UC Irvine

Human Society is complex and involves interaction of many individuals in a society on different levels. Social Science and its fields study how people are organized into groups (Anthropology, Sociology), what are the core motivations of humans (Philosophy), what biological and psychological factors are involved in their behavior (Psychology), how humans compete and cooperate to achieve individual goals and society prosperity (Economics), and how a large society can organize and govern itself (Political Science). Underlying them all are laws of human social world that are the basis of human behavior, organization, interactions and decision making. Just like in Physics these laws can be scientifically studied and expressed using the tools of mathematics.

The tools that have been used in the 4 papers included in the dissertation include: Social Network Analysis, Game Theory, Statistics and general tools of mathematical analysis. In the first 3 papers human organization into groups is explored by using Social Network as a base model of society. The first paper studies specific work behavior and organization in software development communities finding complex pattern of organization and providing a formula that can predict success of a project. The 2nd and 3rd papers use abstract mathematical models based on social networks and game theory to study human interactions, cooperation and success. The papers showed how social network structure plays a role in these interactions and helped to understand the very core of human interaction and how it can be modeled with game theory and what are important considerations for parameters used in creating specific game theory and network models.

The 4th paper looks at human politics and elections and studies bias that can exist prior to elections with manipulation of electoral district maps to favor specific party, which is known as gerrymandering. Using tools of mathematics - functional analysis and statistics, the paper derives equations and core symmetries of biased and unbiased distribution of voters. These symmetries are analogues to physical symmetries that are the basis of physical laws.