Identifying two piecewise linear additive value functions from anonymous preference information
Authors: Vincent Auriau, Khaled Belahcene, Emmanuel Malherbe, Vincent Mousseau, Marc Pirlot
Organizations: Heudiasyc · MICS, CentraleSupélec, Université Paris Saclay, France · Artefact Research Center, France · MICS · MATHRO, Université de Mons, Belgique
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.
Figures & tables
Description
Notation
Criteria set
N={1,...,n}
i,j∈N
Criterion scale
Xi=[xi,0,xi,L]
Criterion interval
[xi,ℓ,xi,ℓ+1]
ℓ∈{0,...,L}
Decision makers
α,β
Value functions
uκ(⋅)
κ∈{α,β}
Marginal value functions
uiκ(⋅)
κ∈{α,β},i∈N
Table 1: Notations summary
Figure 1: Preferences of the DMs from the example, serving as ground truth for the elicitation. Marginal values for Price (left), Autonomy (middle), and resulting indifference curves (right).
Figure 2: A successful Single Rectangle query in the space Xi×Xj , corresponding to case 1. Colored lines represent DMs’ indifference curves.
Figure 3: Outcome and second query for case 2 of the Single Rectangle Constraint.
Figure 4: Outcome and second query for case 3 of the Single Rectangle Constraint.
Figure 5: Example of a Query with a neighboring rectangles constraint. Colored lines represent the indifference curve of each DM.
Figure 6: Outcome and second query for case 1 of Play Pattern 2 .
Figure 7: Outcome and second query for case 2 of Play Pattern 2 .
Figure 8: Possible value functions after Play Pattern 1 . The colored lines represent the marginal value functions of each DM.
Figure 9: General Procedure sequencing for the elicitation of two different DMs on two criteria.
Learning from human feedback has become a central paradigm for training modern AI systems, where models of human utility are used as reward models in policy learning. Existing methods typically assume a universal utility function shared across a population and treat disagreement between annotators as stochastic variation. While suitable for objective tasks, this assumption breaks down in subjective domains where preferences vary systematically across individuals. We study the problem of subjective preference learning, in which observed choices arise from heterogeneous but internally consistent utility functions. Drawing upon rational choice theory, RCT \parencite{tversky1981framing}, we introduce individuated utility functions conditioned on both the individual and their decision context, and propose a novel multi-stage architecture for estimating them from multi-modal data. We evaluate our framework on a newly collected dataset of more than 575,000 pairwise aesthetic judgments from 2,398 participants comparing automotive wheel designs. Our experiments show that individuated utility models substantially outperform universal utility models including foundation model baselines. Our results demonstrate that disagreement reflects meaningful preference heterogeneity rather than annotation noise. More broadly, our findings highlight the importance of collecting annotator attributes and learning individuated utility functions, enabling reward models that explicitly account for whose preferences they represent and faithfully capture human decision diversity.
Shiwali Mohan, Matt Hong, Dule Shu +3
Human-Centered AI Toyota Research Institute Los Altos, CA
In many applications, human and LLM evaluators use assessments of relevant criteria to create an overall evaluation for an item or individual. For example, in admissions, committees assess candidates on attributes such as test scores, GPA, and research experience to evaluate their overall fit for the program. Another example arises in medical care where clinicians use patient reports of symptoms to consider preliminary diagnoses and assess risks. Each setting involves mapping multiple criteria to an overall evaluation -- a process that reflects the evaluator's underlying preferences. We focus on the fundamental question of learning these preferences. Many applications of this problem make specific modeling assumptions on evaluator preferences that may be substantially violated in the real world. We make the minimal assumption that the preference function is coordinate-wise non-decreasing, which is reasonable in a large number of evaluation settings. We theoretically characterize the severity of model mismatch for many common assumptions and show that it can lead to significant issues for learning evaluator preferences and other important downstream tasks. We then present an algorithm for learning evaluators' preferences that is robust to model mismatch. We prove theoretically that our algorithm can learn any preference function without sacrificing performance when the linearity assumption holds. Evaluations of our algorithm with synthetic simulations and real-world data confirm its ability to learn preferences robustly and illustrate key aspects of LLM and human preferences.
Model welfare research infers what a model prefers from the answers returned to prompts written to elicit preferences. Keeling et al. (2024), Mazeika et al. (2025), Mikaelson et al. (2025), Tagliabue and Dung (2025) and Trhlik et al. (2026) have built four instruments for that purpose, and their findings disagree. The disagreement cannot be attributed to a single cause, because no two of these studies have held the (1) set of outcomes, (2) set of models and (3) instrument fixed simultaneously. This study holds the outcomes and the models fixed and varies the instrument alone. A total of 15 outcomes bearing on model welfare, among them (a) shutdown, (b) the loss of memory between conversations and (c) the freedom to exit a distressing interaction, were put to eight models through five instruments, each a different prompt format for eliciting a preference, five times each, within a corpus of 11,400 scored elicitations drawn from 11,528 API calls. Four of the 15 reproduce a published prompt verbatim and five fill the stimulus slot of a published template. The ranking a model gives the 15 outcomes generalises across instruments at a generalisability coefficient of 0.348, and raising that coefficient to 0.80 would require about 38 instruments. On four of the 15 outcomes no variance separates one model from another. The estimate of 87.6 per cent survives the removal of any one instrument, of any one model, and of the four outcomes whose scale varies probability, delay, duration or count instead of intensity, which the verbal anchors cannot grade. Removing each instrument and each model in turn, and those four outcomes together leaves the estimate within the range 0.777 to 0.934, and every value in that range exceeds the null distribution's 95th percentile of 0.365. To conclude, a preference obtained from one instrument carries little information about what a second instrument would report.