A Preference Elicitation Approach for the Ordered Weighted Averaging Criterion using Solution Choice Observations

TL;DR

This paper presents an optimization-based, data-driven method for eliciting preferences in the ordered weighted averaging (OWA) criterion using passive solution choice observations, effectively capturing decision maker preferences under uncertainty.

Contribution

It introduces a novel passive preference elicitation approach for OWA weights using observed choices, avoiding explicit comparisons and handling inconsistencies.

Findings

Method performs well with inconsistent choices.

Outperforms pairwise comparison methods.

Effective in risk-averse decision scenarios.

Abstract

Decisions under uncertainty or with multiple objectives usually require the decision maker to formulate a preference regarding risks or trade-offs. If this preference is known, the ordered weighted averaging (OWA) criterion can be applied to aggregate scenarios or objectives into a single function. Formulating this preference, however, can be challenging, as we need to make explicit what is usually only implicit knowledge. We explore an optimization-based method of preference elicitation to identify appropriate OWA weights. We follow a data-driven approach, assuming the existence of observations, where the decision maker has chosen the preferred solution, but otherwise remains passive during the elicitation process. We then use these observations to determine the underlying preference by finding the preference vector that is at minimum distance to the polyhedra of feasible vectors for each of the observations. Using our optimization-based model, weights are determined by solving an alternating sequence of linear programs and standard OWA problems. Numerical experiments on risk-averse preference vectors for selection, assignment and knapsack problems show that our passive elicitation method compares well against having to conduct pairwise comparisons and performs particularly well when there are inconsistencies in the decision maker's choices.