arXiv subjects

Kangning Wang

Publications and source records attributed to Kangning Wang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Six Candidates Suffice to Win a Voter Majority

A cornerstone of social choice theory is Condorcet's paradox which says that in an election where $n$ voters rank $m$ candidates it is possible that, no matter which candidate is declared the winner, a majority of voters would have preferred an alternative candidate. Instead, can we always choose a small committee of winning candidates that is preferred to any alternative candidate by a majority of voters? Elkind, Lang, and Saffidine raised this question and called such a committee a Condorcet winning set. They showed that winning sets of size $2$ may not exist, but sets of size logarithmic in the number of candidates always do. In this work, we show that Condorcet winning sets of size $6$ always exist, regardless of the number of candidates or the number of voters. More generally, we show that if $\fracα{1 - \ln α} \geq \frac{2}{k + 1}$, then there always exists a committee of size $k$ such that less than an $α$ fraction of the voters prefer an alternate candidate. These are the first nontrivial positive results that apply for all $k \geq 2$. Our proof uses the probabilistic method and the minimax theorem, inspired by recent work on approximately stable committee selection. We construct a distribution over committees that performs sufficiently well (when compared against any candidate on any small subset of the voters) so that this distribution must contain a committee with the desired property in its support.

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arXiv2025

Approximately Efficient Bilateral Trade with Samples

We study the social efficiency of bilateral trade between a seller and a buyer. In the classical Bayesian setting, the celebrated Myerson-Satterthwaite impossibility theorem states that no Bayesian incentive-compatible, individually rational, and budget-balanced mechanism can achieve full efficiency. As a counterpoint, Deng, Mao, Sivan, and Wang (STOC 2022) show that if pricing power is delegated to the right person (either the seller or the buyer), the resulting mechanism can guarantee at least a constant fraction of the ideal (yet unattainable) gains from trade. In practice, the agent with pricing power may not have perfect knowledge of the value distribution of the other party, and instead may rely on samples of that distribution to set a price. We show that for a broad class of sampling and pricing behaviors, the resulting market still guarantees a constant fraction of the ideal gains from trade in expectation. Our analysis hinges on the insight that social welfare under sample-based pricing approximates the seller's optimal revenue -- a result we establish via a reduction to a random walk.

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arXiv2024

Breaking the Metric Voting Distortion Barrier

We consider the following well-studied problem of metric distortion in social choice. Suppose we have an election with $n$ voters and $m$ candidates located in a shared metric space. We would like to design a voting rule that chooses a candidate whose average distance to the voters is small. However, instead of having direct access to the distances in the metric space, the voting rule obtains, from each voter, a ranked list of the candidates in order of distance. Can we design a rule that regardless of the election instance and underlying metric space, chooses a candidate whose cost differs from the true optimum by only a small factor (known as the distortion)? A long line of work culminated in finding optimal deterministic voting rules with metric distortion $3$. However, for randomized voting rules, there is still a gap in our understanding: Even though the best lower bound is $2.112$, the best upper bound is still $3$, attained even by simple rules such as Random Dictatorship. Finding a randomized rule that guarantees distortion $3 - ε$ has been a major challenge in computational social choice, as prevalent approaches to designing voting rules are known to be insufficient. Such a voting rule must use information beyond aggregate comparisons between pairs of candidates, and cannot only assign positive probability to candidates that are voters' top choices. In this work, we give a rule that guarantees distortion less than $2.753$. To do so we study a handful of voting rules that are new to the problem. One is Maximal Lotteries, a rule based on the Nash equilibrium of a natural zero-sum game which dates back to the 60's. The others are novel rules that can be thought of as hybrids of Random Dictatorship and the Copeland rule. Though none of these rules can beat distortion $3$ alone, a randomization between Maximal Lotteries and any of the novel rules can.

