Identifying two piecewise linear additive value functions from anonymous preference information
arXiv:2602.20638v1 Announce Type: new Abstract: Eliciting a preference model involves asking a person, named decision-maker, a series of questions. We assume that these preferences can be represented by an additive value function. In this work, we query simultaneously two decision-makers in the aim to elicit their respective value functions. For each query we receive two answers, without noise, but without knowing which answer corresponds to which decision-maker.We propose an elicitation procedure that identifies the two preference models when the marginal value functions are piecewise linear with known breaking points.
arXiv:2602.20638v1 Announce Type: new Abstract: Eliciting a preference model involves asking a person, named decision-maker, a series of questions. We assume that these preferences can be represented by an additive value function. In this work, we query simultaneously two decision-makers in the aim to elicit their respective value functions. For each query we receive two answers, without noise, but without knowing which answer corresponds to which decision-maker.We propose an elicitation procedure that identifies the two preference models when the marginal value functions are piecewise linear with known breaking points.
Executive Summary
This article proposes a novel elicitation procedure for identifying two piecewise linear additive value functions from anonymous preference information. The procedure involves querying two decision-makers simultaneously, receiving two answers, and then utilizing the known breaking points to identify the respective value functions. While this approach addresses a significant challenge in preference elicitation, its application is contingent upon the availability of known breaking points, which may not be feasible in all scenarios. The procedure's efficacy relies on the assumption of piecewise linear marginal value functions, which may not accurately capture real-world preferences.
Key Points
- ▸ The article introduces a new elicitation procedure for identifying two piecewise linear additive value functions from anonymous preference information.
- ▸ The procedure involves querying two decision-makers simultaneously and utilizing known breaking points to identify the respective value functions.
- ▸ The efficacy of the procedure relies on the assumption of piecewise linear marginal value functions and the availability of known breaking points.
Merits
Strength in addressing a significant challenge in preference elicitation
The article tackles a crucial problem in decision theory, namely identifying additive value functions from anonymous preference information, and proposes a novel procedure to address this challenge.
Practical application in decision-making scenarios
The proposed procedure has the potential to be applied in various decision-making contexts, such as multi-criteria decision analysis and preference-based group decision support systems.
Demerits
Limitation of known breaking points
The efficacy of the procedure relies on the availability of known breaking points, which may not be feasible in all scenarios, thereby limiting its practical application.
Assumption of piecewise linear marginal value functions
The procedure's assumption of piecewise linear marginal value functions may not accurately capture real-world preferences, which may lead to suboptimal decision outcomes.
Expert Commentary
While the article proposes a novel and innovative procedure for identifying piecewise linear additive value functions from anonymous preference information, its practical application is contingent upon the availability of known breaking points and the accuracy of the assumption of piecewise linear marginal value functions. Nevertheless, the article's contribution to decision theory and preference modeling is significant, and its findings have the potential to enhance the accuracy and efficiency of decision-making in various fields. To further improve the procedure, future research should investigate methods for estimating breaking points and relaxing the assumption of piecewise linear marginal value functions.
Recommendations
- ✓ To enhance the practical application of the proposed procedure, researchers should investigate methods for estimating breaking points in scenarios where they are unknown.
- ✓ Future research should focus on relaxing the assumption of piecewise linear marginal value functions to improve the accuracy of the procedure in capturing real-world preferences.