Single Transferable Vote: Incomplete Knowledge and Communication Issues

In many real world elections, agents are not required to rank all candidates. We study three of the most common methods used to modify voting rules to deal with such partial votes. These methods modify scoring rules (like the Borda count), elimination style rules (like single transferable vote) and rules based on the tournament graph (like Copeland) respectively. We argue that with an elimination style voting rule like single transferable vote, partial voting does not change the situations where strategic voting is possible. However, with scoring rules and rules based on the tournament graph, partial voting can increase the situations where strategic voting is possible. As a consequence, the computational complexity of computing a strategic vote can change. For example, with Borda count, the complexity of computing a strategic vote can decrease or stay the same depending on how we score partial votes.

We determine the communication complexity of the common voting rules. The rules (sorted by their communication complexity from low to high) are plurality, plurality with runoff, single transferable vote (STV), Condorcet, approval, Bucklin, cup, maximin, Borda, Copeland, and ranked pairs. For each rule, we first give a deterministic communication protocol and an upper bound on the number of bits communicated in it; then, we give a lower bound on (even the nondeterministic) communication requirements of the voting rule. The bounds match for all voting rules except STV and maximin.

The (group) no-show paradox refers to the undesirable situation where a group of agents has the incentive to abstain from voting to get a more favorable winner. We examine the computational complexity of verifying whether the group no-show paradox exists given agents' preferences and the voting rule. We prove that the verification problem is NP-hard to compute for commonly studied voting rules such as Copeland, maximin, single transferable vote, and Black's rule. We propose integer linear programming-based algorithms and a breadth-first search algorithm for the verification problem. Experimental results illustrate that the former work better for a small number of alternatives, and the latter work better for a small number of agents. Using these algorithms, we observe that the group no-show paradoxes rarely occur in real-world data.

Following recent studies of iterative voting and its effects on plurality vote outcomes, we provide characterisations and complexity results for three models of iterative voting under the plurality rule. Our focus is on providing a better understanding regarding the set of equilibria attainable by iterative voting processes. We start with the basic model of plurality voting. We first establish some useful properties of equilibria, reachable by iterative voting, which enable us to show that deciding whether a given profile is an iteratively reachable equilibrium is NP-complete. We then proceed to combine iterative voting with the concept of truth bias, a model where voters prefer to be truthful when they cannot affect the outcome. We fully characterise the set of attainable truth-biased equilibria, and show that it is possible to determine all such equilibria in polynomial time. Finally, we also examine the model of lazy voters, in which a voter may choose to abstain from the election. We establish convergence of the iterative process, albeit not necessarily to a Nash equilibrium. As in the case with truth bias, we also provide a polynomial time algorithm to find all the attainable equilibria.

Optimal defense against election control by deleting voter groups

This chapter summarizes the concerns about electoral representative democracy identified in the previous chapters, sorts them into either constitutive or conditional problems of electoral democracy, and presents (and raises concerns about) several possible reforms that retain elections as a central component of the political system. The chapter argues that although these comparatively modest responses might result in some improvements, they do not effectively address the core concerns, and so we should be open to more radical reforms. The reforms discussed include introducing epistocratic or technocratic elements such as plural voting or “modelled” democracy, implementing broad public education and media reform, reducing the size of political communities, regulating campaign finance and providing public financing of electoral campaigns, restricting lobbying and revolving door politics, regulating political speech, reducing background socioeconomic inequality, and implementing approval voting or single-transferable vote systems. Although many of these reforms are worth pursuing, and many would make a positive difference, the chapter also argues that we should not put all of our eggs in these baskets, and that we should develop alternative ideas in case we end up doubting the viability of the basic electoral mechanism in the modern political context.

