Algorithmic Approach of Majority Voting With Agents' Inclusiveness for Facility Resource Matching

In a two-sided matching with preferences, an agent has preferences over the agents from the other side. In a head-to-head election between any two matchings, the agent votes for the matching with a better allocation in the pairing based on its preference. A matching M is popular when the number of votes for M is not less than the number of votes for any other matching M' in such an election. A U-popular matching is introduced recently with a two-sided matching model where U and W are the two sets of agents, but only the preferences of the agents from U are emphasized, and the preferences of the agents from W are ignored. The matching, which is popular among the votes of the agents from U, is defined as U-popular. We consider such a model for a one-to-one matching where the agents from U have an inclusive mindset and want to integrate the voting decision of the agents from W into their voting process. In parallel, the agents from W rely more on their ranking on the preference list of the agents from U than their own preferences due to the uncertainty involved in the construction of their preferences. We define an inclusive voting model with such a predominant-subordinate agent scenario (U as predominant, W as subordinate) and prove that the Boston mechanism matching is U-popular under the model. However, it is possible that the U-popular matching is not the choice of the majority of agents. The choice to be neutral is added in the voting process, and the U-neutral matching type is introduced when the majority of agents vote for neutral. We characterize the U-neutral and max-size U-neutral matching under the inclusive voting model and propose a polynomial-time algorithm to determine a max-size U-neutral matching. The experiments we performed with synthetic instances endorse the algorithm based on the theoretical foundations established.