The Topological Methods In Social Welfare Functions

The history of the study for social welfare functions is about two hundred years. Welfare function is a so popular thesis in economics at all times that many famous economists are attracted to discuss this problem. People first use Benthamic methods in this study. But now because of modern social welfare functions coming into being, which makes it possible to consider only individual ordering utilities to study social welfare functions. Chapter one of this paper is a simple introduction of researching backgrounds and developing story about social welfare functions, which let people have a basic understanding about it. In chapter two, we only consider individual ordering utilities, without considering the interpersonal comparability and cardinality. We use topological methods to study social welfare functions and prove Arrow impossibility theorem. In chapter three of this paper, we succeed to the methods in chapter two and obtain impossibility theorem for the case when interpersonal comparisons are admitted but cardinality is still denied.