In this chapter I walk through the how and why of a theory of issue intensity and electoral competition and build the basics of the mathematical model used to explore intensity theory. I lay out six foundational assumptions of the model drawn from existing theories of elections in political science or political economy. The assumptions rule out current explanations for frustrated majorities so that I can show that the combination of issue intensity and electoral competition alone can cause frustrated majorities. I show how costly political action becomes an important part of the story when candidates cannot perfectly observe the issue intensity of voters. I then present a simple mathematical model with numerical examples to provide intuition for analysis in subsequent chapters.