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Understanding Election Rigging: Preferences, Imperfect Information, and Manipulation Strategies

This study delves into the complexities of manipulating election outcomes through improper preference aggregation methods such as voting. It highlights the distinction between theoretical models—which assume perfect information—and practical observations of imperfect information scenarios. We prove that manipulation is NP-Complete theoretically but suggest that practical heuristics can undermine these assumptions. The research also examines agenda rigging by election officers and introduces innovative heuristics that can enhance voting protocols. Our findings emphasize the need for meticulous design in electoral systems to safeguard against manipulation.

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Understanding Election Rigging: Preferences, Imperfect Information, and Manipulation Strategies

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  1. How to Rig Elections and Competitions

  2. Outline • A common way to aggregate agents preferences - voting • But it can be manipulated! • Current models assume perfect information • We analyzed a model of imperfect information • Theoretically, manipulation is hard: NP-Complete proofs • Practically it is not: Heuristics and experimental evaluation • Conclusion, Future work

  3. Why Voting? • Preference aggregation - to a socially desirable decision • Not only agents… • Human decisions among a collection of alternatives • Sport tournaments • But it can be manipulated if we have perfect information • By a single voter or a coalition of voters • By the election officer

  4. Our Model - Imperfect Information • Agenda rigging by the election officer • Linear order • Tree order • Complexity results • Verifying an agenda is in P • Finding a perfect agenda seems to be hard • Empirical results • Easy-to-implement heuristics performed well • Tested against random and real data • Motivation - better design of voting protocols

  5. Basic Definitions • Set of outcomes/candidates, • Imperfect information ballot matrix M, • Voting trees A C B A C B A C A B C D C D

  6. Linear Order Tree • Verifying an agenda is O(n2) - with dynamic programming • A candidate can only benefit by going late in an order • And this is not true for general trees! • Finding an order for a particular candidate to win: • With a non-zero probability - O(n2) • With at least a certain probability

  7. Weak Version of Rigged Agenda • A run - • An order agenda together with the intended outcomes • P[r | M] - a probability that the run will result in our candidate • WIIRA Problem - • Set of candidates, Ω • Imperfect information matrix, M • A favored candidate, ω* • A probability p • Is there a run in which the winner is ω*, s.t. P[r | M] ≥ p ? • NP-C, from the k-HCA problem on tournaments

  8. Balanced Tree Order • Verifying an agenda is O(n2) • Finding an order for a particular candidate to win: • With a non-zero probability - open problem [Lang07] • With at least a certain probability - NP-C [Vu08]

  9. From Theory to Practice “Concern: It might be that there are effective heuristics to manipulate an election, even though manipulation is NP-complete. Discussion: True. The existence of effective heuristics would weaken any practical import of our idea. It would be very interesting to find such heuristics.” [Bartholdi89]

  10. Linear Order – Conversion • Probabilistic data  deterministic data • Simple convert • Threshold convert • Not better than random order

  11. General Approach • Heuristics: • Far adversary . . . . • Best win • Local search • Random order • Two data sets: • Random data- uniform and normal distribution • Real data - 29 teams from the NBA, top 13 tennis players 1 2 m-2 m-1 ω*

  12. Linear Order- Normal Distribution

  13. Linear Order- 13 Tennis Players

  14. Balanced Tree- Normal Distribution

  15. Balanced Tree- 13 Tennis Players

  16. Balanced Tree- 29 NBA Teams

  17. Conclusion • Two voting protocols with incomplete information • Agenda verification is in P • Manipulation by the officer seems to be hard • Far adversary, best win and local search can help a lot! • Future: other voting protocols {hazonn,sarit}@cs.biu.ac.il, {mjw,ped}@csc.liv.ac.uk

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