Influence Across Agents and Issues in Combinatorial and Collective Decision-Making

We consider settings of combinatorial and collective decision-making where a set of agents make choices on a set of issues in sequence based on their preferences over a set of alternatives for each issue. While agents have their initial preferences on issues, they may influence others and be influenced by others, consequently changing their preferences or choices on these issues in the process of decision-making. Though the influence among multiple agents making decisions on one issue and the dependency (influence) among multiple issues decided by one agent have been fully discussed in previous work, the influence from multiple sources across both agents and issues in the context of combinatorial and collective decision-making has been ignored. In this paper, we proposed a preliminary framework to address the influence transcending multiple agents and multiple issues with two rules: weighted influence and one dominant influence.