When Votes Change and Committees Should (Not)

Robert Bredereck; Till Fluschnik; Andrzej Kaczmarczyk

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arXiv · 2005.02300

When Votes Change and Committees Should (Not)

Robert Bredereck·Till Fluschnik·Andrzej Kaczmarczyk

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Abstract

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.

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Robert Bredereck, Till Fluschnik, Andrzej Kaczmarczyk. 2020-05-05. When Votes Change and Committees Should (Not). https://arxiv.org/abs/2005.02300

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