Cake-cutting algorithms, which aim to fairly allocate a continuous resource based on individual agent preferences, have seen significant progress over the past two decades. Much of the research has concentrated on fairness, with comparatively less attention given to other important aspects. In 2010, Chen et al. introduced an algorithm that, in addition to ensuring fairness, was strategyproof---meaning agents had no incentive to misreport their valuations. However, even in the absence of strategic incentives to misreport, agents may still hesitate to reveal their true preferences due to privacy concerns (e.g., when allocating advertising time between firms, revealing preferences could inadvertently expose planned marketing strategies or product launch timelines). In this work, we extend the strategyproof algorithm of Chen et al. by introducing a privacy-preserving dimension. To the best of our knowledge, we present the first private cake-cutting protocol, and, in addition, this protocol is also envy-free and strategyproof. Our approach replaces the algorithm’s centralized computation with a novel adaptation of cryptographic techniques, enabling privacy without compromising fairness or strategyproofness. Thus, our protocol encourages agents to report their true preferences not only because they are not incentivized to lie, but also because they are protected from having their preferences exposed.

In the last few years, a lot of the activity of the computational social choice community has focused on novel mechanisms for reaching decisions by large groups of people. While this research makes meaningful scientific contributions, many of these mechanisms are not quite useful in realistic decision-making settings. Moreover, their radicalism ignores the centuries-old experience we have with large-scale human decision-making, and what it teaches us about what works. We believe it is important the community engage with mechanisms which are widely-used in the real world, as they may hold a key to a deeper understanding of how people reach decisions and the way that helps them do that productively. Moreover, letting the community bring its analysis and understanding to these will allow for algorithmic suggestions that have some chance of being implemented (and, thus, can contribute to the public debate on these topics). In particular, we highlight the relatively less-investigated role of parties and grouping of voters and candidates, and the role of executive capacity in analyzing decision-making structures.

Belief propagation is a widely used incomplete optimization algorithm, whose main theoretical properties hold only under the assumptions that beliefs are not equal. Nevertheless, there is much evidence that equality between beliefs does occur. A method to overcome belief equality by using unary function-nodes is assumed to resolve the problem. We focus on Min-sum, the belief propagation version for solving constraint optimization problems. We prove that on a single cycle graph, belief equality can be avoided only when the algorithm converges to the optimal solution. In any other case, the unary function methods will not prevent equality, rendering some existing results in need of reassessment. We differentiate between belief equality, which includes equal beliefs in a single message, and assignment equality, that prevents a coherent selection of assignments to variables. We show the necessary and satisfying conditions for both.

In peer selection a group of agents must choose a subset of themselves, as winners for, e.g., peer-reviewed grants or prizes. We take a Condorcet view of this aggregation problem, assuming that there is an objective ground-truth ordering over the agents. We study agents that have a noisy perception of this ground truth and give assessments that, even when truthful, can be inaccurate. Our goal is to select the best set of agents according to the underlying ground truth by looking at the potentially unreliable assessments of the peers. Besides being potentially unreliable, we also allow agents to be self-interested, attempting to influence the outcome of the decision in their favour. Hence, we are focused on tackling the problem of impartial (or strategyproof) peer selection – how do we prevent agents from manipulating their reviews while still selecting the most deserving individuals, all in the presence of noisy evaluations? We propose a novel impartial peer selection algorithm, PeerNomination, that aims to fulfil the above desiderata. We provide a comprehensive theoretical analysis of the recall of PeerNomination and prove various properties, including impartiality and monotonicity. We also provide empirical results based on computer simulations to show its effectiveness compared to the state-of-the-art impartial peer selection algorithms. We then investigate the robustness of PeerNomination to various levels of noise in the reviews. In order to maintain good performance under such conditions, we extend PeerNomination by using weights for reviewers which, informally, capture some notion of reliability of the reviewer. We show, theoretically, that the new algorithm preserves strategyproofness and, empirically, that the weights help identify the noisy reviewers and hence to increase selection performance.1

When individuals interact in a social network their opinions can change, at times quite significantly, as a result of social influence. In elections, for example, while they might initially support one candidate, what their friends say may lead them to support another. But how do opinions settle in a social network, as a result of social influence? A recently proposed graph-theoretic metric, the influence gap, has shown to be a reliable predictor of the effect of social influence in two-party elections, albeit only tested on regular and scale-free graphs. Here, we investigate whether the influence gap is able to predict the outcome of multi-party elections on networks exhibiting community structure, i.e., made of highly interconnected components, and therefore more resembling of real-world interaction. To encode communities we build on the classical model of caveman graphs, which we extend to a richer graph family that displays different levels of homophily, i.e., how many connections and opinions are intertwined. Our contribution is three-fold. First, we study the predictive power of the influence gap in the presence of communities. We show that when there is no clear initial majority the influence gap is not a good predictor of the election outcome. When we instead allow for varying majorities, although the influence gap improves as a predictor, counting the initial partisan majority does consistently better, across all levels of homophily. Second, we study the combined effect of the more predictive metrics, as function of the homophily levels. Using regression models, we demonstrate that the influence gap combined with the initial votes count does increase the overall predictive power for some levels of homophily. Third, we study elections with more than two parties. Specifically, we extend the definition of the influence gap to any number of parties, considering various generalisations, and show that the initial votes count has an even higher predictive power when compared to influence gap than it did in the two-party case.

