Dynamic Pie: A Strategy for Modeling Trade-Offs in Compositional Variables over Time

The substance of politics involves competition that evolves over time. While our theories about competition emphasize trade-offs across multiple categories, most empirical models tend to oversimplify them by considering trade-offs between one category and everything else. We propose a research strategy for testing theories about trade-off relationships that shape dynamic compositional variables. This approach improves current methods used to analyze compositional dependent variables by addressing two limitations. First, although scholars have considered compositional dependent variables, they have done so in contexts that were not dynamic. Second, current approaches toward graphical presentations become unwieldy when the compositional dependent variable has more than three categories. We demonstrate the utility of our strategy to expand current theories of party support and political budgeting. In both cases, we can extend trade-offs across pairs of alternatives (e.g., prime minister versus all other parties or spending on defense versus everything else) to competition across multiple alternatives.