Properties of Position Matrices and Their Elections

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