Reasoning with PCP-nets in a Multi-Agent Context

C. Cornelio, U. Grandi, J. Goldsmith, N. Mattei, F. Rossi, K. Brent Venable
AAMAS 2015
Abstract
PCP-nets generalize CP-nets to model conditional preferences with probabilistic uncertainty. In this paper we use PCP-nets in a multi-agent context to compactly represent a collection of CP-nets, thus using probabilistic uncertainty to reconcile possibly conflicting qualitative preferences expressed by a group of agents. We then study two key preference reasoning tasks: finding an optimal outcome which best represents the preferences of the agents, and answering dominance queries. Our theoretical and experimental analysis demonstrates that our techniques are efficient and accurate for both reasoning tasks.

Remarks: Some parematers in the experiments where not clear to understand from quick reading (e.g. bottom-left paragraph on p. 976 “total mean over 100 case”)

Experiments:

Election type Culture Candidates Voters Instances Parameters
Ordinal Impartial Culture {2, 4, 8, 16, 32, 64, 128, 256, 512, 1024} {20} 100 None
Ordinal Impartial Culture {8} [1-30] 100 None
Ordinal Hand-Crafted {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824} {1} 10000 None
Ordinal Hand-Crafted {2, 4, 8, 16, 32, 64, 128} {1} 500 None