Research And Application Of Quota Allocation Method

The question of quota allocation,which has a wide range of applications in political science,management science,and game theory,and attracts much attention in all walks of life,is a very important and common problem.Through the previous research,it was found that the problem of quota allocation in real society can be divided into two categories,which are called the single distribution problem and repeated allocation problem in this paper.The current allocation methods are all proposed for the single allocation problem.For the iterative allocation problem,the most common solution at present is to treat it as a plurality of single allocation problems.According to the B-Y Impossibility Theorem,every distribution will inevitably appear unreasonable and unfair.With the number of repeated distributions increases,this inequality will continue to accumulate,which is unreasonable in the long run.In view of this,a new method based on the share of quota allocation was proposed by this paper,which effectively compensates for the shortcomings of the current allocation method.Firstly,this paper systematically analyzes the current quota allocation and quota allocation methods,points out its shortcomings,and proposes repeated allocation problems.Then a new method to solve the iterative distribution problem is proposed,which is called residual accumulation method.At the same time,the Q-value method to deal with the single distribution problem is also improved.Finally,an example is verified and the main research results are finally obtained as follows:(1)Through research and analysis,a new allocation problem called repeated allocation problem is proposed in this paper.(2)A new method for the fair distribution of places called residual accumulation method,is proposed.This method is mainly used to deal with the problem of iterative allocation.This method considers the iterative allocation problem as a system and guarantees that every allocation in the system satisfies the axiom of share.In this case,the remaining number of places will be accumulated and used as part of the input for the next distribution,so that the results of the entire distribution process will be more fair and reasonable.(3)In this paper,the most commonly used q-value method to deal with single assignment problem is improved.The improved method solves the unreasonable phenomenon caused by the classical q-value method when the number of places allocated is small and the difference between the participants is large,and finally makes the application range wider.(4)It is also very simple and fast to use MATLAB to program the residual accumulative method.This method can also be widely applied to the fair distribution of other resources.(5)The paper first used the case to verify the rationality of the improved Q-value method,and then validates the remaining cumulative method in two different conditions: one is the distribution of total number and the number of parties involved in distribution to validate the condition of invariable(US House of Representatives Allocation);The second is to verify the changes of the total number of seats allocated and the number of all parties allocated(graduate student scholarship quota allocation).It is concluded from the final results that the residual accumulation method is more reasonable than the current common allocation method in dealing with the repeated allocation problem.