Aggregating preferences under incomplete or constrained feedback is a fundamental problem in social choice and related domains. While prior work has established strong impossibility results for pairwise comparisons, this paper extends the inquiry to improvement feedback, where voters express incremental adjustments rather than complete preferences. We provide a complete characterization of the positional scoring rules that can be computed given improvement feedback. Interestingly, while plurality is learnable under improvement feedback—unlike with pairwise feedback—strong impossibility results persist for many other positional scoring rules. Furthermore, we show that improvement feedback, unlike pairwise feedback, does not suffice for the computation of any Condorcet-consistent rule. We complement our theoretical findings with experimental results, providing further insights into the practical implications of improvement feedback for preference aggregation.

Figuring out group choices when people can’t give full opinions is a key challenge in voting and decision-making. Past research showed it’s often impossible to get good results when people only compare two options at a time. This study looks at a different kind of input, where people suggest small improvements instead of ranking everything. We identify which voting methods can still work with this kind of feedback. Interestingly, one popular method (plurality) works here, while it does not in the comparison setting. However, many other voting methods still face major limits. The study also finds that this feedback type doesn’t help with rules meant to reflect the true majority favorite. We add experiments to explore how these ideas might play out in practice.