A Multivariate Complexity Analysis of Lobbying in Multiple Referenda

We extend work by Christian et al. [Review of Economic Design 2007] on lobbying in multiple referenda by first providing a more fine-grained analysis of the computational complexity of the NP-complete LOBBYING problem. Herein, given a binary matrix, the columns represent issues to vote on and the rows correspond to voters making a binary vote on each issue. An issue is approved if a majority of votes has a 1 in the corresponding column. The goal is to get all issues approved by modifying a minimum number of rows to all-1-rows. In our multivariate complexity analysis, we present a more holistic view on the nature of the computational complexity of LOBBYING, providing both (parameterized) tractability and intractability results, depending on various problem parameterizations to be adopted. Moreover, we show non-existence results concerning efficient and effective preprocessing for LOBBYING and introduce natural variants such as RESTRICTED LOBBYING and PARTIAL LOBBYING.

• Type: Journal
• Year: 2012
• Where: AAAI
• Authors: Robert Bredereck, Jiehua Chen, Sepp Hartung, Rolf Niedermeier, Ondrej Suchý, Stefan Kratsch
• Keywords: AAAI 2012, Binary Matrix, Complexity Analysis, Computational Complexity, Intelligent Agents