Voting algorithms are used to choose candidates by an electorate. However, voter participation is variable and uncertain, and projections from polls or past elections are uncertain because voter preferences may change. Furthermore, electoral victory margins are often slim. Variable voter participation or preferences, and slim margins of decision, have implications for choosing a voting algorithm. We focus on approval voting (AV) and compare it to plurality voting (PV), regarding their robustness to uncertainty in voting outcomes. We ask: by how much can voting outcomes change without altering the election outcomes? We see fairly consistent empirical differences between AV and PV. In single-winner elections, PV tends to be more robust to vote uncertainty than AV in races with large victory margins, while AV tends to be more robust at low victory margins. Two conflicting concepts—approval flattening and approval magnification—explain this tendency for reversal of robust dominance between PV and AV. We also examine the robustness to vote uncertainty of PV in elections for proportional representation of parties.

投票算法用于由选民选择候选人。但是，选民的参与是可变且不确定的，而民意测验或以往选举的预测也不确定，因为选民的偏好可能会发生变化。此外，选举获胜的机会通常很小。可变的投票人参与或偏爱以及微小的决策余地，对选择投票算法有影响。我们关注批准投票（AV）并将其与复数投票（PV）进行比较，因为它们对于投票结果不确定性具有鲁棒性。我们问：在不改变选举结果的情况下，投票结果可以改变多少？我们看到AV和PV之间存在相当一致的经验差异。在单获胜者的选举中，PV在具有较大获胜率的比赛中比AV在投票不确定性方面更具优势，而AV往往会在低获胜率的情况下变得更强大。批准扁平化和批准放大率这两个相互矛盾的概念解释了这种逆转PV和AV之间强大支配地位的趋势。我们还研究了党派代表比例选举中PV投票不确定性的鲁棒性。