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"Reverse Gerrymandering": Manipulation in Multi-Group Decision Making

District-based manipulation, or gerrymandering, is usually taken to refer to agents who are in fixed location, and an external division is imposed upon them. However, in many real-world setting, there is an external, fixed division – an organizational chart of a company, or markets for a particular product. In these cases, agents may wish to move around (“reverse gerrymandering”), as each of them tries to maximize their influence across the company’s subunits, or resources are “working” to be allocated to areas where they will be most needed.In this paper we explore an iterative dynamic in this setting, finding that allowing this decentralized system results, in some particular cases, in a stable equilibrium, though in general, the setting may end up in a cycle. We further examine how this decentralized process affects the social welfare of the system.