Abstract
The ties of preference and priorities are commonly seen and widely used in daily life. When the agent considers the priority order of some selected objects to be the same, the final matching result may be affected. People sometimes require strict preference ranking in order to facilitate the use of matching models, which can cause controversy and dissatisfaction with people in the matching. In order to effectively solve the above problems, this paper surveys what these impacts are and how they affect the final result of matching. According to the analysis, it is proven that when there is a preference of indifference, Pareto efficiency is unstable and the deferred acceptance algorithm cannot be used for market matching. In addition, the Pareto-improving draft mechanism has proven to be powerful without imposing a strict preference. This mechanism can also avoid the complex process and other negative consequences of handing ties arbitrarily.
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