Two particular types of election misuse are manipulation and bribery. In manipulation, a group of voters chooses to misrepresent its preferences in order to obtain a more desirable outcome, and in bribery an outside agent, the briber, asks (possibly at a cost) a group of voters to change its votes, to obtain some outcome desirable for the briber. Classical results from political science show that, for any reasonable election system, there are scenarios where at least some voters have an incentive to attempt manipulation.
In this thesis we seek to protect elections from manipulators and bribers by making their computational task of finding good manipulations/bribes prohibitively expensive. When this is not possible, we seek to better understand (and even improve) the algorithmic attacks that manipulators and bribers can employ. In doing so, we develop new models of manipulation and bribery, and provide new approaches to studying the computational complexity of bribery and manipulation in elections.