Voting platforms can offer participants the option to sequentially modify their preferences, whenever they have a reason to do so. But such iterative voting may never converge, meaning that a state where all agents are happy with their submitted preferences may never be reached. This problem has received increasing attention within the area of computational social choice. Yet, the relevant literature hinges on the rather stringent assumption that the agents are able to rank all alternatives they are presented with, i.e., that they hold preferences that are linear orders. We relax this assumption and investigate iterative voting under partial preferences. To that end, we define and study two families of rules that extend the well-known -approval rules in the standard voting framework. Although we show that for none of these rules convergence is guaranteed in general, we also are able to identify natural conditions under which such guarantees can be given. Finally, we conduct simulation experiments to test the practical implications of our results.

中文翻译：

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具有部分偏好的迭代投票


投票平台可以为参与者提供按顺序修改其偏好的选项，只要他们有理由这样做。但这种迭代投票可能永远不会收敛，这意味着所有代理都对其提交的偏好感到满意的状态可能永远无法达到。这个问题在计算社会选择领域受到越来越多的关注。然而，相关文献依赖于相当严格的假设，即代理人能够对他们遇到的所有替代方案进行排序，即他们持有线性顺序的偏好。我们放松这个假设并研究部分偏好下的迭代投票。为此，我们定义并研究了两个规则系列，它们扩展了标准投票框架中众所周知的批准规则。尽管我们表明，一般而言，这些规则的收敛性都不能得到保证，但我们也能够确定可以提供此类保证的自然条件。最后，我们进行模拟实验来测试我们结果的实际意义。