The well-known Condorcet Jury Theorem states that, under majority rule, the better of two alternatives is chosen with probability approaching one as the population grows. We study an asymmetric setting where voters face varying participation costs and share a possibly heuristic belief about their pivotality (ability to influence the outcome). In a costly voting setup where voters abstain if their participation cost is greater than their pivotality estimate, we identify a single property of the heuristic belief---weakly vanishing pivotality---that gives rise to multiple stable equilibria in which elections are nearly tied. In contrast, strongly vanishing pivotality (as in the standard Calculus of Voting model) yields a unique, trivial equilibrium where only zero-cost voters participate as the population grows. We then characterize when nontrivial equilibria satisfy a version of the Jury Theorem: below a sharp threshold, the majority-preferred candidate wins with probability approaching one; above it, both candidates either win with equal probability.

We present a strategy-proof public goods budgeting mechanism where agents determine both the total volume of expanses and the specific allocation. It is constructed as a modification of VCG to a non-typical environment, namely where we do not assume quasi-linear utilities nor direct revelation. We further show that under plausible assumptions it satisfies strategyproofness in strictly dominant strategies, and consequently implements the social optimum as a Coalition-Proof Nash Equilibrium. A primary (albeit not an exclusive) motivation of our model is Participatory Budgeting, where members of a community collectively decide the spending policy of public tax dollars. While incentives alignment in our mechanism, as in classic VCG, is achieved via individual payments we charge from agents, in a PB context that seems unreasonable. Our second main result thus provides that, under further specifications relevant in that context, these payments will vanish in large populations. In the last section we expand the mechanism’s definition to a class of mechanisms in which the designer can prioritize certain outcomes she sees as desirable. In particular we give the example of favoring equitable/egalitarian allocations.

Crowdsourcing platforms use various truth discovery algorithms to aggregate annotations from multiple labelers. In an online setting, however, the main challenge is to decide whether to ask for more annotations for each item to efficiently trade off cost (i.e., the number of annotations) for quality of the aggregated annotations. In this paper, we propose a novel approach for general complex annotation (such as bounding boxes and taxonomy paths), that works in an online crowdsourcing setting. We prove that the expected average similarity of a labeler is linear in their accuracy conditional on the reported label. This enables us to infer reported label accuracy in a broad range of scenarios. We conduct extensive evaluations on real-world crowdsourcing data from Meta and show the effectiveness of our proposed online algorithms in improving the cost-quality trade-off.

Truth discovery is a general name for a broad range of statistical methods aimed to extract the correct answers to questions, based on multiple answers coming from noisy sources. For example, workers in a crowdsourcing platform. In this paper, we consider an extremely simple heuristic for estimating workers' competence using average proximity to other workers. We prove that this estimates well the actual competence level and enables separating high and low quality workers in a wide spectrum of domains and statistical models. Under Gaussian noise, this simple estimate is the unique solution to the MLE with a constant regularization factor. Finally, weighing workers according to their average proximity in a crowdsourcing setting, results in substantial improvement over unweighted aggregation and other truth discovery algorithms in practice.

We study strategic behavior in iterative plurality voting for multiple issues under uncertainty. We introduce a model synthesizing simultaneous multi-issue voting with local dominance theory, in which agents repeatedly update their votes based on sets of vote profiles they deem possible, and determine its convergence properties. After demonstrating that local dominance improvement dynamics may fail to converge, we present two sufficient model refinements that guarantee convergence from any initial vote profile for binary issues: constraining agents to have O-legal preferences, where issues are ordered by importance, and endowing agents with less uncertainty about issues they are modifying than others. Our empirical studies demonstrate that while cycles are common for agents without uncertainty, introducing uncertainty makes convergence almost guaranteed in practice.

When aggregating information from conflicting sources, one’s goal is to find the truth. Most real-value truth discovery (TD) algorithms try to achieve this goal by estimating the competence of each source and then aggregating the conflicting information by weighing each source’s answer proportionally to her competence. However, each of those algorithms requires more than a single source for such estimation and usually does not consider different estimation methods other than a weighted mean. Therefore, in this work we formulate, prove, and empirically test the conditions for an Empirical Bayes Estimator (EBE) to dominate the weighted mean aggregation. Our main result demonstrates that EBE, under mild conditions, can be used as a second step of any TD algorithm in order to reduce the expected error.

