{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T22:55:47Z","timestamp":1769554547534,"version":"3.49.0"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T00:00:00Z","timestamp":1769472000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72271108"],"award-info":[{"award-number":["72271108"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Humanities and Social Science Foundation of Ministry of Education of China","award":["20YJA630028"],"award-info":[{"award-number":["20YJA630028"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Among existing preference elicitation methods, the trade-off method offers an advantage over others in mitigating the influence of probability weighting on preferences, as it does not require assuming a specific form for the probability weighting function. However, when accounting for the dependence of probability weighting on the choice-set outcome range (CSOR), the conventional trade-off method may lead to improper elicitation of preferences due to its inability to control the CSOR. In order to concurrently circumvent the impacts of the CSOR and probability weighting on preferences in the elicitation procedure, we introduce the Range-Fixed Trade-off Method (RFTM) and provide its full derivation and concrete implementation steps under the framework of rank-dependent utility theory (RDU). The RFTM not only retains the advantages of the conventional trade-off method but also evades the effects of the CSOR on preferences by fixing the CSOR. The results of empirical investigations into the efficacy of RFTM indicate that, compared to the existing trade-off method, utility functions derived from RFTM exhibit a lower degree of risk aversion. This result is compatible with existing experimental observations and conclusions, thus implying that RFTM can effectively elicit individual preferences, thereby preventing or mitigating the bias in preferences arising from CSOR variations in the conventional trade-off approach. Furthermore, the experimental results demonstrate that the probability weighting function remains nonlinear even within a fixed CSOR. This indicates that, under the premise of preferences depending on the CSOR, non-expected utility theories still hold promising development prospects in the future. In summary, RFTM not only provides a more effective and reliable approach for preference elicitation but also makes it feasible to study the impact of changes in the CSOR on preferences, thereby providing methodological support for the future development of CSOR-dependent non-expected utility theories.<\/jats:p>","DOI":"10.3390\/systems14020127","type":"journal-article","created":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T09:21:40Z","timestamp":1769505700000},"page":"127","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Range-Fixed Trade-Off Method: A Preference Elicitation Approach Considering the Dependence of Probability Weighting on Outcome Range"],"prefix":"10.3390","volume":"14","author":[{"given":"Rongyuan","family":"Liu","sequence":"first","affiliation":[{"name":"School of Business and Management, Jilin University, Changchun 130012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunhao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Business and Management, Jilin University, Changchun 130012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,27]]},"reference":[{"key":"ref_1","unstructured":"von Neumann, J., and Morgenstern, O. (1947). Theory of Games and Economic Behavior, Princeton University Press. [2nd ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1086\/257177","article-title":"The Utility of Wealth","volume":"60","author":"Markowitz","year":"1952","journal-title":"J. Polit. Econ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1213","DOI":"10.1287\/mnsc.31.10.1213","article-title":"Probability versus Certainty Equivalence Methods in Utility Measurement: Are They Equivalent?","volume":"31","author":"Hershey","year":"1985","journal-title":"Manag. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1287\/mnsc.42.8.1131","article-title":"Eliciting von Neumann\u2013Morgenstern Utilities When Probabilities Are Distorted or Unknown","volume":"42","author":"Wakker","year":"1996","journal-title":"Manag. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"503","DOI":"10.2307\/1907921","article-title":"Le comportement de l\u2019homme rationnel devant le risque: Critique des postulats et axiomes de l\u2019\u00e9cole am\u00e9ricaine","volume":"21","author":"Allais","year":"1953","journal-title":"Econometrica"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/0167-2681(82)90008-7","article-title":"A Theory of Anticipated Utility","volume":"3","author":"Quiggin","year":"1982","journal-title":"J. Econ. Behav. Organ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF00122574","article-title":"Advances in Prospect Theory: Cumulative Representation of Uncertainty","volume":"5","author":"Tversky","year":"1992","journal-title":"J. Risk Uncertain."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1007\/s11238-021-09811-6","article-title":"A Simple Nonparametric Method for Eliciting Prospect Theory\u2019s Value Function and Measuring Loss Aversion under Risk and Ambiguity","volume":"91","author":"Blavatskyy","year":"2021","journal-title":"Theory Decis."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/s11166-008-9040-2","article-title":"Third-Generation Prospect Theory","volume":"36","author":"Schmidt","year":"2008","journal-title":"J. Risk Uncertain."