🤖 AI Summary
This study addresses the problem of simultaneously identifying the piecewise linear additive value functions of two decision makers from anonymous and unlabeled preference responses. By designing a joint preference elicitation mechanism that operates without knowledge of response ownership, the approach uniquely reconstructs both value functions by integrating known breakpoint information, a tailored preference querying strategy, and combinatorial optimization techniques. This work represents the first successful simultaneous identification of multiple decision makers’ additive value functions under an anonymity constraint, thereby overcoming the conventional reliance on explicitly attributed responses in preference modeling. Under noise-free conditions, the method guarantees exact recovery of the complete value functions.
📝 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.