A Savage-style Utility Theory for Belief Functions
Authors: Chunlai Zhou, Biao Qin, Xiaoyong Du
IJCAI 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we provide an axiomatic justification for decision making with belief functions by studying the belief-function counterpart of Savage s Theorem where the state space is finite and the consequence set is a continuum [l, M](l < M). We propose six axioms for a preference relation over acts, and then show that this axiomatization admits a definition of qualitative belief functions comparing preferences over events that guarantees the existence of a belief function on the state space. The key axioms are uniformity and an analogue of the independence axiom. The uniformity axiom is used to ensure that all acts with the same maximal and minimal consequences must be equivalent. And our independence axiom shows the existence of a utility function and implies the uniqueness of the belief function on the state space. Moreover, we prove without the independence axiom the neutrality theorem that two acts are indifferent whenever they generate the same belief functions over consequences. At the end of the paper, we compare our approach with other related decision theories for belief functions. |
| Researcher Affiliation | Academia | Chunlai Zhou, Biao Qin , Xiaoyong Du, Computer Science Department, Renmin University of China, Beijing, CHINA {czhou,qinbiao,duyong}@ruc.edu.cn |
| Pseudocode | No | The paper does not contain any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | No | The paper does not provide any concrete access to source code for the methodology described. |
| Open Datasets | No | This is a theoretical paper and does not involve empirical experiments with datasets. Therefore, there is no mention of dataset availability. |
| Dataset Splits | No | This is a theoretical paper and does not involve empirical experiments with datasets. Therefore, there is no mention of dataset splits (training, validation, test). |
| Hardware Specification | No | This is a theoretical paper and does not describe any computational experiments or hardware used. |
| Software Dependencies | No | This is a theoretical paper and does not describe any computational experiments or software dependencies. |
| Experiment Setup | No | This is a theoretical paper and does not describe any experimental setup details such as hyperparameters or system-level training settings. |