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Added by
Swaprava Nath
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Elections involving a very large voter population often lead to outcomes that surprise many. This is particularly important for the elections in which results affect the economy of a sizable population. A better prediction of the true outcome helps reduce the surprise and keeps the voters prepared. This paper starts from the basic observation that individuals in the underlying population build estimates of the distribution of preferences of the whole population based on their local neighborhoods. The outcome of the election leads to a surprise if these local estimates contradict the outcome of the election for some fixed voting rule. To get a quantitative understanding, we propose a simple mathematical model of the setting where the individuals in the population and their connections (through geographical proximity, social networks etc.) are described by a random graph with connection probabilities that are biased based on the preferences of the individuals. Each individual also has some estimate of the bias in their connections. We show that the election outcome leads to a surprise if the discrepancy between the estimated bias and the true bias in the local connections exceeds a certain threshold, and confirm the phenomenon that surprising outcomes are associated only with {em closely contested elections}. We compare standard voting rules based on their performance on surprise and show that they have different behavior for different parts of the population. It also hints at an impossibility that a single voting rule will be less surprising for {em all} parts of a population. Finally, we experiment with the UK-EU referendum (a.k.a. Brexit) dataset that attest some of our theoretical predictions.
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Multi-round competitions often double or triple the points awarded in the final round, calling it a bonus, to maximize spectators excitement. In a two-player competition with $n$ rounds, we aim to derive the optimal bonus size to maximize the audiences overall expected surprise (as defined in [7]). We model the audiences prior belief over the two players ability levels as a beta distribution. Using a novel analysis that clarifies and simplifies the computation, we find that the optimal bonus depends greatly upon the prior belief and obtain solutions of various forms for both the case of a finite number of rounds and the asymptotic case. In an interesting special case, we show that the optimal bonus approximately and asymptotically equals to the expected lead, the number of points the weaker player will need to come back in expectation. Moreover, we observe that priors with a higher skewness lead to a higher optimal bonus size, and in the symmetric case, priors with a higher uncertainty also lead to a higher optimal bonus size. This matches our intuition since a highly asymmetric prior leads to a high expected lead, and a highly uncertain symmetric prior often leads to a lopsided game, which again benefits from a larger bonus.
We focus on the scenario in which an agent can exploit his information advantage to manipulate the outcome of an election. In particular, we study district-based elections with two candidates, in which the winner of the election is the candidate that wins in the majority of the districts. District-based elections are adopted worldwide (e.g., UK and USA) and are a natural extension of widely studied voting mechanisms (e.g., k-voting and plurality voting). We resort to the Bayesian persuasion framework, where the manipulator (sender) strategically discloses information to the voters (receivers) that update their beliefs rationally. We study both private signaling, in which the sender can use a private communication channel per receiver, and public signaling, in which the sender can use a single communication channel for all the receivers. Furthermore, for the first time, we introduce semi-public signaling in which the sender can use a single communication channel per district. We show that there is a sharp distinction between private and (semi-)public signaling. In particular, optimal private signaling schemes can provide an arbitrarily better probability of victory than (semi-)public ones and can be computed efficiently, while optimal (semi-)public signaling schemes cannot be approximated to within any factor in polynomial time unless P=NP. However, we show that reasonable relaxations allow the design of multi-criteria PTASs for optimal (semi-)public signaling schemes. In doing so, we introduce a novel property, namely comparative stability, and we design a bi-criteria PTAS for public signaling in general Bayesian persuasion problems beyond elections when the senders utility function is state-dependent.
Constructive election control considers the problem of an adversary who seeks to sway the outcome of an electoral process in order to ensure that their favored candidate wins. We consider the computational problem of constructive election control via issue selection. In this problem, a party decides which political issues to focus on to ensure victory for the favored candidate. We also consider a variation in which the goal is to maximize the number of voters supporting the favored candidate. We present strong negative results, showing, for example, that the latter problem is inapproximable for any constant factor. On the positive side, we show that when issues are binary, the problem becomes tractable in several cases, and admits a 2-approximation in the two-candidate case. Finally, we develop integer programming and heuristic methods for these problems.
Prior work on the complexity of bribery assumes that the bribery happens simultaneously, and that the briber has full knowledge of all voters votes. But neither of those assumptions always holds. In many real-world settings, votes come in sequentially, and the briber may have a use-it-or-lose-it moment to decide whether to bribe/alter a given vote, and at the time of making that decision, the briber may not know what votes remaining voters are planning on casting. In this paper, we introduce a model for, and initiate the study of, bribery in such an online, sequential setting. We show that even for election systems whose winner-determination problem is polynomial-time computable, an online, sequential setting may vastly increase the complexity of bribery, in fact jumping the problem up to completeness for high levels of the polynomial hierarchy or even PSPACE. On the other hand, we show that for some natural, important election systems, such a dramatic complexity increase does not occur, and we pinpoint the complexity of their bribery problems in the online, sequential setting.
Previous work on voter control, which refers to situations where a chair seeks to change the outcome of an election by deleting, adding, or partitioning voters, takes for granted that the chair knows all the voters preferences and that all votes are cast simultaneously. However, elections are often held sequentially and the chair thus knows only the previously cast votes and not the future ones, yet needs to decide instantaneously which control action to take. We introduce a framework that models online voter control in sequential elections. We show that the related problems can be much harder than in the standard (non-online) case: For certain election systems, even with efficient winner problems, online control by deleting, adding, or partitioning voters is PSPACE-complete, even if there are only two candidates. In addition, we obtain (by a new characterization of coNP in terms of weight-bounded alternating Turing machines) completeness for coNP in the deleting/adding cases with a bounded deletion/addition limit, and we obtain completeness for NP in the partition cases with an additional restriction. We also show that for plurality, online control by deleting or adding voters is in P, and for partitioning voters is coNP-hard.
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