Gerrymandering: A Briber's Perspective
Abstract
We initiate the study of bribery problem in the context of gerrymandering and reverse gerrymandering. In our most general problem, the input is a set of voters having votes over a set of alternatives, a graph on the voters, a partition of voters into connected districts, cost of every voter for changing her district, a budget for the briber, and a favorite alternative of the briber. The briber needs to compute if the given partition can be modified so that (i) the favorite alternative of the briber wins the resulting election, (ii) the modification is budget feasible, and (iii) every new district is connected. We study four natural variants of the above problem  the graph on voter being arbitrary vs complete graph (corresponds to removing connectedness requirement for districts) and the cost of bribing every voter being uniform vs nonuniform. We show that all the four problems are NPcomplete even under quite restrictive scenarios. Hence our results show that district based elections are quite resistant under this new kind of electoral attack. We complement our hardness results with polynomial time algorithms in some other cases.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 DOI:
 10.48550/arXiv.1909.01583
 arXiv:
 arXiv:1909.01583
 Bibcode:
 2019arXiv190901583D
 Keywords:

 Computer Science  Computer Science and Game Theory;
 Computer Science  Data Structures and Algorithms;
 Computer Science  Multiagent Systems;
 Computer Science  Social and Information Networks
 EPrint:
 Under submission