Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Identifying two piecewise linear additive value functions from anonymous preference information

Vincent Auriau, Khaled Belahcene, Emmanuel Malherbe, Vincent Mousseau, Marc Pirlot

TL;DR

An elicitation procedure is proposed that identifies the two preference models when the marginal value functions are piecewise linear with known breaking points.

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.

Identifying two piecewise linear additive value functions from anonymous preference information

TL;DR

An elicitation procedure is proposed that identifies the two preference models when the marginal value functions are piecewise linear with known breaking points.

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.
Paper Structure (17 sections, 1 theorem, 20 equations, 9 figures, 1 table, 5 algorithms)

This paper contains 17 sections, 1 theorem, 20 equations, 9 figures, 1 table, 5 algorithms.

Table of Contents

  1. Background and Related Work
  2. Problem setting
  3. Play Patterns
  4. Obtaining Single-Rectangle Preference Information
  5. Exploiting Single-Rectangle Preference Information
  6. Obtaining Neighboring-Rectangles Preference Information
  7. Exploiting Neighboring-Rectangles Preference Information.
  8. Propagation Patterns
  9. Identification with two single rectangle constraints
  10. Identification with Single Rectangle and a Neighboring Rectangles queries
  11. General Elicitation Procedure
  12. Initialization
  13. Full elicitation of criteria $i$ and $j$
  14. Elicitation of the remaining criteria
  15. Details for Equation \ref{['eq:k_t']}
  16. ...and 2 more sections

Key Result

Theorem 1

It is possible to elicit two piecewise linear additive preference models based on anonymized preference information using a finite number of indifference queries.

Figures (9)

  • 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 $\mathcal{X}_i \times \mathcal{X}_j$, 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.
  • ...and 4 more figures

Theorems & Definitions (5)

  • Example 1
  • Theorem 1
  • Example 2
  • Example 3
  • Example 4