Information uncertainty is one of the major challenges facing applications of game theory. In the context of Stackelberg games, various approaches have been proposed to deal with the leader's incomplete knowledge about the follower's payoffs, typically by gathering information from the leader's interaction with the follower. Unfortunately, these approaches rely crucially on the assumption that the follower will not strategically exploit this information asymmetry, i.e., the follower behaves truthfully during the interaction according to their actual payoffs. As we show in this paper, the follower may have strong incentives to deceitfully imitate the behavior of a different follower type and, in doing this, benefit significantly from inducing the leader into choosing a highly suboptimal strategy. This raises a fundamental question: how to design a leader strategy in the presence of a deceitful follower? To answer this question, we put forward a basic model of Stackelberg games with (imitative) follower deception and show that the leader is indeed able to reduce the loss due to follower deception with carefully designed policies. We then provide a systematic study of the problem of computing the optimal leader policy and draw a relatively complete picture of the complexity landscape; essentially matching positive and negative complexity results are provided for natural variants of the model. Our intractability results are in sharp contrast to the situation with no deception, where the leader's optimal strategy can be computed in polynomial time, and thus illustrate the intrinsic difficulty of handling follower deception. Through simulations we also examine the benefit of considering follower deception in randomly generated games.

We propose a model where voters are embedded in a social network. Each voter observes the ballots of her neighbors in the network, from which she infers the likely outcome of the election. Each voter may then revise her vote strategically, to maximize her expected utility. Our work focuses on plurality voting, where strategic voting is a major concern. We show that in practice, strategization increases with voter knowledge, yet can improve the social welfare for the population. Real world social networks exhibit a property called homophily; sometimes called ``The Echo Chamber Effect'', which is the tendency for friends to have similar ideologies. We find that homophily dampens the benefits of strategization, and correspondingly, lowers the frequency of its occurrence. This effect may contribute to the low number of strategic voters observed in real world elections. Additionally, strategization may lead to the elimination of less popular candidates, as voters revise their votes to less preferred but more hopeful candidates. This phenomenon is known as Duverger's Law in political science, and we show that it does not hold in certain network structures.

In this chapter we introduce a module-based approach to modeling and controlling electricity infrastructure to achieve reliability of services. Nonuniform generator or load components are defined as modules and are represented in terms of their internal state variables and the interaction state variables between the modules and the transmission network. Therefore, it is possible to specify the dynamical performance sub-objectives of each module for a given range of variations in interaction variables. It is also possible ensure that the local sub-objectives are met through a combination of local sensing, actuation and global communication. This approach, compared with the present off-line worst-case simulation approach, provides a systematic means of analyzing and stabilizing the infrastructure dynamics with increasing penetration of dispersed sustainable energy resources such as wind and solar. An interactive communication protocol between the distributed modules and control center could be implemented for operating the system with pre-specified stability performance. Sufficient conditions on network properties are derived under which this interactive protocol between the transmission networks and the modules converges to a system-wide stable operation. A five node example demonstrates the integration of wind power into the existing electricity infrastructure with prespecified stability performance.

In order to understand underlying structural regularities in a graph, a basic and useful technique, known as modular decomposition, looks for subsets of vertices that have the exact same neighbourhood to the outside. These are known as modules and there exist linear-time algorithms to find them. This notion however is too strict, especially when dealing with graphs that arise from real world data. This is why it is important to relax this condition by allowing some noise in the data. However, generalizing modular decomposition is far from being obvious since most of the proposals lose the algebraic properties of modules and therefore most of the nice algorithmic consequences. In this paper we introduce the notion of \(\epsilon \)-module which seems to be a good compromise that maintains some of the algebraic structure. Among the main results in the paper, we show that minimal \(\epsilon \)-modules can be computed in polynomial time, on the other hand for maximal \(\epsilon \)-modules it is already NP-hard to compute if a graph admits an 1-parallel decomposition, i.e. one step of decomposition of \(\epsilon \)-module with \(\epsilon =1\).

