The online election campaign planning problem: Optimizing election campaign strategies with inaccurate information

Effective management of election campaigns involves dynamic decision-making under uncertainty. Traditional approaches rely heavily on pre-planned strategies that often fail to adapt to real-time changes in voter sentiment and external factors. This paper introduces the Online Election Campaign Planning Problem (OECPP) to optimize the scheduling of campaign activities in the context of U.S. presidential elections. OECPP incorporates sequentially updated predictions that represent assessments of the impact of campaign activities over the course of the campaign. Since these predictions evolve in response to new information and their accuracy cannot be fully assessed without perfect information, we develop deterministic and randomized online algorithms for OECPP that can operate effectively under unreliable and evolving predictions. We evaluate the performance of our algorithms using the competitive ratio (CR), a metric particularly useful when probabilistic modeling is impractical. We begin by establishing a tight upper bound on the CR of the online algorithms for the OECPP under unreliable reward predictions. We then introduce a sequential setup-based CR metric to capture the value of reoptimization as new predictions arrive, and we design deterministic and randomized algorithms that are optimal under this metric. Using data from U.S. presidential elections, we show that randomized online algorithms can significantly outperform their deterministic counterparts in terms of empirical CR. We also find that the effectiveness of randomized algorithms is driven by two factors: the selection of prediction samples for generating activity scenarios and the randomization cut-off, which determines the scenarios to be randomized. The benefit of randomization is non-monotonic, and the best empirical CR is achieved by selectively adding prediction samples to the randomization set.