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：在选民偏好不完整或不确定的情况下如何确定选举获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，并选择最可能获胜者（MPW）——即获胜概率最大的候选人。本文提出另一种获胜者解释，即根据候选人的期望表现选择最期望获胜者（MEW）。我们将选民偏好的不确定性分离为生成步骤和观测步骤，从而得到一个结合不完整投票概况和概率投票概况的统一投票框架。利用该框架，我们证明了在不完整选民偏好下MEW的理论计算复杂性，进而识别出一系列易于处理的情形，涵盖多种投票概况，包括基于流行的重复插入模型（RIM）及其特例Mallows模型的情形。我们针对不同选民偏好类型开发了专用求解器，用以量化个体选民对候选人的偏好表现，并提出了一种优化计算的剪枝策略。通过在实际基准测试和合成基准测试上的广泛评估，我们展示了所提求解器和剪枝策略的实用性。