Solving election manipulation using integer partitioning problems

• Authors: Andrew Lin
• Venue: The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
• Year: 2011

An interesting problem of multi-agent systems is that of voting, in which the preferences of autonomous agents are to be combined. Applications of voting include modeling social structures, search engine ranking, and choosing a leader among computational agents. In the setting of voting, it is very important that each agent presents truthful information about his or her preferences, and not manipulate. The choice of election system may encourage or discourage voters from manipulating. Because manipulation often results in undesirable consequences, making the determination of such intractable is an important goal. An interesting metric on the robustness of an election system concerns the frequency in which opportunities of manipulations occur in a given election system. Previous work by Walsh has evaluated the frequency of manipulation in the context of very specific election systems, particularly veto, when the number of candidates is limited to at most three, by showing that manipulation problems in these systems can be directly viewed as problems of (Two-Way) Partition, and then using the best known heuristics of Partition. Walsh also claimed similar results hold for k-candidate veto election by way of problems involving multi-way partitions. We show that the results for k-candidate veto elections do not follow directly from common versions of partition problems and require non-trivial modifications to Multi-Way Partition. With these modifications, we confirm Walsh's claim that these elections are also vulnerable to manipulation. Our new computational problems also allow one to evaluate manipulation in the general case of k-candidate scoring protocols. We investigate the complexity of manipulating scoring protocols using new algorithms we derive by extending the known algorithms of Multi-Way Partition. It is our conclusion that the problems of manipulation in more general scoring protocols of four or more candidates are not vulnerable to manipulation using extensions of the current known algorithms of Multi-Way Partition. This may be due to weaknesses in these algorithms or complexity in manipulating general scoring protocols.