Dorothea Baumeister

Computational Aspects of Approval Voting

“Yes, we can!” – Barack Obama’s campaign slogan inspired enough of his supporters to go to the polls and give him their “yes” votes that he won the 2008 U.S. presidential election. And this happened notwithstanding the fact that many other voters said “no” when pollsters asked if they viewed Barack Obama as qualified for the office. “Yes” and “no” are perhaps the most basic ways for us, as voters, to express our preferences about candidates, and “yes” and “no” are what approval voting is all about.

How hard is it to bribe the judges? a study of the complexity of bribery in judgment aggregation

Endriss et al. [1,2] initiated the complexity-theoretic study of problems related to judgment aggregation. We extend their results for manipulating two specific judgment aggregation procedures to a whole class of such procedures, and we obtain stronger results by considering not only the classical complexity (NP-hardness) but the parameterized complexity (W[2]-hardness) of these problems with respect to natural parameters. Furthermore, we introduce and study the closely related issue of bribery in judgment aggregation, inspired by work on bribery in voting (see, e.g., [3,4,5]). In manipulation scenarios one of the judges seeks to influence the outcome of the judgment aggregation procedure used by reporting an insincere judgment set. In bribery scenarios, however, an external actor, the briber, seeks to influence the outcome of the judgment aggregation procedure used by bribing some of the judges without exceeding his or her budget. We study three variants of bribery and show W[2]-hardness of the corresponding problems for natural parameters and for one specific judgment aggregation procedure. We also show that in certain special cases one can determine in polynomial time whether there is a successful bribery action.

Complexity of manipulation and bribery in judgment aggregation for uniform premise-based quota rules ☆

Endriss et al. (2012) initiated the complexity-theoretic study of problems related to judgment aggregation. We extend their results on the manipulation of two specific judgment aggregation procedures to a whole class of such procedures, namely to uniform premise-based quota rules. In addition, we consider incomplete judgment sets and the notions of top-respecting and closeness-respecting preferences introduced by Dietrich and List (2007). This complements previous work on the complexity of manipulation in judgment aggregation that focused on Hamming-distance-respecting preferences only, which we also study here. Furthermore, inspired by work on bribery in voting (Faliszewski and Rothe, in press), we introduce and study the closely related issue of bribery in judgment aggregation.

Computational Aspects of Manipulation and Control in Judgment Aggregation

We study computational aspects of various forms of manipulation and control in judgment aggregation, with a focus on the premise-based procedure. For manipulation, we in particular consider incomplete judgment sets and the notions of top-respecting and closeness-respecting preferences introduced by Dietrich and List [13]. This complements previous work on the complexity of manipulation in judgment aggregation that focused on Hamming-distance-induced preferences [14,6], which we also study here. Regarding control, we introduce the notion of control by bundling judges and show that the premise-based procedure is resistant to it in terms of NP-hardness.

Preference Aggregation by Voting

Anna, Belle, and Chris want to spend the afternoon together. They consider to either play miniature golf, or go on a bicycle tour, or go for a swim. However, they cannot come to an agreement, as not all of them have the same preferences.

Positional scoring-based allocation of indivisible goods

We define a family of rules for dividing m indivisible goods among agents, parameterized by a scoring vector and a social welfare aggregation function. We assume that agents’ preferences over sets of goods are additive, but that the input is ordinal: each agent reports her preferences simply by ranking single goods. Similarly to positional scoring rules in voting, a scoring vector

Winner Determination and Manipulation in Minisum and Minimax Committee Elections

s = (s_1, \ldots , s_m)

The complexity of computing minimal unidirectional covering sets

s=(s1,…,sm) consists of m nonincreasing, nonnegative weights, where