arXiv subjects

Lirong Xia

Publications and source records attributed to Lirong Xia.

At least 37 records · Page 2Linked to original sources

arXiv2023

Smoothed Differential Privacy

Differential privacy (DP) is a widely-accepted and widely-applied notion of privacy based on worst-case analysis. Often, DP classifies most mechanisms without additive noise as non-private (Dwork et al., 2014). Thus, additive noises are added to improve privacy (to achieve DP). However, in many real-world applications, adding additive noise is undesirable (Bagdasaryan et al., 2019) and sometimes prohibited (Liu et al., 2020). In this paper, we propose a natural extension of DP following the worst average-case idea behind the celebrated smoothed analysis (Spielman & Teng, May 2004). Our notion, smoothed DP, can effectively measure the privacy leakage of mechanisms without additive noises under realistic settings. We prove that any discrete mechanism with sampling procedures is more private than what DP predicts, while many continuous mechanisms with sampling procedures are still non-private under smoothed DP. In addition, we prove several desirable properties of smoothed DP, including composition, robustness to post-processing, and distribution reduction. Based on those properties, we propose an efficient algorithm to calculate the privacy parameters for smoothed DP. Experimentally, we verify that, according to smoothed DP, the discrete sampling mechanisms are private in real-world elections, and some discrete neural networks can be private without adding any additive noise. We believe that these results contribute to the theoretical foundation of realistic privacy measures beyond worst-case analysis.

cs.CR↗

arXiv2023

LLM-augmented Preference Learning from Natural Language

Finding preferences expressed in natural language is an important but challenging task. State-of-the-art(SotA) methods leverage transformer-based models such as BERT, RoBERTa, etc. and graph neural architectures such as graph attention networks. Since Large Language Models (LLMs) are equipped to deal with larger context lengths and have much larger model sizes than the transformer-based model, we investigate their ability to classify comparative text directly. This work aims to serve as a first step towards using LLMs for the CPC task. We design and conduct a set of experiments that format the classification task into an input prompt for the LLM and a methodology to get a fixed-format response that can be automatically evaluated. Comparing performances with existing methods, we see that pre-trained LLMs are able to outperform the previous SotA models with no fine-tuning involved. Our results show that the LLMs can consistently outperform the SotA when the target text is large -- i.e. composed of multiple sentences --, and are still comparable to the SotA performance in shorter text. We also find that few-shot learning yields better performance than zero-shot learning.

cs.CL↗

arXiv2023

Determining Winners in Elections with Absent Votes

An important question in elections is the determine whether a candidate can be a winner when some votes are absent. We study this determining winner with the absent votes (WAV) problem when the votes are top-truncated. We show that the WAV problem is NP-complete for the single transferable vote, Maximin, and Copeland, and propose a special case of positional scoring rule such that the problem can be computed in polynomial time. Our results in top-truncated rankings differ from the results in full rankings as their hardness results still hold when the number of candidates or the number of missing votes are bounded, while we show that the problem can be solved in polynomial time in either case.

cs.GT↗

arXiv2023

Trading Off Voting Axioms for Privacy

In this paper, we investigate tradeoffs among differential privacy (DP) and several important voting axioms: Pareto efficiency, SD-efficiency, PC-efficiency, Condorcet consistency, and Condorcet loser criterion. We provide upper and lower bounds on the two-way tradeoffs between DP and each axiom. We also provide upper and lower bounds on three-way tradeoffs among DP and every pairwise combination of all the axioms, showing that, while the axioms are compatible without DP, their upper bounds cannot be achieved simultaneously under DP. Our results illustrate the effect of DP on the satisfaction and compatibility of voting axioms.

cs.GT↗

arXiv2023

Most Equitable Voting Rules

In social choice theory, anonymity (all agents being treated equally) and neutrality (all alternatives being treated equally) are widely regarded as ``minimal demands'' and ``uncontroversial'' axioms of equity and fairness. However, the ANR impossibility -- there is no voting rule that satisfies anonymity, neutrality, and resolvability (always choosing one winner) -- holds even in the simple setting of two alternatives and two agents. How to design voting rules that optimally satisfy anonymity, neutrality, and resolvability remains an open question. We address the optimal design question for a wide range of preferences and decisions that include ranked lists and committees. Our conceptual contribution is a novel and strong notion of most equitable refinements that optimally preserves anonymity and neutrality for any irresolute rule that satisfies the two axioms. Our technical contributions are twofold. First, we characterize the conditions for the ANR impossibility to hold under general settings, especially when the number of agents is large. Second, we propose the most-favorable-permutation (MFP) tie-breaking to compute a most equitable refinement and design a polynomial-time algorithm to compute MFP when agents' preferences are full rankings.

cs.GT↗

arXiv2023

The Impact of a Coalition: Assessing the Likelihood of Voter Influence in Large Elections

For centuries, it has been widely believed that the influence of a small coalition of voters is negligible in a large election. Consequently, there is a large body of literature on characterizing the likelihood for an election to be influenced when the votes follow certain distributions, especially the likelihood of being manipulable by a single voter under the i.i.d. uniform distribution, known as the Impartial Culture (IC). In this paper, we extend previous studies in three aspects: (1) we propose a more general semi-random model, where a distribution adversary chooses a worst-case distribution and then a contamination adversary modifies up to $ψ$ portion of the data, (2) we consider many coalitional influence problems, including coalitional manipulation, margin of victory, and various vote controls and bribery, and (3) we consider arbitrary and variable coalition size $B$. Our main theorem provides asymptotically tight bounds on the semi-random likelihood of the existence of a size-$B$ coalition that can successfully influence the election under a wide range of voting rules. Applications of the main theorem and its proof techniques resolve long-standing open questions about the likelihood of coalitional manipulability under IC, by showing that the likelihood is $Θ\left(\min\left\{\frac{B}{\sqrt n}, 1\right\}\right)$ for many commonly-studied voting rules. The main technical contribution is a characterization of the semi-random likelihood for a Poisson multinomial variable (PMV) to be unstable, which we believe to be a general and useful technique with independent interest.

