[Paper Review] Detecting Possible Manipulators in Elections

Palash Dey, Neeldhara Misra+1 more|arXiv (Cornell University)|May 4, 2015

Game Theory and Voting Systems38 references11 citations

TL;DR

This paper introduces computational frameworks to detect potential manipulators in elections by formulating and solving problems like Coalitional Possible Manipulators (CPM) and its variants. It presents polynomial-time algorithms for common voting rules and shows that detection can be tractable even when manipulation is computationally hard, as demonstrated in the Borda rule case.

ABSTRACT

Manipulation is a problem of fundamental importance in the context of voting in which the voters exercise their votes strategically instead of voting honestly to prevent selection of an alternative that is less preferred. The Gibbard-Satterthwaite theorem shows that there is no strategy-proof voting rule that simultaneously satisfies certain combinations of desirable properties. Researchers have attempted to get around the impossibility results in several ways such as domain restriction and computational hardness of manipulation. However these approaches have been shown to have limitations. Since prevention of manipulation seems to be elusive, an interesting research direction therefore is detection of manipulation. Motivated by this, we initiate the study of detection of possible manipulators in an election.We formulate two pertinent computational problems - Coalitional Possible Manipulators (CPM) and Coalitional Possible Manipulators given Winner (CPMW), where a suspect group of voters is provided as input to compute whether they can be a potential coalition of possible manipulators. In the absence of any suspect group, we formulate two more computational problems namely Coalitional Possible Manipulators Search (CPMS), and Coalitional Possible Manipulators Search given Winner (CPMSW). We provide polynomial time algorithms for these problems, for several popular voting rules. For a few other voting rules, we show that these problems are in NP-complete. We observe that detecting manipulation maybe easy even when manipulation is hard, as seen for example, in the case of the Borda voting rule.

Motivation & Objective

• To address the challenge of detecting strategic manipulation in voting systems, where voters act non-honestly to influence outcomes.
• To formalize computational problems for identifying suspect voter groups as potential manipulators, both with and without prior suspect groups.
• To determine the computational complexity of detecting manipulation under various voting rules, especially contrasting cases where manipulation is hard but detection is easy.
• To provide efficient algorithms for detection in widely used voting rules, offering practical tools for election integrity monitoring.

Proposed method

• Formulate the Coalitional Possible Manipulators (CPM) problem: given a set of voters, determine if they could form a coalition that manipulates the election outcome.
• Introduce CPMW, which adds the constraint that the manipulation must lead to a specific winner, enhancing practical relevance.
• Define CPMS and CPMSW as search problems to identify suspect groups when no such group is provided a priori.
• Develop polynomial-time algorithms for CPM and related problems under approval, plurality, and veto voting rules.
• Prove NP-completeness for CPM under certain rules like STV and maximin, indicating computational difficulty in some settings.
• Analyze the complexity gap between manipulation (often hard) and detection (sometimes easy), exemplified by the Borda rule.

Experimental results

Research questions

• RQ1 Can we efficiently detect whether a given group of voters could have manipulated an election outcome under common voting rules?
• RQ2 Is it computationally feasible to search for suspect coalitions of voters who might have manipulated an election, without prior knowledge of the group?
• RQ3 Does the computational hardness of manipulation imply a corresponding hardness in detecting manipulation?
• RQ4 For which voting rules can detection of possible manipulators be solved in polynomial time?

Key findings

• Polynomial-time algorithms exist for detecting possible manipulators under approval, plurality, and veto voting rules.
• The Borda voting rule exemplifies a case where manipulation is computationally hard, yet detection of possible manipulators remains tractable.
• For some voting rules like STV and maximin, the detection problem is NP-complete, indicating inherent computational difficulty.
• The formulation of CPMW allows detection under the constraint that manipulation must lead to a specific winner, enhancing real-world applicability.
• The study reveals a key insight: detection of manipulation can be computationally easy even when manipulation itself is hard, challenging assumptions about the relationship between the two problems.