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arXiv2024

Majorized Bayesian Persuasion and Fair Selection

We address the fundamental problem of selection under uncertainty by modeling it from the perspective of Bayesian persuasion. In our model, a decision maker with imperfect information always selects the option with the highest expected value. We seek to achieve fairness among the options by revealing additional information to the decision maker and hence influencing its subsequent selection. To measure fairness, we adopt the notion of majorization, aiming at simultaneously approximately maximizing all symmetric, monotone, concave functions over the utilities of the options. As our main result, we design a novel information revelation policy that achieves a logarithmic-approximation to majorization in polynomial time. On the other hand, no policy, regardless of its running time, can achieve a constant-approximation to majorization. Our work is the first non-trivial majorization result in the Bayesian persuasion literature with multi-dimensional information sets.

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arXiv2023

Prior-Independent Auctions for Heterogeneous Bidders

We study the design of prior-independent auctions in a setting with heterogeneous bidders. In particular, we consider the setting of selling to $n$ bidders whose values are drawn from $n$ independent but not necessarily identical distributions. We work in the robust auction design regime, where we assume the seller has no knowledge of the bidders' value distributions and must design a mechanism that is prior-independent. While there have been many strong results on prior-independent auction design in the i.i.d. setting, not much is known for the heterogeneous setting, even though the latter is of significant practical importance. Unfortunately, no prior-independent mechanism can hope to always guarantee any approximation to Myerson's revenue in the heterogeneous setting; similarly, no prior-independent mechanism can consistently do better than the second-price auction. In light of this, we design a family of (parametrized) randomized auctions which approximates at least one of these benchmarks: For heterogeneous bidders with regular value distributions, our mechanisms either achieve a good approximation of the expected revenue of an optimal mechanism (which knows the bidders' distributions) or exceeds that of the second-price auction by a certain multiplicative factor. The factor in the latter case naturally trades off with the approximation ratio of the former case. We show that our mechanism is optimal for such a trade-off between the two cases by establishing a matching lower bound. Our result extends to selling $k$ identical items to heterogeneous bidders with an additional $O\big(\ln^2 k\big)$-factor in our trade-off between the two cases.

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arXiv2023

Fair Price Discrimination

A seller is pricing identical copies of a good to a stream of unit-demand buyers. Each buyer has a value on the good as his private information. The seller only knows the empirical value distribution of the buyer population and chooses the revenue-optimal price. We consider a widely studied third-degree price discrimination model where an information intermediary with perfect knowledge of the arriving buyer's value sends a signal to the seller, hence changing the seller's posterior and inducing the seller to set a personalized posted price. Prior work of Bergemann, Brooks, and Morris (American Economic Review, 2015) has shown the existence of a signaling scheme that preserves seller revenue, while always selling the item, hence maximizing consumer surplus. In a departure from prior work, we ask whether the consumer surplus generated is fairly distributed among buyers with different values. To this end, we aim to maximize welfare functions that reward more balanced surplus allocations. Our main result is the surprising existence of a novel signaling scheme that simultaneously $8$-approximates all welfare functions that are non-negative, monotonically increasing, symmetric, and concave, compared with any other signaling scheme. Classical examples of such welfare functions include the utilitarian social welfare, the Nash welfare, and the max-min welfare. Such a guarantee cannot be given by any consumer-surplus-maximizing scheme -- which are the ones typically studied in the literature. In addition, our scheme is socially efficient, and has the fairness property that buyers with higher values enjoy higher expected surplus, which is not always the case for existing schemes.

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arXiv2023

Optimal Pricing Schemes for an Impatient Buyer

A patient seller aims to sell a good to an impatient buyer (i.e., one who discounts utility over time). The buyer will remain in the market for a period of time $T$, and her private value is drawn from a publicly known distribution. What is the revenue-optimal pricing-curve (sequence of (price, time) pairs) for the seller? Is randomization of help here? Is the revenue-optimal pricing curve computable in polynomial time? We answer these questions in this paper. We give an efficient algorithm for computing the revenue-optimal pricing curve. We show that pricing curves, that post a price at each point of time and let the buyer pick her utility maximizing time to buy, are revenue-optimal among a much broader class of sequential lottery mechanisms. I.e., mechanisms that allow the seller to post a menu of lotteries at each point of time cannot get any higher revenue than pricing curves. We also show that the even broader class of mechanisms that allow the menu of lotteries to be adaptively set, can earn strictly higher revenue than that of pricing curves, and the revenue gap can be as big as the support size of the buyer's value distribution.

