The complexity of online voter control in sequential elections

  • Edith Hemaspaandra
  • Lane A. Hemaspaandra
  • Jörg Rothe

DOI: 10.1007/s10458-016-9349-1

Cite this article as:
Hemaspaandra, E., Hemaspaandra, L.A. & Rothe, J. Auton Agent Multi-Agent Syst (2016). doi:10.1007/s10458-016-9349-1


Previous work on voter control, which refers to situations where a chair seeks to change the outcome of an election by deleting, adding, or partitioning voters, takes for granted that the chair knows all the voters’ preferences and that all votes are cast simultaneously. However, elections are often held sequentially and the chair thus knows only the previously cast votes and not the future ones, yet needs to decide instantaneously which control action to take. We introduce a framework that models online voter control in sequential elections. We show that the related problems can be much harder than in the standard (non-online) case: For certain election systems, even with efficient winner problems, online control by deleting, adding, or partitioning voters is \(\mathrm {PSPACE}\)-complete, even if there are only two candidates. In addition, we obtain (by a new characterization of coNP in terms of weight-bounded alternating Turing machines) completeness for \({\mathrm {coNP}}\) in the deleting/adding cases with a bounded deletion/addition limit, and we obtain completeness for \({\mathrm {NP}}\) in the partition cases with an additional restriction. We also show that for plurality, online control by deleting or adding voters is in \({\mathrm {P}}\), and for partitioning voters is \({\mathrm {coNP}}\)-hard.


Computational social choice Voter control of elections Sequential elections Online control 

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Edith Hemaspaandra
    • 1
  • Lane A. Hemaspaandra
    • 2
  • Jörg Rothe
    • 3
  1. 1.Department of Computer ScienceRochester Institute of TechnologyRochesterUSA
  2. 2.Department of Computer ScienceUniversity of RochesterRochesterUSA
  3. 3.Institut für InformatikHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany

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