# Model of Multi-Branch Trees for Efficient Resource Allocation
## 5 Discussion  
We propose a new budget allocation method that determines all projects' relative evaluation values by integrating assessments among projects in small groups. Using this method, adopting internal assessment within each group is considered to be quite rational because an insider generally has a very firm grasp of one's group and projects. In fact, internal assessment also lightens the evaluation cost of budget allocators compared with an overall examination. Our method is simple because each evaluator determines the relative weights of projects whose number corresponds to the number of one's child nodes, the relative weights of all projects are calculated just as they satisfy the relative weights determined by each evaluator, and allocation is determined by using the gross. As shown in Section 4, this is one of the methods whereby assessment costs are minimized because all evaluators assess all projects through the division of labor. The method is thus regarded as a method that uses backward induction [25; 26] because allocation is finally determined which keeps the relative weight rates of all evaluators. We will analyze aspects of our method through comparison with methods of backward induction in the literature for further extensions. Our method is also one of the methods that satisfies allocational efficiency, where the lowest evaluators in a tree structure assess all projects of their departments and the assessments are completely maintained in the final allocation, as shown in Section 4. Although this simple policy is reflected in an empirical view because we modify a widely adopted method based on incrementalism, our method is deterministic and procedurally defined. Although this method is for budget allocation for either medium-scale or small-scale organizations, it is possible to substitute an organization, a section, a policy, or a person for a project. Therefore, the range of application for this method is very wide and includes budget allocation at large-scale organizations, labor evaluation, and the assessment of employees. As shown in Section 4, we considered the incentive compatibility of the method. Let us assume that there is a malicious director, say [PERSON], among the lowest evaluators on a tree structure, and thus, [PERSON] wants to get more money by controlling their own assessments of projects in a department that they themselves manage. If [PERSON] can select the projects that [PERSON]'s bosses assess, one could control the budget allocation as one wants. Therefore, the projects that [PERSON]'s bosses assess must be selected either by the bosses themselves or randomly. As shown in the theorem of incentive compatibility in Section 4, our method is safe from such a malicious director if [PERSON] cannot control [PERSON]'s bosses' choices. As discussed in the Introduction section, moreover, the bosses may not assess projects because they may not have special knowledge on them. This is why the bosses require reports on sales points of the projects from the directors. In consideration of this point, any evaluator must select and assess the projects that they are in charge of after all of one's lower evaluators in a tree structure have completed their assessment of the projects that they are in charge of. This study on our method is a first step, and thus, many issues still remain. In the current version of our study, the issue of estimation is out of scope although important. This is because there is no guarantee that a relative weight of a project assessed by any evaluator is correctly measured. This point suggests that we must systematically consider errors in estimation if this is adopted for practical use. For further studies, two kinds of errors that occur during an evaluation should be investigated. One is that internal assessment within each group is not necessarily appropriate. We cannot prevent an insider from underestimation or overestimation caused by various types of human relationships or preconceived ideas.