# The Complexity of Online Bribery in Sequential Elections (Extended Abstract)

## TL;DR

This paper explores the increased computational complexity of bribery in sequential elections where votes arrive over time and the briber has limited information, revealing that such settings can be significantly harder than simultaneous models.

## Contribution

It introduces a new model for online, sequential bribery in elections and analyzes how this setting affects computational complexity, highlighting cases of increased difficulty.

## Key findings

- Sequential bribery can be PSPACE-complete even for polynomial-time winner problems.
- Some election systems do not experience increased complexity in the online bribery setting.
- The paper characterizes the complexity for various election systems in the sequential bribery context.

## Abstract

Prior work on the complexity of bribery assumes that the bribery happens simultaneously, and that the briber has full knowledge of all voters' votes. But neither of those assumptions always holds. In many real-world settings, votes come in sequentially, and the briber may have a use-it-or-lose-it moment to decide whether to bribe/alter a given vote, and at the time of making that decision, the briber may not know what votes remaining voters are planning on casting. In this paper, we introduce a model for, and initiate the study of, bribery in such an online, sequential setting. We show that even for election systems whose winner-determination problem is polynomial-time computable, an online, sequential setting may vastly increase the complexity of bribery, in fact jumping the problem up to completeness for high levels of the polynomial hierarchy or even PSPACE. On the other hand, we show that for some natural, important election systems, such a dramatic complexity increase does not occur, and we pinpoint the complexity of their bribery problems in the online, sequential setting.