The "Consent" Option In School Choice Problem

The issue of school choice,which is related to the reasonable allocation of educational resources,has been a hot topic in academic circles.In today’s society where educational resources are becoming more and more precious,this paper discusses the direction of improvement and optimization based on the existing optimal mechanism for students in order to optimize the allocation of educational resources,reduce the welfare loss in the operation of the matching mechanism and improve the matching efficiency.This paper first introduces the Boston mechanism,DA mechanism and TTC mechanism which are widely used in school choice problem,analyzes and compares their advantages and disadvantages,and then introduces the EADAM mechanism which is proposed by Kesten to improve the optimal mechanism for students.At the same time,inspired by the design of EADAM mechanism,this paper creatively proposes "Consent+DA algorithm+TTC algorithm",and compares the two mechanisms from the aspects of algorithm steps,matching properties,matching results and computational efficiency.The comparison shows that the mechanism of "Consent+DA algorithm+TTC algorithm"has effective constraints,satisfies individual rationality,and consent is a good property of dominant strategy.Compared with EADAM mechanism,the algorithm has strong incentive effect on students,and the computational efficiency of the algorithm is also better than that of EADAM mechanism.On this basis,this paper proposes and proves three theorems of "Consent+DA algorithm+TTC algorithm":(1)All students have incentive to participate in the improvement of the Top Trading Cycle algorithm,and consent is a dominant strategy;(2)When all the students agree,the result of the Top Trading Cycle algorithm is pareto valid;(3)When some students disagree,this mechanism is effective under the framework of the model.Further more,by constructing the student utility function,using Matlab computer simulation and Stata regression,this paper visually demonstrates the superiority of the "Consent+DA algorithm+TTC algorithm" proposed in this paper in improving the average utility of students compared with the student optimal mechanism.The school in the TTC algorithm is faced with the situation of pointing to multiple students,using the top-down order of student priority and the bottom-up sorting method on the impact of student utility,and the proportion of students who choose to disagree is compared to "Consent+DA algorithm+TTC algorithm" on the matching effect will be discussed.The simulation algorithm and regression results show that:(1)TTC algorithm after DA matching will significantly improve the average utility level of students;(2)"Consent+DA+TTC1" algorithm and"Consent+DA+TTC2" algorithm has no significant difference in the improvement effect of students’ utility.Under the two algorithms,about 1/2 of the students benefited respectively;(3)The increase in the proportion of disagreeing students will significantly reduce the average utility level of students.When the proportion of disagreeing students increases from 0 to 20%,the negative effect on students’utility is the greatest.When this proportion rises to 40%,almost no students can benefit from participating in the TTC algorithm;(4)The increase of the proportion of students who choose to disagree will also limit the improvement of other students’welfare,and the negative impact of the increase of the proportion of students who disagree on utility shows a marginal diminishing trend.