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arXiv2022

Regret Minimization with Noisy Observations

In a typical optimization problem, the task is to pick one of a number of options with the lowest cost or the highest value. In practice, these cost/value quantities often come through processes such as measurement or machine learning, which are noisy, with quantifiable noise distributions. To take these noise distributions into account, one approach is to assume a prior for the values, use it to build a posterior, and then apply standard stochastic optimization to pick a solution. However, in many practical applications, such prior distributions may not be available. In this paper, we study such scenarios using a regret minimization model. In our model, the task is to pick the highest one out of $n$ values. The values are unknown and chosen by an adversary, but can be observed through noisy channels, where additive noises are stochastically drawn from known distributions. The goal is to minimize the regret of our selection, defined as the expected difference between the highest and the selected value on the worst-case choices of values. We show that the naïve algorithm of picking the highest observed value has regret arbitrarily worse than the optimum, even when $n = 2$ and the noises are unbiased in expectation. On the other hand, we propose an algorithm which gives a constant-approximation to the optimal regret for any $n$. Our algorithm is conceptually simple, computationally efficient, and requires only minimal knowledge of the noise distributions.

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arXiv2022

The Limits of an Information Intermediary in Auction Design

We study the limits of an information intermediary in the classical Bayesian auction, where a revenue-maximizing seller sells one item to $n$ buyers with independent private values. In addition, we have an intermediary who knows the buyers' private values, and can map these to a public signal so as to increase consumer surplus. This model generalizes the single-buyer setting proposed by Bergemann, Brooks, and Morris, who present a signaling scheme that raises the optimal consumer surplus, by guaranteeing that the item is always sold and the seller gets the same revenue as without signaling. Our work aims to understand how this result ports to the setting with multiple buyers. We likewise define the benchmark for the optimal consumer surplus: one where the auction is efficient (i.e., the item is always sold to the highest-valued buyer) and the revenue of the seller is unchanged. We show that no signaling scheme can guarantee this benchmark even for $n=2$ buyers with $2$-point valuation distributions. Indeed, no signaling scheme can be efficient while preserving any non-trivial fraction of the original consumer surplus, and no signaling scheme can guarantee consumer surplus better than a factor of $\frac{1}{2}$ compared to the benchmark. These impossibility results are existential (beyond computational), and provide a sharp separation between the single and multi-buyer settings. In light of this impossibility, we develop signaling schemes with good approximation guarantees to the benchmark. Our main technical result is an $O(1)$-approximation for i.i.d. regular buyers, via signaling schemes that are conceptually simple and computable in polynomial time. We also present an extension to the case of general independent distributions.

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arXiv2021

Approximately Efficient Bilateral Trade

We study bilateral trade between two strategic agents. The celebrated result of Myerson and Satterthwaite states that in general, no incentive-compatible, individually rational and weakly budget balanced mechanism can be efficient. I.e., no mechanism with these properties can guarantee a trade whenever buyer value exceeds seller cost. Given this, a natural question is whether there exists a mechanism with these properties that guarantees a constant fraction of the first-best gains-from-trade, namely a constant fraction of the gains-from-trade attainable whenever buyer's value weakly exceeds seller's cost. In this work, we positively resolve this long-standing open question on constant-factor approximation, mentioned in several previous works, using a simple mechanism.

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arXiv2021

Approximate Core for Committee Selection via Multilinear Extension and Market Clearing

Motivated by civic problems such as participatory budgeting and multiwinner elections, we consider the problem of public good allocation: Given a set of indivisible projects (or candidates) of different sizes, and voters with different monotone utility functions over subsets of these candidates, the goal is to choose a budget-constrained subset of these candidates (or a committee) that provides fair utility to the voters. The notion of fairness we adopt is that of core stability from cooperative game theory: No subset of voters should be able to choose another blocking committee of proportionally smaller size that provides strictly larger utility to all voters that deviate. The core provides a strong notion of fairness, subsuming other notions that have been widely studied in computational social choice. It is well-known that an exact core need not exist even when utility functions of the voters are additive across candidates. We therefore relax the problem to allow approximation: Voters can only deviate to the blocking committee if after they choose any extra candidate (called an additament), their utility still increases by an $α$ factor. If no blocking committee exists under this definition, we call this an $α$-core. Our main result is that an $α$-core, for $α< 67.37$, always exists when utilities of the voters are arbitrary monotone submodular functions, and this can be computed in polynomial time. This result improves to $α< 9.27$ for additive utilities, albeit without the polynomial time guarantee. Our results are a significant improvement over prior work that only shows logarithmic approximations for the case of additive utilities. We complement our results with a lower bound of $α> 1.015$ for submodular utilities, and a lower bound of any function in the number of voters and candidates for general monotone utilities.

