Conditional Approval Voting: Winner Determination, Strategic Control and Proportionality Considerations

Picture a group of friends in Warsaw deciding on a shared meal: a starter and a main course. One among them loves pierogi and would like to go for bigos afterwards--easy to vote for in the classical approval voting setting. Meanwhile, another in the group, while also approving bigos with pierogi, opts for placki ziemniaczane, if żurek is the chosen starter. How could such a voter express their intricate culinary preferences? The answer unfolds in the work of Barrot and Lang (2016), where they introduce Conditional Approval Voting: a framework tailored for handling complex preferences over interdependent issues, in the approval setting. During the talk, I'll provide a brief overview of three recent works, exploring various conditional approval voting rules and addressing algorithmic and axiomatic challenges related to winner determination, strategic control, and proportional representation.