How Hard is Bribery in Party Based Elections?

In a party-based election voters are grouped into parties and the voters belonging to the same party are assumed to cast their votes according to the fixed party preference over the set of candidates. For such elections, we investigate the complexity of the following problem: can we make some distinguished candidate win (or lose) the election by bribing at most k voters to switch from their original parties to parties with similar preferences? Here, we adopt the Kendall-Tau distance and the Hamming distance to measure the similarity of the party preferences. We achieve a wide range of complexity results for this problem under a variety of voting rules, including Borda, r-Approval, Condorcet, Copeland for every 0 ≤ α ≤ 1 and Maximin.