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arXiv2021

An $Ω(\log n)$ Lower Bound for Online Matching on the Line

For online matching with the line metric, we present a lower bound of $Ω(\log n)$ on the approximation ratio of any online (possibly randomized) algorithm. This beats the previous best lower bound of $Ω(\sqrt{\log n})$ and matches the known upper bound of $O(\log n)$.

cs.DS↗

arXiv2021

Interactive Communication in Bilateral Trade

We define a model of interactive communication where two agents with private types can exchange information before a game is played. The model contains Bayesian persuasion as a special case of a one-round communication protocol. We define message complexity corresponding to the minimum number of interactive rounds necessary to achieve the best possible outcome. Our main result is that for bilateral trade, agents don't stop talking until they reach an efficient outcome: Either agents achieve an efficient allocation in finitely many rounds of communication; or the optimal communication protocol has infinite number of rounds. We show an important class of bilateral trade settings where efficient allocation is achievable with a small number of rounds of communication.

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arXiv2021

Optimal Algorithms for Multiwinner Elections and the Chamberlin-Courant Rule

We consider the algorithmic question of choosing a subset of candidates of a given size $k$ from a set of $m$ candidates, with knowledge of voters' ordinal rankings over all candidates. We consider the well-known and classic scoring rule for achieving diverse representation: the Chamberlin-Courant (CC) or $1$-Borda rule, where the score of a committee is the average over the voters, of the rank of the best candidate in the committee for that voter; and its generalization to the average of the top $s$ best candidates, called the $s$-Borda rule. Our first result is an improved analysis of the natural and well-studied greedy heuristic. We show that greedy achieves a $\left(1 - \frac{2}{k+1}\right)$-approximation to the maximization (or satisfaction) version of CC rule, and a $\left(1 - \frac{2s}{k+1}\right)$-approximation to the $s$-Borda score. Our result improves on the best known approximation algorithm for this problem. We show that these bounds are almost tight. For the dissatisfaction (or minimization) version of the problem, we show that the score of $\frac{m+1}{k+1}$ can be viewed as an optimal benchmark for the CC rule, as it is essentially the best achievable score of any polynomial-time algorithm even when the optimal score is a polynomial factor smaller (under standard computational complexity assumptions). We show that another well-studied algorithm for this problem, called the Banzhaf rule, attains this benchmark. We finally show that for the $s$-Borda rule, when the optimal value is small, these algorithms can be improved by a factor of $\tilde Ω(\sqrt{s})$ via LP rounding. Our upper and lower bounds are a significant improvement over previous results, and taken together, not only enable us to perform a finer comparison of greedy algorithms for these problems, but also provide analytic justification for using such algorithms in practice.

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arXiv2021

Fair for All: Best-effort Fairness Guarantees for Classification

Standard approaches to group-based notions of fairness, such as \emph{parity} and \emph{equalized odds}, try to equalize absolute measures of performance across known groups (based on race, gender, etc.). Consequently, a group that is inherently harder to classify may hold back the performance on other groups; and no guarantees can be provided for unforeseen groups. Instead, we propose a fairness notion whose guarantee, on each group $g$ in a class $\mathcal{G}$, is relative to the performance of the best classifier on $g$. We apply this notion to broad classes of groups, in particular, where (a) $\mathcal{G}$ consists of all possible groups (subsets) in the data, and (b) $\mathcal{G}$ is more streamlined. For the first setting, which is akin to groups being completely unknown, we devise the {\sc PF} (Proportional Fairness) classifier, which guarantees, on any possible group $g$, an accuracy that is proportional to that of the optimal classifier for $g$, scaled by the relative size of $g$ in the data set. Due to including all possible groups, some of which could be too complex to be relevant, the worst-case theoretical guarantees here have to be proportionally weaker for smaller subsets. For the second setting, we devise the {\sc BeFair} (Best-effort Fair) framework which seeks an accuracy, on every $g \in \mathcal{G}$, which approximates that of the optimal classifier on $g$, independent of the size of $g$. Aiming for such a guarantee results in a non-convex problem, and we design novel techniques to get around this difficulty when $\mathcal{G}$ is the set of linear hypotheses. We test our algorithms on real-world data sets, and present interesting comparative insights on their performance.

