Computational voting theory: game-theoretic and combinatorial aspects

For at least two thousand years, voting has been used as one of the most effective ways to aggregate people's ordinal preferences. In the last 50 years, the rapid development of Computer Science has revolutionize every aspect of the world, including voting. This motivates us to study (1) conceptually, how computational thinking changes the traditional voting theory, and (2) methodologically, how to better use voting for preference/information aggregation with the help of Computer Science. My Ph.D. work seeks to investigate and foster the interplay between Computer Science and Voting Theory. In this thesis, I will discuss two specific research directions pursued in my Ph.D. work, one for each question asked above. The first focuses on investigating how computational thinking affects the game-theoretic aspects of voting. More precisely, I will discuss the rationale and possibility of using computational complexity to protect voting from a type of strategic behavior of the voters, called manipulation. The second studies a voting setting called Combinatorial Voting, where the set of alternative is exponentially large and has a combinatorial structure. I will focus on the design and analysis of novel voting rules for combinatorial voting that balance computational efficiency and the expressivity of the voting language, in light of some recent developments in Artificial Intelligence.