Research On Compatibility Of Characteristics And Application Of Random Matching

Under the background of the shortage of high quality resources in contemporary society,the rational allocation of market resources is of great significance to maintaining social stability.The purpose of the matching mechanism is to improve the utilization rate of resources while maintaining the fairness of the majority as much as possible.The research results are widely used in practical problems such as school choice and house allocation.In the course of research,the shortcomings of the results of deterministic matching are more obvious in fairness,random matching is more concerned with its better fairness properties,and has the advantage of being able to predict and evaluate the results before implementation of the matching.So the research of random matching has important theoretical and practical significance.In this paper,we study the random matching model with finite model conditions,and focus on the compatibility between stochastic dominance efficiency,stochastic dominance strategy-proof and equal treatment of equals,which are commonly used to judge the mechanism.When there exist objective indifferences among the goods to be allocated,the number of species becomes the finite condition of the model.The paper first proves that when the number of species is two,the matching result of PS mechanism satisfies the above three properties at the same time.In other words,three properties are compatible.Secondly,when the number of species is three,the paper gives two types of conclusions.We prove that there is no matching mechanism that satisfies the above three properties when the total number of items to be allocated is four or five.And when the preference is further restricted,the matching result of the PS mechanism satisfies the above three properties at the same time.In the end,based on the analysis of the current situation of computer aided allocation rule in the admissions process of students entering junior middle schools,this paper establishes a stochastic matching model of the rule,analyzes the existing problems through the model,and puts forward suggestions for improving the rule based on random matching theory.In the current educational environment,improving the rule by RSD mechanism can effectively achieve more fairness.In the long run,the equalization of quality education resources can better achieve educational equity.