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：鉴于在大规模候选集（$m$个候选人）上指定完整序数偏好的困难性，本研究探讨通过询问选民关于$t < m$个候选人的信息即可计算的投票规则。相较于先前聚焦于该问题特定实例的研究，本文完整刻画了对于任意$1 \leq t < m$可计算的位置计分规则集合——值得注意的是该集合不包含简单多数规则。进而将此结果推广至单一可转移投票（淘汰制投票），证明了类似的不可能性定理。这些否定结论具有信息论意义，且与查询次数无关。最后，针对可通过有限规模查询计算的计分规则，我们给出了确定性或随机化算法为确定得分最高候选人所需查询次数的参数化上下界。虽然确定性算法的上下界之间不存在间隙，但确定随机化算法的精确查询复杂度仍是一个具有挑战性的开放问题——我们解决了其中一个特殊情形。