Dynamics based on a second poll from plurality approval

Determine how voters should choose approval ballots when a second poll is elicited using the $k$-Plurality Approval protocol, and establish whether a leader-rule-like process initialized with that protocol converges to alternatives with low metric distortion.

Background

The authors propose studying iterative dynamics rather than having voters use the protocol only once. In the suggested process, the initial kk-Plurality Approval outcome is used to elicit a second poll, after which voters must decide how to vote given the additional information.

The paper leaves unresolved both the appropriate voting behavior in response to the second poll and the long-run behavior of a process analogous to the leader rule of Laslier. In particular, it asks whether such dynamics converge to alternatives whose metric distortion is low.

References

Another interesting question raised by our work is regarding the performance of dynamics. For instance, assume that instead of directly voting using our protocol, we elicit a second poll using it. How should voters vote given this additional information? Would perhaps a process akin to \citet{Lasl09a}'s leader rule eventually converge to alternatives with low distortion if we start off with our protocol?

— A Constant Metric Distortion Protocol for Approval Voting Given Plurality Polls  (2608.28340 - Frank et al., 28 Aug 2026) in Section 5, Conclusion and Open Questions

This also ties in with one limitation of our protocol: it is not strategyproof. In both the plurality elicitation phase and the approval phase it can be beneficial for voters to deviate from the protocol. Is it possible to quantify the impact of these deviations?

— A Constant Metric Distortion Protocol for Approval Voting Given Plurality Polls  (2608.28340 - Frank et al., 28 Aug 2026) in Section 5, Conclusion and Open Questions