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11166-017-9266-y","article-title":"Accommodating Stake Effects under Prospect Theory","volume":"55","author":"Bouchouicha","year":"2017","journal-title":"J. Risk Uncertain."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"693","DOI":"10.3982\/ECTA11733","article-title":"Cautious Expected Utility and the Certainty Effect","volume":"83","author":"Dillenberger","year":"2015","journal-title":"Econometrica"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2812","DOI":"10.1287\/mnsc.2017.2744","article-title":"Range-Dependent Utility","volume":"64","author":"Kontek","year":"2018","journal-title":"Manag. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1287\/mnsc.2016.2588","article-title":"Target-Adjusted Utility Functions and Expected-Utility Paradoxes","volume":"64","author":"Schneider","year":"2018","journal-title":"Manag. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"eade7972","DOI":"10.1126\/sciadv.ade7972","article-title":"Dynamic Prospect Theory: Two Core Decision Theories Coexist in the Gambling Behavior of Monkeys and Humans","volume":"9","author":"Tymula","year":"2023","journal-title":"Sci. Adv."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1497","DOI":"10.1287\/mnsc.46.11.1497.12080","article-title":"Parameter-Free Elicitation of Utility and Probability Weighting Functions","volume":"46","author":"Abdellaoui","year":"2000","journal-title":"Manag. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1023\/B:RISK.0000026096.48985.a3","article-title":"Is Probability Weighting Sensitive to the Magnitude of Consequences? An Experimental Investigation on Losses","volume":"28","year":"2004","journal-title":"J. Risk Uncertain."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1322","DOI":"10.1287\/mnsc.1070.0846","article-title":"An Empirical Test of Gain\u2013Loss Separability in Prospect Theory","volume":"54","author":"Wu","year":"2008","journal-title":"Manag. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s11166-010-9090-0","article-title":"Rationality on the Rise: Why Relative Risk Aversion Increases with Stake Size","volume":"40","author":"Bruhin","year":"2010","journal-title":"J. Risk Uncertain."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"263","DOI":"10.2307\/1914185","article-title":"Prospect Theory: An Analysis of Decision under Risk","volume":"47","author":"Kahneman","year":"1979","journal-title":"Econometrica"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"120994","DOI":"10.1016\/j.ins.2024.120994","article-title":"Large Group Decision-Making with a Rough Integrated Asymmetric Cloud Model under Multi-Granularity Linguistic Environment","volume":"678","author":"Jiang","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.3846\/tede.2025.23597","article-title":"Classification and Identification of Medical Insurance Fraud: A Case-Based Reasoning Approach","volume":"31","author":"Liu","year":"2025","journal-title":"Technol. Econ. Dev. Econ."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"102821","DOI":"10.1016\/j.jmp.2023.102821","article-title":"A Contextual Range-Dependent Model for Choice under Risk","volume":"118","author":"Baucells","year":"2024","journal-title":"J. Math. Psychol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"175","DOI":"10.3758\/BF03193146","article-title":"G*Power 3: A Flexible Statistical Power Analysis Program for the Social, Behavioral, and Biomedical Sciences","volume":"39","author":"Faul","year":"2007","journal-title":"Behav. Res. Methods"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s10683-006-9159-4","article-title":"z-Tree: Zurich Toolbox for Ready-Made Economic Experiments","volume":"10","author":"Fischbacher","year":"2007","journal-title":"Exp. Econ."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/0167-2681(90)90086-S","article-title":"The Effect on the Preference-Reversal Phenomenon of Using Choice Indifferences","volume":"13","author":"Bostic","year":"1990","journal-title":"J. Econ. Behav. Organ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"497","DOI":"10.2307\/2998573","article-title":"The Probability Weighting Function","volume":"66","author":"Prelec","year":"1998","journal-title":"Econometrica"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1006\/cogp.1998.0710","article-title":"On the Shape of the Probability Weighting Function","volume":"38","author":"Gonzalez","year":"1999","journal-title":"Cogn. Psychol."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Wakker, P.P. (2010). Prospect Theory: For Risk and Ambiguity, Cambridge University Press.","DOI":"10.1017\/CBO9780511779329"},{"key":"ref_29","unstructured":"National Health Commission of the People\u2019s Republic of China, Ministry of Education of the People\u2019s Republic of China, Ministry of Science and Technology of the People\u2019s Republic of China, and National Administration of Traditional Chinese Medicine (2026, January 20). Measures for Ethical Review of Life Science and Medical Research Involving Human Beings, Available online: https:\/\/www.gov.cn\/zhengce\/zhengceku\/2023-02\/28\/content_5743658.htm."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/2\/127\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T09:45:19Z","timestamp":1769507119000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/2\/127"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,27]]},"references-count":29,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["systems14020127"],"URL":"https:\/\/doi.org\/10.3390\/systems14020127","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,27]]}}}