It is important to study how strategic agents can affect the outcome of an election. There has been a long line of research in the computational study of elections on the complexity of manipulative actions such as manipulation and bribery. These problems model scenarios such as voters casting strategic votes and agents campaigning for voters to change their votes to make a desired candidate win. A common assumption is that the preferences of the voters follow the structure of a domain restriction such as single peakedness, and so manipulators only consider votes that also satisfy this restriction. We introduce the model where the preferences of the voters define their own restriction and strategic actions must ``conform'' by using only these votes. In this model, the election after manipulation will retain common domain restrictions. We explore the computational complexity of conformant manipulative actions and we discuss how conformant manipulative actions relate to other manipulative actions.

Determining the complexity of election attack problems is a major research direction in the computational study of voting problems. The paper "Towards completing the puzzle: complexity of control by replacing, adding, and deleting candidates or voters" by Erd\'elyi et al. (JAAMAS 2021) provides a comprehensive study of the complexity of control problems. The sole open problem is constructive control by replacing voters for 2-Approval. We show that this case is in P, strengthening the recent RP (randomized polynomial-time) upper bound due to Fitzsimmons and Hemaspaandra (IJCAI 2022). We show this by transforming 2-Approval CCRV to weighted matching. We also use this approach to show that priced bribery for 2-Veto elections is in P. With this result, and the accompanying (unsurprising) result that priced bribery for 3-Veto elections is NP-complete, this settles the complexity for $k$-Approval and $k$-Veto standard control and bribery cases.

The computational study of elections generally assumes that the preferences of the electorate come in as a list of votes. Depending on the context, it may be much more natural to represent the preferences of the electorate succinctly, as the distinct votes and their counts. Though the succinct representation may be exponentially smaller than the nonsuccinct, we find only one natural case where the complexity increases, in sharp contrast to the case where each voter has a weight, where the complexity usually increases.

We must properly model attacks and the preferences of the electorate for the computational study of attacks on elections to give us insight into the hardness of attacks in practice. Theoretical and empirical analysis are equally important methods to understand election attacks. I discuss my recent work on domain restrictions on partial preferences and on new election attacks. I propose further study into modeling realistic election attacks and the advancement of the current state of empirical analysis of their hardness by using more advanced statistical techniques.