Axiomatising Incomplete Preferences through Sets of Desirable Gambles
Authors: Marco Zaffalon, Enrique Miranda
JAIR 2017 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Our main goal in this paper is to establish a bridge between the axiomatisations of incomplete preferences and imprecise probability models. ... Axiomatisations of rational decision making with incomplete preferences came much later, though, through the works of Seidenfeld et al. (1995), Bewley (2002), Nau (2006), and, more recently, Ok et al. (2012) and Galaabaatar and Karni (2013). ... We establish the equivalence of two very general theories: the first is the decision-theoretic formalisation of incomplete preferences based on the mixture independence axiom; the second is the theory of coherent sets of desirable gambles (bounded variables) developed in the context of imprecise probability and extended here to vector-valued gambles. ... Appendix B contains the proofs of all the results in the paper. |
| Researcher Affiliation | Academia | Marco Zaffalon EMAIL IDSIA Galleria 2 CH-6928 Manno (Lugano), Switzerland; Enrique Miranda EMAIL Department of Statistics and Operations Research University of Oviedo C-Federico Garc ıa Lorca, 18 33007 Oviedo, Spain. |
| Pseudocode | No | The paper describes theoretical concepts, definitions, theorems, propositions, lemmas, and proofs within a mathematical framework. It does not include any sections explicitly labeled as 'Pseudocode' or 'Algorithm', nor are there any structured code-like blocks detailing procedures. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide links to code repositories or mention code in supplementary materials for the methodology described. |
| Open Datasets | No | This paper is purely theoretical, focusing on axiomatizing preferences and exploring equivalences between decision-making theories. It does not use any datasets, public or otherwise, for experimental validation. |
| Dataset Splits | No | The paper is theoretical and does not involve experiments with datasets. Therefore, there are no mentions of training, test, or validation dataset splits. |
| Hardware Specification | No | The paper describes a theoretical framework and does not report on experimental results that would require specific hardware. No details about GPUs, CPUs, or other computing resources are provided. |
| Software Dependencies | No | The paper presents a theoretical mathematical framework. It does not describe any computational experiments or implementations that would necessitate listing specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical in nature, focusing on axiomatizing preferences and mathematical equivalences. It does not describe any experiments, therefore, no experimental setup details, hyperparameters, or training configurations are provided. |