Bribery for Coalitions in Parliamentary Elections

We study the computational complexity of bribery in parliamentary voting, in settings where the briber is (also) interested in the success of an entire set of political parties - a ``coalition'' - rather than an individual party. We introduce two variants of the problem: the Coalition-Bribery Problem (CB) and the Coalition-Bribery-with-Preferred-party Problem (CBP). In CB, the goal is to maximize the total number of seats held by a coalition, while in CBP, there are two objectives: to maximize the votes for the preferred party, while also ensuring that the total number of seats held by the coalition is above the target support (e.g. majority). We study the complexity of these bribery problems under two positional scoring functions - Plurality and Borda - and for multiple bribery types - $1$-bribery, $\$$-bribery, swap-bribery, and coalition-shift-bribery. We also consider both the case where seats are only allotted to parties whose number of votes passes some minimum support level and the case with no such minimum. We provide polynomial-time algorithms to solve some of these problems and prove that the others are NP-hard.