It remains an open question how to determine the winner of an election when voter preferences are incomplete or uncertain. One option is to assume some probability space over the voting profile and select the Most Probable Winner (MPW) -- the candidate or candidates with the best chance of winning. In this paper, we propose an alternative winner interpretation, selecting the Most Expected Winner (MEW) according to the expected performance of the candidates. We separate the uncertainty in voter preferences into the generation step and the observation step, which gives rise to a unified voting profile combining both incomplete and probabilistic voting profiles. We use this framework to establish the theoretical hardness of \mew over incomplete voter preferences, and then identify a collection of tractable cases for a variety of voting profiles, including those based on the popular Repeated Insertion Model (RIM) and its special case, the Mallows model. We develop solvers customized for various voter preference types to quantify the candidate performance for the individual voters, and propose a pruning strategy that optimizes computation. The performance of the proposed solvers and pruning strategy is evaluated extensively on real and synthetic benchmarks, showing that our methods are practical.

翻译：当选民偏好不完整或不确定时，如何确定选举胜者仍是一个悬而未决的问题。一种方案是假设投票概况上存在某个概率空间，并选择最可能胜者（MPW）——即获胜概率最大的候选人或候选人组合。本文提出另一种胜者解释，根据候选人的期望表现选择最期望胜者（MEW）。我们将选民偏好的不确定性分解为生成步骤与观察步骤，由此形成统一投票概况，融合了不完整投票概况与概率投票概况。利用该框架，我们证明了在不完整选民偏好下MEW问题的理论难度，进而识别出一系列可处理情形，适用于多种投票概况，包括基于流行的重复插入模型（RIM）及其特例Mallows模型。我们针对不同选民偏好类型定制求解器，用于量化单个选民视角下的候选人表现，并提出优化计算的剪枝策略。通过在真实与合成基准上的广泛评估，表明我们提出的求解器与剪枝策略具有实用性。