Abstract Badges are endemic to online interaction sites, from question and answer (Q&A) websites to ride sharing, as systems for rewarding participants for their contributions. This article studies how badge design affects people's contributions and behavior over time. Past work has shown that badges “steer” people's behavior toward substantially increasing the amount of contributions before obtaining the badge, and immediately decreasing their contributions thereafter, returning to their baseline contribution levels. In contrast, we find that the steering effect depends on the type of user, as modeled by the rate and intensity of the user's contributions. We use these measures to distinguish between different groups of user activity, including users who are not affected by the badge system despite being significant contributors to the site. We provide a predictive model of how users change their activity group over the course of their lifetime in the system. We demonstrate our approach empirically in three different Q&A sites on Stack Exchange with hundreds of thousands of users, for two types of activities (editing and voting on posts).

Belief propagation, an algorithm for solving problems represented by graphical models, has long been known to converge to the optimal solution when the graph is a tree. When the graph representing the problem includes a single cycle, the algorithm either converges to the optimal solution or performs periodic oscillations. While the conditions that trigger these two behaviors have been established, the question regarding the convergence and divergence of the algorithm on graphs that include more than one cycle is still open.Focusing on Max-sum, the version of belief propagation for solving distributed constraint optimization problems (DCOPs), we extend the theory on the behavior of belief propagation in general – and Max-sum specifically – when solving problems represented by graphs with multiple cycles. This includes: 1) Generalizing the results obtained for graphs with a single cycle to graphs with multiple cycles, by using backtrack cost trees (BCT). 2) Proving that when the algorithm is applied to adjacent symmetric cycles, the use of a large enough damping factor guarantees convergence to the optimal solution.

While manipulative attacks on elections have been well-studied, only recently has attention turned to attacks that account for geographic information, which are extremely common in the real world. The most well known in the media is gerrymandering, in which district border-lines are changed to increase a party's chance to win, but a different geographical manipulation involves influencing the election by selecting the location of polling places, as many people are not willing to go to any distance to vote. In this paper we initiate the study of this manipulation. We find that while it is easy to manipulate the selection of polling places on the line, it becomes difficult already on the plane or in the case of more than two candidates. Moreover, we show that for more than two candidates the problem is inapproximable. However, we find a few restricted cases on the plane where some algorithms perform well. Finally, we discuss how existing results for standard control actions hold in the geographic setting, consider additional control actions in the geographic setting, and suggest directions for future study.

Much of the social choice literature examines direct voting systems, in which voters submit their ranked preferences over candidates and a voting rule picks a winner. Real-world elections and decision-making processes are often more complex and involve multiple stages. For instance, one popular voting system filters candidates through primaries: first, voters affiliated with each political party vote over candidates of their own party and the voting rule picks a candidate from each party, which then compete in a general election.We present a model to analyze such multi-stage elections, and conduct the first quantitative comparison (to the best of our knowledge) of the direct and primary voting systems with two political parties in terms of the quality of the elected candidate. Our main result is that every voting rule is guaranteed to perform almost as well (i.e., within a constant factor) under the primary system as under the direct system. Surprisingly, the converse does not hold: we show settings in which there exist voting rules that perform significantly better under the primary system than under the direct system.

District-based manipulation, or gerrymandering, is usually taken to refer to agents who are in fixed location, and an external division is imposed upon them. However, in many real-world setting, there is an external, fixed division – an organizational chart of a company, or markets for a particular product. In these cases, agents may wish to move around (“reverse gerrymandering”), as each of them tries to maximize their influence across the company’s subunits, or resources are “working” to be allocated to areas where they will be most needed.In this paper we explore an iterative dynamic in this setting, finding that allowing this decentralized system results, in some particular cases, in a stable equilibrium, though in general, the setting may end up in a cycle. We further examine how this decentralized process affects the social welfare of the system.

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.

Badges are endemic to online interaction sites, from Question and Answer (Q&A) websites to ride sharing, as systems for rewarding participants for their contributions. This paper studies how badge design affects people's contributions and behavior over time. Past work has shown that badges "steer'' people's behavior toward substantially increasing the amount of contributions before obtaining the badge, and immediately decreasing their contributions thereafter, returning to their baseline contribution levels. In contrast, we find that the steering effect depends on the type of user, as modeled by the rate and intensity of the user's contributions. We use these measures to distinguish between different groups of user activity, including users who are not affected by the badge system despite being significant contributors to the site. We provide a predictive model of how users change their activity group over the course of their lifetime in the system. We demonstrate our approach empirically in three different Q&A sites on Stack Exchange with hundreds of thousands of users, and we discuss the implications for system designers.

