A Dynamic Model of Presidential Nomination Campaigns

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Abstract
Recent campaigns have demonstrated the importance of dynamic elements in affecting the selection of presidential nominees. This paper develops a mathematical model to analyze these dynamics. The heart of the model is the assumed relationship between the ability to acquire resources and success in primaries and caucuses. The expenditure of resources leads to greater electoral success, while greater electoral success (in particular, exceeding expectations in a primary or caucus) leads to greater resource-gathering capabilities. A difference equation model of these relationships is proposed. I prove that any campaign of this form is necessarily unstable, which implies that most candidates will be “winnowed out” necessarily, while only a very few, but at least one candidate, will necessarily “have momentum.” This result is true whether there are two or many contenders. However, I also argue that the larger the number of candidates, the stronger the dynamic forces, and thus the more rapid the “winnowing out” process.

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