cs.LG↗

arXiv2021

Centrality with Diversity

Graph centrality measures use the structure of a network to quantify central or "important" nodes, with applications in web search, social media analysis, and graphical data mining generally. Traditional centrality measures such as the well known PageRank interpret a directed edge as a vote in favor of the importance of the linked node. We study the case where nodes may belong to diverse communities or interests and investigate centrality measures that can identify nodes that are simultaneously important to many such diverse communities. We propose a family of diverse centrality measures formed as fixed point solutions to a generalized nonlinear eigenvalue problem. Our measure can be efficiently computed on large graphs by iterated best response and we study its normative properties on both random graph models and real-world data. We find that we are consistently and efficiently able to identify the most important diverse nodes of a graph, that is, those that are simultaneously central to multiple communities.

cs.SI↗

arXiv2020

Online Stochastic Matching with Edge Arrivals

Online bipartite matching with edge arrivals remained a major open question for a long time until a recent negative result by [Gamlath et al. FOCS 2019], who showed that no online policy is better than the straightforward greedy algorithm, i.e., no online algorithm has a worst-case competitive ratio better than $0.5$. In this work, we consider the bipartite matching problem with edge arrivals in a natural stochastic framework, i.e., Bayesian setting where each edge of the graph is independently realized according to a known probability distribution. We focus on a natural class of prune & greedy online policies motivated by practical considerations from a multitude of online matching platforms. Any prune & greedy algorithm consists of two stages: first, it decreases the probabilities of some edges in the stochastic instance and then runs greedy algorithm on the pruned graph. We propose prune & greedy algorithms that are $0.552$-competitive on the instances that can be pruned to a $2$-regular stochastic bipartite graph, and $0.503$-competitive on arbitrary bipartite graphs. The algorithms and our analysis significantly deviate from the prior work. We first obtain analytically manageable lower bound on the size of the matching, which leads to a non linear optimization problem. We further reduce this problem to a continuous optimization with a constant number of parameters that can be solved using standard software tools.

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arXiv2020

Approximately Stable Committee Selection

In the committee selection problem, we are given $m$ candidates, and $n$ voters. Candidates can have different weights. A committee is a subset of candidates, and its weight is the sum of weights of its candidates. Each voter expresses an ordinal ranking over all possible committees. The only assumption we make on preferences is monotonicity: If $S \subseteq S'$ are two committees, then any voter weakly prefers $S'$ to $S$. We study a general notion of group fairness via stability: A committee of given total weight $K$ is stable if no coalition of voters can deviate and choose a committee of proportional weight, so that all these voters strictly prefer the new committee to the existing one. Extending this notion to approximation, for parameter $c \ge 1$, a committee $S$ of weight $K$ is said to be $c$-approximately stable if for any other committee $S'$ of weight $K'$, the fraction of voters that strictly prefer $S'$ to $S$ is strictly less than $\frac{c K'}{K}$. When $c = 1$, this condition is equivalent to classical core stability. The question we ask is: Does a $c$-approximately stable committee of weight at most any given value $K$ always exist for constant $c$? It is relatively easy to show that there exist monotone preferences for which $c \ge 2$. However, even for simple and widely studied preference structures, a non-trivial upper bound on $c$ has been elusive. In this paper, we show that $c = O(1)$ for all monotone preference structures. Our proof proceeds via showing an existence result for a randomized notion of stability, and iteratively rounding the resulting fractional solution.

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