Electing a single committee of a small size is a classical and well-understood voting situation. Being interested in a sequence of committees, we introduce and study two time-dependent multistage models based on simple Plurality voting. Therein, we are given a sequence of voting profiles (stages) over the same set of agents and candidates, and our task is to find a small committee for each stage of high score. In the conservative model we additionally require that any two consecutive committees have a small symmetric difference. Analogously, in the revolutionary model we require large symmetric differences. We prove both models to be NP-hard even for a constant number of agents, and, based on this, initiate a parameterized complexity analysis for the most natural parameters and combinations thereof. Among other results, we prove both models to be in XP yet W[1]-hard regarding the number of stages, and that being revolutionary seems to be "easier" than being conservative: If the (upper- resp. lower-) bound on the size of symmetric differences is constant, the conservative model remains NP-hard while the revolutionary model becomes polynomial-time solvable.

翻译：选举单一的小规模委员会是经典且研究充分的投票情境。针对连续的委员会序列，我们引入并研究了基于简单多数投票的两种时间依赖性多阶段模型。在该模型中，我们获得一系列投票概貌（阶段），这些概貌基于相同的候选人与投票者集合，任务是为每个阶段选出具有高得分的小型委员会。在保守模型中，我们额外要求任意两个连续委员会具有较小的对称差。类似地，在革命模型中则要求较大的对称差。我们证明即使投票者数量为常数，这两个模型均为NP难问题，并由此针对最自然的参数及其组合展开参数化复杂性分析。除其他结果外，我们证明这两个模型均属于XP类，但关于阶段数具有W[1]-难度，同时革命模型似乎比保守模型“更易处理”：若对称差的上（或下）界为常数，保守模型仍保持NP难，而革命模型可在多项式时间内求解。