The generation of preferences represented as CP-nets for experiments and empirical testing has typically been done in an ad hoc manner that may have introduced a large statistical bias in previous experimental work. We present novel polynomial-time algorithms for generating CP-nets with n nodes and maximum in-degree c uniformly at random. We extend this result to several statistical cultures commonly used in the social choice and preference reasoning literature. A CP-net is composed of both a graph and underlying cp-statements; our algorithm is the first to provably generate both the graph structure and cp-statements, and hence the underlying preference orders themselves, uniformly at random. We have released this code as a free and open source project. We use the uniform generation algorithm to investigate the maximum and expected flipping lengths, i.e., the maximum length over all outcomes o and o', of a minimal proof that o is preferred to o'. Using our new statistical evidence, we conjecture that, for CP-nets with binary variables and complete conditional preference tables, the expected flipping length is polynomial in the number of preference variables. This has positive implications for the usability of CP-nets as compact preference models.

Conditional preference networks (CP-nets) are a commonly studied compact formalism for modeling preferences. To study the properties of CP-nets or the performance of CP-net algorithms on average, one needs to generate CP-nets in an equiprobable manner. We discuss common problems with naive generation, including sampling bias, which invalidates the base assumptions of many statistical tests and can undermine the results of an experimental study. We provide a novel algorithm for provably generating acyclic CP-nets uniformly at random. Our method is computationally efficient and allows for multi-valued domains and arbitrary bounds on the indegree in the dependency graph.