Motivated by the difficulty of specifying complete ordinal preferences over a large set of $m$ candidates, we study voting rules that are computable by querying voters about $t < m$ candidates. Generalizing prior works that focused on specific instances of this problem, our paper fully characterizes the set of positional scoring rules that can be computed for any $1 \leq t < m$, which notably does not include plurality. We then extend this to show a similar impossibility result for single transferable vote (elimination voting). These negative results are information-theoretic and agnostic to the number of queries. Finally, for scoring rules that are computable with limited-sized queries, we give parameterized upper and lower bounds on the number of such queries a deterministic or randomized algorithm must make to determine the score-maximizing candidate. While there is no gap between our bounds for deterministic algorithms, identifying the exact query complexity for randomized algorithms is a challenging open problem, of which we solve one special case.

翻译：受限于在大量候选者（共$m$个）中指定完整序数偏好的困难性，本文研究通过向选民查询$t < m$个候选者即可计算的投票规则。既往工作聚焦于该问题的特定实例，而本文则全面刻画了对于任意$1 \leq t < m$可计算的定位评分规则集——值得注意的是，该集合不包含多数制规则。我们进一步将此结论推广至单一可转移投票（淘汰制投票），揭示其存在类似的不可能性。这些否定性结论属于信息论范畴，与查询次数无关。最后，针对可通过有限规模查询计算的评分规则，我们给出了确定性或随机算法为确定得分最大化候选者所需查询次数的参数化上界与下界。尽管确定性算法的上下界无差距，但确定随机算法的精确查询复杂度仍是一个具有挑战性的开放问题，本文仅解决了其中一个特例。