We propose a market-inspired bidding scheme for the assignment of paper reviews in large academic conferences. We provide an analysis of the incentives of reviewers during the bidding phase, when reviewers have both private costs and some information about the demand for each paper; and their goal is to obtain the best possible k papers for a predetermined k. We show that by assigning `budgets' to reviewers and a `price' for every paper that is (roughly) proportional to its demand, the best response of a reviewer is to bid sincerely, i.e., on her most favorite papers, and match the budget even when it is not enforced. This game-theoretic analysis is based on a simple, prototypical assignment algorithm. We show via extensive simulations on bidding data from real conferences, that our bidding scheme would substantially improve both the bid distribution and the resulting assignment.

A population of voters must elect representatives among themselves to decide on a sequence of possibly unforeseen binary issues. Voters care only about the final decision, not the elected representatives. The disutility of a voter is proportional to the fraction of issues, where his preferences disagree with the decision. While an issue-by-issue vote by all voters would maximize social welfare, we are interested in how well the preferences of the population can be approximated by a small committee. We show that a k-sortition (a random committee of k voters with the majority vote within the committee) leads to an outcome within the factor 1+O(1/√ k) of the optimal social cost for any number of voters n, any number of issues m, and any preference profile. For a small number of issues m, the social cost can be made even closer to optimal by delegation procedures that weigh committee members according to their number of followers. However, for large m, we demonstrate that the k-sortition is the worst-case optimal rule within a broad family of committee-based rules that take into account metric information about the preference profile of the whole population.

We present a Spades bidding algorithm that is superior to recreational human players and to publicly available bots. Like in Bridge, the game of Spades is composed of two independent phases, bidding and playing. This paper focuses on the bidding algorithm, since this phase holds a precise challenge: based on the input, choose the bid that maximizes the agent's winning probability. Our Bidding-in-Spades (BIS) algorithm heuristically determines the bidding strategy by comparing the expected utility of each possible bid. A major challenge is how to estimate these expected utilities. To this end, we propose a set of domain-specific heuristics, and then correct them via machine learning using data from real-world players. The BIS algorithm we present can be attached to any playing algorithm. It beats rule-based bidding bots when all use the same playing component. When combined with a rule-based playing algorithm, it is superior to the average recreational human.

Abstract Plurality voting is perhaps the most commonly used way to aggregate the preferences of multiple voters. Yet, there is no consensus on how people vote strategically, even in very simple settings. The purpose of this paper is to provide a comprehensive study of people’s voting behavior in various online settings under the plurality rule. We implemented voting games that replicate two common real-world voting scenarios in controlled experiments. In the first, a single voter votes once after seeing a pre-election poll. In the second game, a group of voters play an iterative game, and change their vote as the game progresses (as in online voting). The winning candidate in each game (and hence the subject’s payment) is determined using the plurality rule. For each of these settings we generated hundreds of game instances, varying conditions such as the number of voters, subjects’ preferences over candidates and the poll information that was made available to the subjects prior to voting. We show that people can be classified into several groups, one of which is not engaged in any strategic behavior, while the largest group demonstrates both a tendency for strategic compromise, and a bias toward voting for the leader in the poll. We provide a detailed analysis of this group behavior for both settings, and how it depends on the poll information. Our study has insight for multi-agent system designers in uncovering patterns that provide reasonable predictions of voters’ behaviors, which may facilitate the design of agents that support people or act autonomously in voting systems.

Decision making under uncertainty is a key component of many AI settings, and in particular of voting scenarios where strategic agents are trying to reach a joint decision. The common approach to handle uncertainty is by maximizing expected utility, which requires a cardinal utility function as well as detailed probabilistic information. However, often such probabilities are not easy to estimate or apply.To this end, we present a framework that allows for “shades of gray” of likelihood without probabilities. Specifically, we create a hierarchy of sets of world states based on a prospective poll, with inner sets contain more likely outcomes. This hierarchy of likelihoods allows us to define what we term ordinally-dominated strategies. We use this approach to justify various known voting heuristics as bounded-rational strategies.

The paper presents two randomized facility location mechanisms for 3 agents on a circle, that are strategyproof and are strictly better than selecting a random dictator. First lower bounds for the problem are also presented.

Graph minors are a primary tool in understanding the structure of undirected graphs, with many conceptual and algorithmic implications. We propose new variants of directed graph minors and directed graph embeddings, by modifying familiar definitions. For the class of 2-terminal directed acyclic graphs (TDAGs) our two definitions coincide, and the class is closed under both operations. The usefulness of our directed minor operations is demonstrated by characterizing all TDAGs with serial-parallel width at most k; a class of networks known to guarantee bounded negative externality in nonatomic routing games. Our characterization implies that a TDAG has serial-parallel width of 1 if and only if it is a directed series-parallel graph. We also study the computational complexity of finding a directed minor and computing the serial-parallel width.

