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.