Given a set of candidates and a set of voters, a multi-winner election is conducted when the goal is to choose a group of candidates, that is, a committee. The most common examples of committee are Parliament, committee in an organization\/society, selection panel, judges for a competition, project team, etc. However, there are many other, somehow unlikely, scenarios that can be captured as committee selection such as the selection of movies to be played in a plane, shortlisting research papers for publication, shortlisting tasks, selecting locations for police-stations\/fire-stations in a city, and many more. Thus, a committee generally speaking is chosen to perform some specific tasks for the society. Therefore, it is important that a committee is chosen \u201chonestly\u201d. In the election, voters are asked to rank the candidates depending on their preferences over the candidates. Thereafter, the preferences of voters are aggregated using some voting rule to select the committee. Hence, to choose a committee honestly, it is important that an election is conducted honestly. Now, the questions are (i) how can an election be manipulated?, and (ii) how can we prevent it? If we know the answer to the first question and we also know that such manipulation is \u201chard\u201d for some voting rule R, then if the committee is chosen with voting rule R, then there are very few chances of manipulation. Therefore, it is important to study the computational complexity of various means of manipulating an election. The complexity of manipulation problem is well-studied for single-winner voting rules, while the same is not true for multi-winner voting rules. For single-winner elections, it has been shown that some manipulations are easy to carry out when the number of candidates or voters is small, while some are hard. Therefore, it is interesting to study the complexity of manipulation problems when the committee size is small, or the number of voters is small, or the number of candidates is small. In other words, it is interesting to study parameterized complexity of manipulation problems, when parameterized by the committee size, or the number of voters, or the number of candidates. In this project, we propose to study a family of manipulation problems for multi-winner election.

The grant was provided for doing research under the mentorship of Prof. Saket Saurabh at The Institute of Mathematical Sciences, Chennai. We worked on graph-theoretic problems and the problems in computational social choice theory in the paradigm of parameterized complexity.

The fellowship was provided for doing Ph.D.