Without monetary payments, the Gibbard-Satterthwaite theorem proves that under mild requirements all truthful social choice mechanisms must be dictatorships. When payments are allowed, the Vickrey-Clarke-Groves (VCG) mechanism implements the value-maximizing choice, and has many other good properties: it is strategy-proof, onto, deterministic, individually rational, and does not not make positive transfers to the agents. By Roberts' theorem, with three or more alternatives, the weighted VCG mechanisms are essentially unique for domains with quasi-linear utilities. The goal of this paper is to characterize domains of non-quasi-linear utilities where "reasonable'' mechanisms (with VCG-like properties) exist. Our main result is a tight characterization of the maximal non quasi-linear utility domain, which we call the largest parallel domain. We extend Roberts' theorem to parallel domains, and use the generalized theorem to prove two impossibility results. First, any reasonable mechanism must be dictatorial when the type domain is quasi-linear together with any single non-parallel type. Second, for richer utility domains that still differ very slightly from quasi-linearity, every strategy-proof, onto and deterministic mechanism must be a dictatorship.

A key issue in cooperative game theory is coalitional stability, usually captured by the notion of the core---the set of outcomes that are resistant to group deviations. However, some coalitional games have empty cores, and any outcome in such a game is unstable. We investigate the possibility of stabilizing a coalitional game by using subsidies. We consider scenarios where an external party that is interested in having the players work together offers a supplemental payment to the grand coalition, or, more generally, a particular coalition structure. This payment is conditional on players not deviating from this coalition structure, and may be divided among the players in any way they wish. We define the cost of stability as the minimum external payment that stabilizes the game. We provide tight bounds on the cost of stability, both for games where the coalitional values are nonnegative (profit-sharing games) and for games where the coalitional values are nonpositive (cost-sharing games), under natural assumptions on the characteristic function, such as superadditivity, anonymity, or both. We also investigate the relationship between the cost of stability and several variants of the least core. Finally, we study the computational complexity of problems related to the cost of stability, with a focus on weighted voting games.

Power companies such as Southern California Edison (SCE) uses Demand Response (DR) contracts to incentivize consumers to reduce their power consumption during periods when demand forecast exceeds supply. Current mechanisms in use offer contracts to consumers independent of one another, do not take into consideration consumers' heterogeneity in consumption profile or reliability, and fail to achieve high participation. We introduce DR-VCG, a new DR mechanism that offers a flexible set of contracts (which may include the standard SCE contracts) and uses VCG pricing. We prove that DR-VCG elicits truthful bids, incentivizes honest preparation efforts, and enables efficient computation of allocation and prices. With simple fixed-penalty contracts, the optimization goal of the mechanism is an upper bound on probability that the reduction target is missed. Extensive simulations show that compared to the current mechanism deployed by SCE, the DR-VCG mechanism achieves higher participation, increased reliability, and significantly reduced total expenses.

Understanding the nature of strategic voting is the holy grail of social choice theory, where game-theory, social science and recently computational approaches are all applied in order to model the incentives and behavior of voters. In a recent paper, Meir et al.[EC'14] made another step in this direction, by suggesting a behavioral game-theoretic model for voters under uncertainty. For a specific variation of best-response heuristics, they proved initial existence and convergence results in the Plurality voting system. This paper extends the model in multiple directions, considering voters with different uncertainty levels, simultaneous strategic decisions, and a more permissive notion of best-response. It is proved that a voting equilibrium exists even in the most general case. Further, any society voting in an iterative setting is guaranteed to converge to an equilibrium. An alternative behavior is analyzed, where voters try to minimize their worst-case regret. As it turns out, the two behaviors coincide in the simple setting of Meir et al.[EC'14], but not in the general case.

We put forward a new model of congestion games where agents have uncertainty over the routes used by other agents. We take a non-probabilistic approach, assuming that each agent knows that the number of agents using an edge is within a certain range. Given this uncertainty, we model agents who either minimize their worst-case cost (WCC) or their worst-case regret (WCR), and study implications on equilibrium existence, convergence through adaptive play, and efficiency. Under the WCC behavior the game reduces to a modified congestion game, and welfare improves when agents have moderate uncertainty. Under WCR behavior the game is not, in general, a congestion game, but we show convergence and efficiency bounds for a simple class of games.