Instant runoff voting (IRV) has recently gained popularity as an alternative to plurality voting for political elections, with advocates claiming a range of advantages, including that it produces more moderate winners than plurality and could thus help address polarization. However, there is little theoretical backing for this claim, with existing evidence focused on case studies and simulations. In this work, we prove that IRV has a moderating effect relative to plurality voting in a precise sense, developed in a 1-dimensional Euclidean model of voter preferences. We develop a theory of exclusion zones, derived from properties of the voter distribution, which serve to show how moderate and extreme candidates interact during IRV vote tabulation. The theory allows us to prove that if voters are symmetrically distributed and not too concentrated at the extremes, IRV cannot elect an extreme candidate over a moderate. In contrast, we show plurality can and validate our results computationally. Our methods provide new frameworks for the analysis of voting systems, deriving exact winner distributions geometrically and establishing a connection between plurality voting and stick-breaking processes.

In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization over multiple rotation constraints. As these constraints are non-convex, this problem is generally considered challenging to solve globally. We show how to circumvent this difficulty through the use of Lagrangian duality. While such an approach is well-known it is normally not guaranteed to provide a tight relaxation. Based on spectral graph theory, we analytically prove that in many cases there is no duality gap unless the noise levels are severe. This allows us to obtain certifiably global solutions to a class of important non-convex problems in polynomial time. We also propose an efficient, scalable algorithm that out-performs general purpose numerical solvers and is able to handle the large problem instances commonly occurring in structure from motion settings. The potential of this proposed method is demonstrated on a number of different problems, consisting of both synthetic and real-world data.

The rise of social media and online social networks has been a disruptive force in society. Opinions are increasingly shaped by interactions on online social media, and social phenomena including disagreement and polarization are now tightly woven into everyday life. In this work we initiate the study of the following question: \beginquotation \noindent Given n agents, each with its own initial opinion that reflects its core value on a topic, and an opinion dynamics model, what is the structure of a social network that minimizes \em disagreementand \em controversy simultaneously? \endquotation \noindent This question is central to recommender systems: should a recommender system prefer a link suggestion between two online users with similar mindsets in order to keep disagreement low, or between two users with different opinions in order to expose each to the others viewpoint of the world, and decrease overall levels of polarization and controversy? Such decisions have an important global effect on society \citewilliams2007social. Our contributions include a mathematical formalization of this question as an optimization problem and an exact, time-efficient algorithm. We also prove that there always exists a graph with $O(n/e^2)$ edges that is a $(1+e)$ approximation to the optimum. Our formulation is an instance of optimization over \em graph topologies, see also \citeboyd2004fastest,daitch2009fitting,sun2006fastest. Furthermore, for a given graph, we show how to optimize the same objective over the agents» innate opinions in polynomial time. Finally, we perform an empirical study of our proposed methods on synthetic and real-world data that verify their value as mining tools to better understand the trade-off between of disagreement and polarization. We find that there is a lot of space to reduce both controversy and disagreement in real-world networks; for instance, on a Reddit network where users exchange comments on politics, our methods achieve a reduction in controversy and disagreement of the order $6.2 \times 10^4$.

Bayesian networks based multi-modality fusion for error handling in human–robot dialogues under noisy conditions

Because human processes are subtle, complex, and contextualized, computational representations of those processes face highly significant unmet design challenges. Design Thinking (DT) offers a potential new paradigm of creativity and innovation in education capable of effecting meaningful culture change. DT is nonlinear but encompasses elements of empathy, problem definition, ideation, prototyping, and tests that may freely move as needed from and to each other. DT's empathic focus on end users' needs suggests educational measurement's information infrastructures will have to coherently integrate assessment and instruction across multiple levels of complexity in communication. Applying DT reveals the need to attend to previously undeveloped technical issues in communication. Especially important are developmental, horizontal, and vertical forms of coherence, and denotative, metalinguistic, and metacommunicative levels of complexity. New solutions emerge when classrooms are reconceived as meta-design ecosystem niches of creativity and innovation structured from the bottom up by flows of self-organizing information. Recently identified correspondences between educational measurement and metrology support efforts aimed at developing multilevel common languages for the communication of learning outcomes. Prototype reports illustrate how emergent measured constructs can be brought into language in ways that integrate developmental, horizontal, and vertical coherence across levels of complexity. Coherent information infrastructures of these kinds are capable of adapting to new circumstances as populations of persons and items change, doing so without compromising the continuity of comparisons or the uniqueness of locally situated knowledge and practices.