Preference structures through different lenses

Collective decision-making problems, such as elections or resource allocation, require aggregating individual preferences into a collective outcome. Although each agent relies on her own evaluation criteria to form her preferences, it is generally acknowledged in computational social choice (COMSOC) that individual preferences are often shaped and driven, at least to some extent, by an underlying preference structure. A classical and widely studied example is the single-peaked axis, where alternatives are arranged along a line, each agent has a most-preferred alternative (the peak), and her preference decreases as one moves away from this peak in either direction. A concrete illustration is the left–right political axis: while political preferences are complex, involving various evaluation criteria unique to each agent, it has repeatedly been observed that they tend to organize around this dimension. Beyond single-peakedness, a wide variety of preference structures have been studied in COMSOC. These structures provide both theoretical insight and computational benefits, such as stronger guarantees on collective decisions or more efficient algorithms. In this talk, I will first review some recent work on preference structures, including my own. I will then open a new research direction (I am about to explore), motivated by a simple observation: to elicit individual preferences, a common language of expression is often required - thus, the agents may be asked to express their preferences as full or partial rankings, approval ballots, pairwise comparisons, etc. These formats act as an interface between agents’ internal preferences and the data we observe, and inevitably constrain or distort the information that can be expressed. Understanding how preference formats shape the structures we are able to identify is therefore crucial for reliable and interpretable collective decision-making.