Summary:Buoyancy and its dual property antibuoyancy relate to the Pigou-Dalton principal of progressive transfers. When capacities satisfying the antibuoyancy property are used in Choquet integration, the effective weights applied are decreasing with respect to the inputs when arranged in increasing order. As well as this property having useful interpretations for measures of welfare and species diversity, it also allows for efficient solutions when the Choquet integral is used as an objective function in optimisation. In this contribution, we explore two weaker properties, which can be interpreted in terms of overall behavior with the capacity being buoyant or antibuoyant on average. One of these is expressed simply in terms of the Shapley interaction indices and amounts to buoyancy holding on average between pairs of weights, while the other looks at buoyancy of the cardinality indices. We explore the relationship between these and other capacity properties, formulate linear constraints that can be used when learning capacity weights from data, propose some random generation methods and finally present some numerical experiments to validate their usefulness.
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ISSN:0040-5833
1573-7187
DOI:10.1007/s11238-025-10039-x