Abstract
We show that a strongly independent preorder on a possibly infinite dimensional convex set that satisfies two of the following conditions must satisfy the third: (i) the Archimedean continuity condition; (ii) mixture continuity; and (iii) comparability under the preorder is an equivalence relation. In addition, if the preorder is nontrivial (has nonempty asymmetric part) and satisfies two of the following conditions, it must satisfy the third: (i') a modest strengthening of the Archimedean condition; (ii) mixture continuity; and (iii') completeness. Applications to decision making under conditions of risk and uncertainty are provided, illustrating the relevance of infinite dimensionality. (C) 2018 Elsevier B.V. All rights reserved.
| Original language | English |
|---|---|
| Pages (from-to) | 141-145 |
| Number of pages | 5 |
| Journal | Mathematical Social Sciences |
| Volume | 93 |
| DOIs | |
| Publication status | Published - May 2018 |
| MoE publication type | A1 Journal article-refereed |
Funding
David McCarthy thanks the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 750012H) for support. We are grateful to Teruji Thomas and two referees for very helpful comments.
Keywords
- MULTI-UTILITY REPRESENTATIONS
- INCOMPLETE PREFERENCES
- EXPECTED UTILITY
Fingerprint
Dive into the research topics of 'Continuity and completeness of strongly independent preorders'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver