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Kai Wilker

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2 papers

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AAAI Conference 2020 Conference Paper

Approval-Based Apportionment

Markus Brill
Paul Gölz
Dominik Peters
Ulrike Schmidt-Kraepelin
Kai Wilker

In the apportionment problem, a ﬁxed number of seats must be distributed among parties in proportion to the number of voters supporting each party. We study a generalization of this setting, in which voters cast approval ballots over parties, such that each voter can support multiple parties. This approval-based apportionment setting generalizes traditional apportionment and is a natural restriction of approval-based multiwinner elections, where approval ballots range over individual candidates. Using techniques from both apportionment and multiwinner elections, we are able to provide representation guarantees that are currently out of reach in the general setting of multiwinner elections: First, we show that core-stable committees are guaranteed to exist and can be found in polynomial time. Second, we demonstrate that extended justiﬁed representation is compatible with committee monotonicity.

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AAAI Conference 2019 Conference Paper

Fair Knapsack

Till Fluschnik
Piotr Skowron
Mervin Triphaus
Kai Wilker

We study the following multiagent variant of the knapsack problem. We are given a set of items, a set of voters, and a value of the budget; each item is endowed with a cost and each voter assigns to each item a certain value. The goal is to select a subset of items with the total cost not exceeding the budget, in a way that is consistent with the voters’ preferences. Since the preferences of the voters over the items can vary significantly, we need a way of aggregating these preferences, in order to select the socially best valid knapsack. We study three approaches to aggregating voters’ preferences, which are motivated by the literature on multiwinner elections and fair allocation. This way we introduce the concepts of individually best, diverse, and fair knapsack. We study the computational complexity (including parameterized complexity, and complexity under restricted domains) of the aforementioned multiagent variants of knapsack.

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