Analysis of Social Integration through Inspection Policy

Abstract

This paper applies the inspection policy in reliability theory to social integrations. As a result of shortage of labor forces due to the declining birthrate, many developed countries are increasingly accepting immigrants. However, it has been shown that the acceptance of immigrants increases anti-immigrant sentiment among host citizens and leads to large-scale riots. While social integration policies such as language education for new immigrants and support for labor market can reduce anti-immigrant sentiment, they need high costs. It is necessary to detect the anti-immigrant sentiment based on regular public polls and implement social integration. However, there is no empirical study that proposes the expected costs until the anti-immigrant sentiment is detected and discuss the optimal checking times which minimize them. We formulate three stochastic models, replacing inspection of units with check of the social structure such as people’s feelings for immigrants and failure with riot. This paper proposes extended stochastic models of social structures considering the suppression of a riot. We obtain the expected costs until a riot ends and discuss optimal checking times which minimize them analytically and numerically. These methods used in this paper could be applied to some social problems occurred in the world.