##### Meng -- Dictatorship and Connectedness for Two-Agent Mechanisms with Weak Preferences
• Agents $$1,2,...,I$$
• Alternatives $$a_1,a_2,...a_K$$
• Each agent partitions the alternatives into subgroups.
• The agent has strict preferences over their subgroups, but is indifferent among options within a subgroup.
• This is basically relaxing things so that indifference $$\sim$$ is allowed in addition to strong preferences $$\succ$$
• Ex: In social choice problems, each subgroup is a singleton.
• Ex: In housing assignment, any two alternatives that give an agent the same house are in the same subgroup for that agent.