Resolving the Complexity of Some Fundamental Problems in Computational Social Choice

This thesis is in the area called computational social choice which is an intersection area of algorithms and social choice theory.Comment: Ph.D. Thesi

The Shield that Never Was: Societies with Single-Peaked Preferences are More Open to Manipulation and Control

Much work has been devoted, during the past twenty years, to using complexity to protect elections from manipulation and control. Many results have been obtained showing NP-hardness shields, and recently there has been much focus on whether such worst-case hardness protections can be bypassed by frequently correct heuristics or by approximations. This paper takes a very different approach: We argue that when electorates follow the canonical political science model of societal preferences the complexity shield never existed in the first place. In particular, we show that for electorates having single-peaked preferences, many existing NP-hardness results on manipulation and control evaporate.Comment: 38 pages, 2 figure

Design of Experiments for Learning Personalized Visual Preferences of Occupants In Private Offices

Occupants working in offices with controllable shading and lighting systems often perform adaptive actions (raising/lowering shades, increasing/decreasing light levels) in an attempt to restore their preferred state of the room. This preference for different room conditions (states) has been shown to vary from person to person and may be affected by exterior conditions. This paper presents an online data-driven methodology which actively queries a new occupant for learning their personalized visual preferences. Preference is governed by a latent preference relation equivalent to a scalar utility function (the higher the utility, the higher the preference for that state). Information about user preferences is available via pairwise - comparison queries (duels between two different states). We model our uncertainty about the utility via a Gaussian Process (GP) prior and the probability of the winner of each duel by means of a Bernoulli likelihood. This generalized preference model is then used in conjunction with different acquisition functions (pure exploration, expected improvement, dueling Thompson sampling) to drive the elicitation process by actively selecting new queries to pose to the occupant. Two different sets of experiments were conducted, focused on actively selecting new duels: (i) to learn the structure of utility everywhere with fewest possible queries and (ii) to learn the maximum of the utility with fewest possible queries. We illustrate the benefits of our frameworks by showing that our approach needs drastically fewer duels for inferring the structure or the maximum of underlying latent utility function as opposed to randomized data collection. The results of this study can be used to develop efficient, real-time adaptive shading and lighting controls

Combinatorial Voter Control in Elections

Voter control problems model situations such as an external agent trying to affect the result of an election by adding voters, for example by convincing some voters to vote who would otherwise not attend the election. Traditionally, voters are added one at a time, with the goal of making a distinguished alternative win by adding a minimum number of voters. In this paper, we initiate the study of combinatorial variants of control by adding voters: In our setting, when we choose to add a voter~$v$, we also have to add a whole bundle $\kappa(v)$ of voters associated with $v$. We study the computational complexity of this problem for two of the most basic voting rules, namely the Plurality rule and the Condorcet rule.Comment: An extended abstract appears in MFCS 201

Computational aspects of voting: a literature survey

Preference aggregation is a topic of study in different fields such as philosophy, mathematics, economics and political science. Recently, computational aspects of preference aggregation have gained especial attention and “computational politics” has emerged as a marked line of research in computer science with a clear concentration on voting protocols. The field of voting systems, rooted in social choice theory, has expanded notably in both depth and breadth in the last few decades. A significant amount of this growth comes from studies concerning the computational aspects of voting systems. This thesis comprehensively reviews the work on voting systems (from a computing perspective) by listing, classifying and comparing the results obtained by different researchers in the field. This survey covers a wide range of new and historical results yet provides a profound commentary on related work as individual studies and in relation to other related work and to the field in general. The deliverables serve as an overview where students and novice researchers in the field can start and also as a depository that can be referred to when searching for specific results. A comprehensive literature survey of the computational aspects of voting is a task that has not been undertaken yet and is initially realized here. Part of this research was dedicated to creating a web-depository that contains material and references related to the topic based on the survey. The purpose was to create a dynamic version of the survey that can be updated with latest findings and as an online practical reference

Possible Winners in Noisy Elections

We consider the problem of predicting winners in elections, for the case where we are given complete knowledge about all possible candidates, all possible voters (together with their preferences), but where it is uncertain either which candidates exactly register for the election or which voters cast their votes. Under reasonable assumptions, our problems reduce to counting variants of election control problems. We either give polynomial-time algorithms or prove #P-completeness results for counting variants of control by adding/deleting candidates/voters for Plurality, k-Approval, Approval, Condorcet, and Maximin voting rules. We consider both the general case, where voters' preferences are unrestricted, and the case where voters' preferences are single-peaked.Comment: 34 page