Fundamentals for Political Scientists: Relations & Functions Will H. Moore September 14, 2005 Hagle (1995:7) opines that “functions are valuable to social scientists because most relation- ships can be modelled in the form of a function.” I would add that functions are valuable for those political scientists who want to make specific theoretical claims and/or use statistics to test the implications of theories of politics. In other words, functions are valuable be- cause they are explicit: they make very specific arguments about relationships. In addition, functions play a key role in developing statistical models. What is a function? Functions may be defined in several ways, each developed more fully below. To get us started functions provide a specific description of the association or re- lationship between two (or among several) concepts (in theoretical work) or variables (in empirical work). In other words, a function describes the relationship between ordered pairs of sets under special conditions (specified below). That said, some students can come away from an introduction to relations and functions with a misguided notion that the key to developing sound theory is to master a wide array of functions and then see which one applies to a given theoretical or statistical problem. One might characterize this as a ‘toolbox’ approach to political science, where different functions are hammers and wrenches to be tried here and there until one finds one that works. Perhaps such an approach would yield insight, but I am not sanguine: one’s thinking about politics is unlikely to be usefully informed by mastery of different functional forms. Instead, a general working knowledge of functions can be used to sharpen one’s thinking and bring greater specificity to one’s theories of politics. In particular, learning to be able to translate verbal conjectures into graphs and/or equations that represent those conjectures is a valuable skill to develop. That skill is essential for anyone who wants to do formal modelling. Finally, such a working knowledge is critical to mastering the material in statistics courses and will help one select appropriate statistical models for hypothesis testing. 1