Edoardo Grillo (Collegio Carlo Alberto)

“Dynamic Campaign Spending”

Abstract

We build a model of electoral campaigning in which two candidates allocate money over time to control the movement of relative popularity. If any gain in a candidate’s popularity tends to decay over time (making it harder for the candidate to maintain or increase her lead when she is already ahead) then the candidates increase their spending over time ahead of the election. Relative popularity follows a modified Brownian motion whose long-run mean depends only on the ratio of starting budgets. We also explore an extension of the model in which the candidates’ budgets evolve over time in response to movements in relative popularity. If building an early lead in the polls helps candidates raise more money that they can put to use in the later stages of the campaign, then candidates have a stronger incentive to spend early, and resources are allocated more evenly over time.