Gerrymandering is the process by which parties manipulate boundaries of electoral districts in order to maximize the number of districts they can win. Demographic trends show an increasingly strong correlation between residence and party affiliation; some party’s supporters congregate in cities, while others stay in more rural areas. We investigate both theoretically and empirically the effect of this trend on a party's ability to gerrymander in a two-party model ("urban party" and "rural party"). Along the way, we propose a definition of the gerrymandering power of a party, and an algorithmic approach for near-optimal gerrymandering in large instances. Our results suggest that beyond a fairly small concentration of urban party's voters, the gerrymandering power of a party depends almost entirely on the level of concentration, and not on the party's share of the population. As partisan separation grows, the gerrymandering power of both parties converge so that each party can gerrymander to get only slightly more than what its voting share warrants, bringing about, ultimately, a more representative outcome. Moreover, there seems to be an asymmetry between the gerrymandering power of the parties, with the rural party being more capable of gerrymandering.

Partial Cooperation is a paradigm and a corresponding model, proposed to represent multi-agent systems in which agents are willing to cooperate to achieve a global goal, as long as some minimal threshold on their personal utility is satisfied. Distributed local search algorithms were proposed in order to solve asymmetric distributed constraint optimization problems (ADCOPs) in which agents are partially cooperative. We contribute by: 1) extending the partial cooperative model to allow it to represent dynamic cooperation intentions, affected by changes in agents’ wealth, in accordance with social studies literature. 2) proposing a novel local search algorithm in which agents receive indications of others’ preferences on their actions and thus, can perform actions that are socially beneficial. Our empirical study reveals the advantage of the proposed algorithm in multiple benchmarks. Specifically, on realistic meeting scheduling problems it overcomes limitations of standard local search algorithms.

Iterative voting is a social choice mechanism that assumes all voters are strategic, and allows voters to change their stated preferences as the vote progresses until an equilibrium is reached (at which point no player wishes to change their vote). Previous research established that this process converges to an equilibrium for the plurality and veto voting methods and for no other scoring rule. We consider iterative voting for non-scoring rules, examining the major ones, and show that none of them converge when assuming (as most research has so far) that voters pursue a best response strategy. We investigate other potential voter strategies, with a more heuristic flavor (since for most of these voting rules, calculating the best response is NP-hard); we show that they also do not converge. We then conduct an empirical analysis of the iterative voting winners for these non-scoring rules, and compare the winner quality of various strategies.

We study an important crowdsourcing setting where agents evaluate one another and, based on these evaluations, a subset of agents are selected. This setting is ubiquitous when peer review is used for distributing awards in a team, allocating funding to scientists, and selecting publications for conferences. The fundamental challenge when applying crowdsourcing in these settings is that agents may misreport their reviews of others to increase their chances of being selected. We propose a new strategyproof (impartial) mechanism called Dollar Partition that satisfies desirable axiomatic properties. We then show, using a detailed experiment with parameter values derived from target real world domains, that our mechanism performs better on average, and in the worst case, than other strategyproof mechanisms in the literature.

In multiagent systems, social choice functions can help aggregate the distinct preferences that agents have over alternatives, enabling them to settle on a single choice. Despite the basic manipulability of all reasonable voting systems, it would still be desirable to find ways to reach plausible outcomes, which are stable states, i.e., a situation where no agent would wish to change its vote. One possibility is an iterative process in which, after everyone initially votes, participants may change their votes, one voter at a time. This technique, explored in previous work, converges to a Nash equilibrium when Plurality voting is used, along with a tie-breaking rule that chooses a winner according to a linear order of preferences over candidates. In this paper, we both consider limitations of the iterative voting method, as well as expanding upon it. We demonstrate the significance of tie-breaking rules, showing that no iterative scoring rule converges for all tie-breaking. However, using a restricted tie-breaking rule (such as the linear order rule used in previous work) does not by itself ensure convergence. We prove that in addition to plurality, the veto voting rule converges as well using a linear order tie-breaking rule. However, we show that these two voting rules are the only scoring rules that converge, regardless of tie-breaking mechanism.

We study a game with \emph{strategic} vendors (the agents) who own multiple items and a single buyer with a submodular valuation function. The goal of the vendors is to maximize their revenue via pricing of the items, given that the buyer will buy the set of items that maximizes his net payoff.% (valuation minus the prices). We show this game may not always have a pure Nash equilibrium, in contrast to previous results for the special case where each vendor owns a single item. We do so by relating our game to an intermediate, discrete game in which the vendors only choose the available items, and their prices are set exogenously afterwards. We further make use of the intermediate game to provide tight bounds on the price of anarchy for the subset games that have pure Nash equilibria; we find that the optimal PoA reached in the previous special cases does not hold, but only a logarithmic one. Finally, we show that for a special case of submodular functions, efficient pure Nash equilibria always exist.

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.

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.