Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence How to Change a Group’s Collective Decision? Noam Hazon Raz Lin Sarit Kraus Department of Computer Science Bar-Ilan University Ramat Gan Israel 52900 fhazonn,linraz,[email protected] Abstract the members of the group have a specific (and restricted) type of preferences, and tends to avoid computational aspects. Persuasion is a common social and economic ac- The work in social choice literature studies manipulation and tivity. It usually arises when conflicting interests bribery and considers richer (and more complex) preference among agents exist, and one of the agents wishes models, but an explicit model of persuasion has not been con- to sway the opinions of others. This paper consid- sidered in this context (we discuss the connection to manipu- ers the problem of an automated agent that needs to lation and bribery in Section 3). influence the decision of a group of self-interested In this paper we model persuasion in the context of social agents that must reach an agreement on a joint ac- choice. Specifically, we assume that there is one agent, the tion. For example, consider an automated agent sender thereafter, that needs to influence the decision of a that aims to reduce the energy consumption of a group of self-interested agents. The group members reach an nonresidential building, by convincing a group of agreement through a voting procedure, which is a common people who share an office to agree on an economy mechanism by which a collective decision is made. In a vot- mode of the air-conditioning and low light inten- ing procedure, participants (voters) express their preferences sity. In this paper we present four problems that via votes, and a voting rule then defines the social outcome address issues of minimality and safety of the per- chosen as a function of the votes cast. suasion process. We discuss the relationships to In every election, there is a need for a reliable entity, similar problems from social choice, and show that responsible for handling the elections; we assume that the if the agents are using Plurality or Veto as their sender is that entity. During the election, each voter submits voting rule all of our problems are in P. We also her vote to the sender, that determines the winner. Thus, the show that with K-Approval, Bucklin and Borda vot- sender will have complete information on the voters’ pref- ing rules some problems become intractable. We erences. Since the voters will agree to use only a reliable thus present heuristics for efficient persuasion with entity as the election organizer, we assume that the sender is Borda, and evaluate them through simulations. compelled (say, by law) to report the true winner of the elec- tion, according to the pre-specified voting rule. However, the 1 Introduction sender may still affect the elections in the following way. Af- ter all the voters submit their votes, the sender may suggest Persuasion is a tool that enables social influence in many cru- that some of them change their minds and commit to different cial areas of human interaction in both personal and business votes. These voters are not allowed to vote again or change relationships. Persuasion is a key component that shapes mar- their votes arbitrarily. Instead, they are given the opportunity keting campaigns [Tybout, 1978], litigation [Bell and Loftus, to approve or disapprove the vote suggested to them by the 1985], and domestic and international political policy [Cobb sender. The voters are not compelled to accept the sender’s and Kuklinski, 1997]. As computers make decisions with suggestion, and they may want to retain their current vote. people in increasingly complex settings, a need has arisen for However, as a reliable entity, the sender sends a suggestion the ability of computers to influence people to adopt strate- only to voters who benefit from her suggestions. gies that will benefit themselves and the group. Consider the example of the agent that tries to reduce the This paper considers an automated agent that needs to in- energy consumption of a nonresidential building where hu- fluence the decision of a group of self-interested agents that man occupants do not have direct financial incentive to save must reach an agreement on a joint action. Traditionally, energy. If the agent is able to convince some of the oc- most of the work on group persuasion appears in economic cupants to agree to her suggestion, then the overall energy and political science literature (see [Lupia, 1992] for a brief consumption of the building will be reduced. Suppose that survey)1. Previous work in these areas usually assumes that the listener. We follow the works in economic which use this term in 1We note that “persuasion” is also a common term in the field any situation where an agent with some preferences tries to influence of argumentation, where there is a dialog between the persuader and the decision of other agents. 198 there are 4 options, and 9 people, with the following prefer- the election organizer, this assumption is well-justified (see ences. Two people prefer 3 4 1 2, two people prefer also [Xia, 2012] which renders this distinction). 4 2 1 3, two people prefer 2 3 1 4 and three In this paper, we investigate the algorithmic aspects of the people prefer 1 2 3 4. Suppose also that 1 is the four persuasion problems. We show that all problems are easy option with the lowest energy consumption and 2 is the most when using Plurality or Veto voting rules. Although PERSUA- wasteful option. Using the Borda rule, which will be defined SION is easy for K-Approval and Bucklin, we show that k- later, the chosen alternative is 2. However, if the agent per- PERSUASION and k-SAFE-PERSUASION are hard (in terms of suades the first two people to approve the vote 3 1 4 2 computational complexity) with these rules. With Borda, all instead of their original vote, option 1 will be selected, which of our problems are hard. We thus propose heuristics for k- is more energy efficient and is also preferred over option 2 PERSUASION and k-SAFE-PERSUASION with Borda, and evalu- by the people that were convinced. We note that since the ate their performance through simulations. Our heuristics are people do not know the preferences of the others, they will not complete, but they are proven correct, e.g., if the heuristic not have an incentive to submit a non-truthful vote in order for SAFE-PERSUASION finds a set of suggestions, it is guar- to manipulate the system. In addition, as a reliable entity, anteed to be safe and benefit the sender and the voters. the agent’s decision making should be operated with trans- parency, so she cannot decide on an alternative by her own, 2 Preliminaries and Definitions ignoring the preferences of the people, and she cannot change their votes without their approval. We have a set of actions (also referred to as alternatives) We propose four variants of the group persuasion problem. A = fa1; : : : ; amg and a set of voters V = f1; : : : ; ng. Each The basic problem is PERSUASION, where we ask the sender voter i is represented by her preference Ri, which is a to- to find a set of voters together with suggestions that will ben- tal order over A; we will also refer to total orders over A as efit her and these voters. Since sending messages to many votes. For readability, we will sometimes denote the order Ri voters may be costly (in terms of time or money), we are by i (and thus a 6i a). Given a preference Ri, we will de- also interested in an optimization version, where the sender is note the alternative that is ranked in the j-th position in Ri as interested in influencing the election while sending the least Ri(j), and by rank(a; Ri) the position of alternative a in Ri. number of messages. The corresponding decision problem is The vector R = (R1;:::;Rn) is called a preference profile. k-PERSUASION. Since the voters are not compelled to accept We have one sender, s, which also has preferences over the the sender’s suggestions (even though they are guaranteed a available actions, denoted Rs. more favorable alternative should they all accept the sugges- We will use voting rules to determine which action will tions), the sender or the voters may attain an even worse out- be selected. A voting rule F is a mapping from the set of come if not all the voters accept the senders suggestions. The all preference profiles to the set of actions. The voting rules set of suggestions that can never lead to a worse outcome is that we consider assign scores to all alternatives; one winner called safe, and we introduce the safe variants of the PERSUA- is then selected among the alternatives with the highest score SION and k-PERSUASION problems, SAFE-PERSUASION and k- using a tie-breaking rule. To simplify the analysis, we assume SAFE-PERSUASION, respectively. Our suggested problems are that the tie-breaking rule is lexicographic, i.e., given a set of very similar to other problems in social choice. Specifically, tied alternatives, it selects one that is maximal with respect to PERSUASION is very similar to the unweighted coalition ma- a fixed ordering . nipulation problem (UCM) [Conitzer and Sandholm, 2002; We will now define the voting rules considered in this pa- Conitzer et al., 2007] and k-PERSUASION is very similar to per.