Complexity of Optimal Lobbying in Threshold Aggregation

Ilan Nehama

Optimal Lobbying is the problem a lobbyist or a campaign manager faces in a full-information voting scenario of a
multi-issue referendum when trying to influence the result. The Lobby is faced with a profile that specifies for each
voter and each issue whether the voter approves or rejects the issue, and seeks to find the smallest set of voters it
must influence to change their vote, for a desired outcome to be obtained. This computational problem also describes
problems arising in other scenarios of aggregating complex opinions, such as principal-agents incentives scheme in a
complex combinatorial problem, and bribery and manipulation in Truth-Functional Judgement Aggregation. We study the
computational complexity of Optimal Lobbying when the issues are aggregated using an anonymous monotone function and
the family of desired outcomes is an upward-closed family. We analyze this problem with regard to two parameters: the
minimal number of supporters needed to pass an issue, and the size of the maximal minterm of the desired set. We show
that for the extreme values of the parameters, the problem is tractable, and provide algorithms. On the other hand, we
prove intractability of the problem for the non-extremal values, which are common values for the parameters.

July, 2013
Published in: 
Proceedings of the 4th International Conference, ADT 2015, p. 379-395