Metric distortion Under Probabilistic Voting

Understand

Metric distortion in social choice is a framework for evaluating how well voting rules minimize social cost when both voters and candidates exist in a shared metric space, with a voter's cost defined by their distance to a candidate.

• Voters submit rankings, and the rule aggregates these rankings to determine a winner.
• We extend this framework to incorporate probabilistic voting, recognizing that real-world voters exhibit randomness in how they vote.
• Our extension includes various probability functions, notably the widely studied Plackett-Luce (PL) model.