Algorithmic aspects of manipulation and anonymization in social choice and social networks

This thesis presents a study of several combinatorial problems related to social choice and social networks. The main concern is their computational complexity, with an emphasis on their parameterized complexity. The goal is to devise efficient algorithms for each of the problems studied here, or to prove that, under widely-accepted assumptions, such algorithms cannot exist. The problems discussed in Chapter 3 and in Chapter 4 are about manipulating a given election, where some relationships between the entities of the election are assumed. This can be seen as if the election occurs on top of an underlying social network, connecting the voters participating in the election or the candidates which the voters vote on. The problem discussed in Chapter 3, COMBINATORIAL CANDIDATE CONTROL, following the paper by Chen et al. [42], is about manipulating an election by changing the set of candidates which the voters vote on. That is, there is an external agent who can add new candidates or delete existing candidates. A combinatorial structure over the candidates is assumed, such that whenever the external agent adds or removes a candidate, a predefined set of candidates (related to the chosen candidate) are added or removed from the election. The problem discussed in Chapter 4, COMBINATORIAL SHIFT BRIBERY, following the paper by Bredereck et al. [31], is also about manipulating an election. Here, however, the external agent can change the way some voters vote. Specifically, a combinatorial structure over the voters is assumed, such that the external agent can change the position of its preferred candidate in sets of voters, following some predefined patterns. The problem discussed in Chapter 5, ELECTION ANONYMIZATION, following the paper by Talmon [139], is also about elections. The main concern here, however, is preserving the privacy of the voters, when the votes are published, along with some additional (private) information. The task is to transform a given election such that each vote would appear at least k times. By doing so, even an adversary which knows how some voters vote, cannot identify individual voters.