Detecting Possible Manipulators in Elections

Manipulation is a problem of fundamental importance in the context of voting rules in which the voters vote strategically instead of voting honestly to avoid 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, etc. However these approaches have been shown to have limitations. Since prevention of manipulation seems to be elusive, a natural research direction therefore is detection of manipulation. Motivated by this, we study detection of possible manipulators in an election. We formulate two pertinent computational problems - Coalitional Possible Manipulators (CPM) and Coalitional Possible Manipulators given Winner (CPMW). For several popular voting rules, we provide polynomial time algorithms for both the CPM and CPMW problems. For certain other voting rules, we show that these two problems are in NPC. A striking observation of our study is that detecting manipulation is surprisingly easy for a few well known voting rules. We then move on to weighted elections and show similar results.