Finding a common time slot for a group event is a daily conundrum and illustrates key features of group decision-making. It is a complex interplay of individual incentives and group dynamics. A participant would like the final time to be convenient for her, but she is also expected to be cooperative towards other people's preferences. We combine large-scale data analysis with theoretical models from the voting literature to investigate strategic behaviors in event scheduling. We analyze all Doodle polls created in the US from July-September 2011 (over 340,000 polls), consisting of both hidden polls (a user cannot see other responses) and open polls (a user can see all previous responses). By analyzing the differences in behavior in hidden and open polls, we gain unique insights into strategies that people apply in a natural decision-making setting. Responders in open polls are more likely to approve slots that are very popular or very unpopular, but not intermediate slots. We show that this behavior is inconsistent with models that have been proposed in the voting literature, and propose a new model based on combining personal and social utilities to explain the data.

Bidding games are extensive form games, where in each turn players bid in order to determine who will play next. Zero-sum bidding games (also known as Richman games) have been extensively studied, focusing on the fraction of the initial budget that can guaranty the victory of each player [Lazarus et al.'99, Develin & Payne '10].

We suggest a new model for strategic voting based on local dominance, where voters consider a set of possible outcomes without assigning probabilities to them. We prove that voting equilibria under the Plurality rule exist for a broad class of local dominance relations. Furthermore, we show that local dominance-based dynamics quickly converge to an equilibrium if voters start from the truthful state, and we provide weaker convergence guarantees in more general settings. Using extensive simulations of strategic voting on generated and real profiles, we show that emerging equilibria replicate widely known patterns of human voting behavior such as Duverger's law, and that they generally improve the quality of the winner compared to non-strategic voting.

We consider judgment aggregation over multiple independent issues, where the chairperson has her own opinion, and can try to bias the outcome by bundling several issues together. Since for each bundle judges must give a uniform answer on all issues, different partitions of the issues may result in an outcome that significantly differs from the "true," issue-wise, decision. We prove that the bundling problem faced by the chairperson, i.e. trying to bias the outcome towards her own opinion, is computationally difficult in the worst case. Then we study the probability that an effective bundling attack exists as the disparity between the opinions of the judges and the chair varies. We show that if every judge initially agrees with the chair on every issue with probability of at least 1/2, then there is almost always a bundling attack (i.e. a partition) where the opinion of the chair on all issues is approved. Moreover, such a partition can be found efficiently. In contrast, when the probability is lower than 1/2 then the chair cannot force her opinion using bundling even on a single issue.

The increasing use of group discounts has provided opportunities for buying groups with diverse preferences to coordinate their behavior in order to exploit the best offers from multiple vendors. We analyze this problem from the viewpoint of the vendors, asking under what conditions a vendor should adopt a volume-based price schedule rather than posting a fixed price, either as a monopolist or when competing with other vendors. When vendors have uncertainty about buyers' valuations specified by a known distribution, we show that a vendor is always better off posting a fixed price, provided that buyers' types are i.i.d. and that other vendors also use fixed prices. We also show that these assumptions cannot be relaxed: if buyers are not i.i.d., or other vendors post discount schedules, then posting a schedule may yield higher profit for the vendor. We provide similar results under a distribution-free uncertainty model, where vendors minimize their maximum regret over all type realizations.

We study the stability of cooperative games played over an interaction network, in a model that was introduced by Myerson ['77]. We show that the cost of stability of such games (i.e., the subsidy required to stabilize the game) can be bounded in terms of natural parameters of their underlying interaction networks. Specifically, we prove that if the treewidth of the interaction network H is k, then the relative cost of stability of any game played over H is at most k + 1, and if the pathwidth of H is k', then the relative cost of stability is at most k'. We show that these bounds are tight for all k≥ 2and all k' ≥ 1, respectively.

We propose a natural model for agent failures in congestion games. In our model, each of the agents may fail to participate in the game, introducing uncertainty regarding the set of active agents. We examine how such uncertainty may change the Nash equilibria (NE) of the game. We prove that although the perturbed game induced by the failure model is not always a congestion game, it still admits at least one pure Nash equilibrium. Then, we turn to examine the effect of failures on the maximal social cost in any NE of the perturbed game. We show that in the limit case where failure probability is negligible new equilibria never emerge, and that the social cost may decrease but it never increases. For the case of non-negligible failure probabilities, we provide a full characterization of the maximal impact of failures on the social cost under worst-case equilibrium outcomes.

