An important question in elections is the determine whether a candidate can be a winner when some votes are absent. We study this determining winner with the absent votes (WAV) problem when the votes are top-truncated. We show that the WAV problem is NP-complete for the single transferable vote, Maximin, and Copeland, and propose a special case of positional scoring rule such that the problem can be computed in polynomial time. Our results in top-truncated rankings differ from the results in full rankings as their hardness results still hold when the number of candidates or the number of missing votes are bounded, while we show that the problem can be solved in polynomial time in either case.

翻译：选举中的一个重要问题是在部分选票缺席时确定候选人是否可能成为获胜者。我们研究了当选票为顶部截断排序时，确定缺席投票获胜者（WAV）问题。我们证明，对于单记可转移投票、马克西明规则和科普兰规则，WAV问题是NP完全的，同时提出了一种位置评分规则的特例，使得该问题可在多项式时间内求解。我们在顶部截断排序中的结果与完整排序中的结果不同——在完整排序中，当候选人数或缺失投票数有界时，其困难性结果仍然成立，而我们表明在这两种情况下该问题均可在多项式时间内解决。