Properties of Position Matrices and Their Elections

We study the properties of elections that have a given position matrix (in such elections each candidate is ranked on each position by a number of voters specified in the matrix). We show that counting elections that generate a given position matrix is #P-complete. Consequently, sampling such elections uniformly at random seems challenging and we propose a simpler algorithm, without hard guarantees. Next, we consider the problem of testing if a given matrix can be implemented by an election with a certain structure (such as single-peakedness or group-separability). Finally, we consider the problem of checking if a given position matrix can be implemented by an election with a Condorcet winner. We complement our theoretical findings with experiments.

Authors

• Niclas Boehmer Harvard University Hasso Plattner Institute, University of Potsdam
• Jin-Yi Cai University of Wisconsin-Madison
• Piotr Faliszewski AGH University
• Austen Z. Fan University of Wisconsin-Madison
• Łukasz Janeczko AGH University of Science and Technology
• Andrzej Kaczmarczyk AGH University
• Tomasz Wąs University of Oxford

Keywords

• GTEP: Social Choice / Voting