We study strategyproof (SP) mechanisms for the location of a facility on a discrete graph. We give a full characterization of SP mechanisms on lines and on sufficiently large cycles. Interestingly, the characterization deviates from the one given by Schummer and Vohra (2004) for the continuous case. In particular, it is shown that an SP mechanism on a cycle is close to dictatorial, but all agents can affect the outcome, in contrast to the continuous case. Our characterization is also used to derive a lower bound on the approximation ratio with respect to the social cost that can be achieved by an SP mechanism on certain graphs. Finally, we show how the representation of such graphs as subsets of the binary cube reveals common properties of SP mechanisms and enables one to extend the lower bound to related domains.

In the well known Prisoner’s Dilemma, two people that are following the only rational behavior end up in the worst possible outcome. Unfortunately, this example is a useful analogy for many situations in real life, where (individually) rational behavior leads to a disaster for the society. With the rapid delegation of decision making to automated agents, the role of game theory within artificial intelligence is becoming increasingly important. In particular, game-theoretical principles must be taken into account in the design of systems and environments in which agents operate (human and automated alike). My research focuses on mechanism design (see [Nisan and Ronen, 2001] for background). More specifically, on ways to incentivize self-interested agents to cooperate in a way that will benefit the entire society. This cooperation arises not by forcing them or by relying on their good intentions, but by changing the “rules of the game” so that the best individual decision would be to cooperate. The research is multi-disciplinary in nature, involving tools and ideas from economics, computer science, mathematics, artificial intelligence, and cognitive science. This proposal briefly describes my recent work on prompting cooperation in two related domains, and outlines some future directions. I will conclude with some remarks on the strong assumption of rationality that underlies standard gametheoretic analysis and how it can be relaxed in the quest for cooperation.

Cooperation among automated agents is becoming increasingly important in various artificial intelligence applications.Coalitional (i.e., cooperative) game theory supplies conceptual and mathematical tools useful in the analysis of such interactions, and in particular in the achievement of stable outcomes among self-interested agents.Here, we study the minimal external subsidy required to stabilize the core of a coalitional game.Following the Cost of Stability (CoS) model introduced by Bachrach et al. [2009a], we give tight bounds on the required subsidy under various restrictions on the social structure of the game.We then compare the extended core induced by subsidies with the least core of the game, proving tight bounds on the ratio between the minimal subsidy and the minimal demand relaxation that each lead to stability.

We consider optimizing the coalition structure in Coalitional Skill Games (CSGs), a succinct representation of coalitional games. In CSGs, the value of a coalition depends on the tasks its members can achieve. The tasks require various skills to complete them, and agents may have different skill sets. The optimal coalition structure is a partition of the agents to coalitions, that maximizes the sum of utilities obtained by the coalitions. We show that CSGs can represent any characteristic function, and consider optimal coalition structure generation in this representation. We provide hardness results, showing that in general CSGs, as well as in very restricted versions of them, computing the optimal coalition structure is hard. On the positive side, we show that the problem can be reformulated as constraint satisfaction on a hyper graph, and present an algorithm that finds the optimal coalition structure in polynomial time for instances with bounded tree-width and number of tasks.

Multi-agent decision problems, in which independent agents have to agree on a joint plan of action or allocation of resources, are central to AI. In such situations, agents' individual preferences over available alternatives may vary, and they may try to reconcile these differences by voting. Based on the fact that agents may have incentives to vote strategically and misreport their real preferences, a number of recent papers have explored different possibilities for avoiding or eliminating such manipulations. In contrast to most prior work, this paper focuses on convergence of strategic behavior to a decision from which no voter will want to deviate. We consider scenarios where voters cannot coordinate their actions, but are allowed to change their vote after observing the current outcome. We focus on the Plurality voting rule, and study the conditions under which this iterative game is guaranteed to converge to a Nash equilibrium (i.e., to a decision that is stable against further unilateral manipulations). We show for the first time how convergence depends on the exact attributes of the game, such as the tie-breaking scheme, and on assumptions regarding agents' weights and strategies.

Although recent years have seen a surge of interest in the computational aspects of social choice, no specific attention has previously been devoted to elections with multiple winners, e.g., elections of an assembly or committee. In this paper, we characterize the worst-case complexity of manipulation and control in the context of four prominent multi-winner voting systems, under different formulations of the strategic agent’s goal.