Bypassing Combinatorial Protections: Polynomial-Time Algorithms for Single-Peaked Electorates

For many election systems, bribery (and related) attacks have been shown NP-hard using constructions on combinatorially rich structures such as partitions and covers. It is important to learn how robust these hardness protection results are, in order to find whether they can be relied on in practice. This paper shows that for voters who follow the most central politicalscience model of electorates--single-peaked preferences--those protections vanish. By using single-peaked preferences to simplify combinatorial covering challenges, we show that NPhard bribery problems--including those for Kemeny and Llull elections--fall to polynomial time. By using single-peaked preferences to simplify combinatorial partition challenges, we show that NP-hard partition-of-voters problems fall to polynomial time. We furthermore show that for single-peaked electorates, the winner problems for Dodgson and Kemeny elections, though p 2-complete in the general case, fall to polynomial time. And we completely...

• Type: Conference
• Year: 2010
• Where: AAAI
• Authors: Felix Brandt, Markus Brill, Edith Hemaspaandra, Lane A. Hemaspaandra
• Keywords: AAAI 2010, Intelligent Agents, Polynomial Time, Show, Single-peaked Preferences