econ.TH↗

arXiv2023

Accelerating Voting by Quantum Computation

Studying the computational complexity and designing fast algorithms for determining winners under voting rules are classical and fundamental questions in computational social choice. In this paper, we accelerate voting by leveraging quantum computation: we propose a quantum-accelerated voting algorithm that can be applied to any anonymous voting rule. We show that our algorithm can be quadratically faster than any classical algorithm (based on sampling with replacement) under a wide range of common voting rules, including positional scoring rules, Copeland, and single transferable voting (STV). Precisely, our quantum-accelerated voting algorithm outputs the correct winner with high probability in $Θ\left(\frac{n}{\text{MOV}}\right)$ time, where $n$ is the number of votes and $\text{MOV}$ is {\em margin of victory}, the smallest number of voters to change the winner. In contrast, any classical voting algorithm based on sampling with replacement requires $Ω\left(\frac{n^2}{\text{MOV}^2}\right)$ time under a large class of voting rules. Our theoretical results are supported by experiments under plurality, Borda, Copeland, and STV.

cs.CY↗

arXiv2023

The Wisdom of Strategic Voting

We study the voting game where agents' preferences are endogenously decided by the information they receive, and they can collaborate in a group. We show that strategic voting behaviors have a positive impact on leading to the ``correct'' decision, outperforming the common non-strategic behavior of informative voting and sincere voting. Our results give merit to strategic voting for making good decisions. To this end, we investigate a natural model, where voters' preferences between two alternatives depend on a discrete state variable that is not directly observable. Each voter receives a private signal that is correlated with the state variable. We reveal a surprising equilibrium between a strategy profile being a strong equilibrium and leading to the decision favored by the majority of agents conditioned on them knowing the ground truth (referred to as the informed majority decision): as the size of the vote goes to infinity, every $\varepsilon$-strong Bayes Nash Equilibrium with $\varepsilon$ converging to $0$ formed by strategic agents leads to the informed majority decision with probability converging to $1$. On the other hand, we show that informative voting leads to the informed majority decision only under unbiased instances, and sincere voting leads to the informed majority decision only when it also forms an equilibrium.

cs.GT↗

arXiv2023

First-Choice Maximality Meets Ex-ante and Ex-post Fairness

For the assignment problem where multiple indivisible items are allocated to a group of agents given their ordinal preferences, we design randomized mechanisms that satisfy first-choice maximality (FCM), i.e., maximizing the number of agents assigned their first choices, together with Pareto efficiency (PE). Our mechanisms also provide guarantees of ex-ante and ex-post fairness. The generalized eager Boston mechanism is ex-ante envy-free, and ex-post envy-free up to one item (EF1). The generalized probabilistic Boston mechanism is also ex-post EF1, and satisfies ex-ante efficiency instead of fairness. We also show that no strategyproof mechanism satisfies ex-post PE, EF1, and FCM simultaneously. In doing so, we expand the frontiers of simultaneously providing efficiency and both ex-ante and ex-post fairness guarantees for the assignment problem.

cs.GT↗

arXiv2023

Average Envy-freeness for Indivisible Items

In fair division applications, agents may have unequal entitlements reflecting their different contributions. Moreover, the contributions of agents may depend on the allocation itself. Previous fairness notions designed for agents with equal or pre-determined entitlement fail to characterize fairness in these collaborative allocation scenarios. We propose a novel fairness notion of average envy-freeness (AEF), where the envy of agents is defined on the average value of items in the bundles. Average envy-freeness provides a reasonable comparison between agents based on the items they receive and reflects their entitlements. We study the complexity of finding AEF and its relaxation, average envy-freeness up to one item (AEF-1). While deciding if an AEF allocation exists is NP-complete, an AEF-1 allocation is guaranteed to exist and can be computed in polynomial time. We also study allocation with quotas, i.e. restrictions on the sizes of bundles. We prove that finding AEF-1 allocation satisfying a quota is NP-hard. Nevertheless, in the instances with a fixed number of agents, we propose polynomial-time algorithms to find AEF-1 allocation with a quota for binary valuation and approximated AEF-1 allocation with a quota for general valuation.

cs.GT↗

arXiv2023

Strategic Behavior is Bliss: Iterative Voting Improves Social Welfare

Recent work in iterative voting has defined the additive dynamic price of anarchy (ADPoA) as the difference in social welfare between the truthful and worst-case equilibrium profiles resulting from repeated strategic manipulations. While iterative plurality has been shown to only return alternatives with at most one less initial votes than the truthful winner, it is less understood how agents' welfare changes in equilibrium. To this end, we differentiate agents' utility from their manipulation mechanism and determine iterative plurality's ADPoA in the worst- and average-cases. We first prove that the worst-case ADPoA is linear in the number of agents. To overcome this negative result, we study the average-case ADPoA and prove that equilibrium winners have a constant order welfare advantage over the truthful winner in expectation. Our positive results illustrate the prospect for social welfare to increase due to strategic manipulation.

cs.GT↗

arXiv2023

Convergence of Multi-Issue Iterative Voting under Uncertainty

We study the effect of strategic behavior in iterative voting for multiple issues under uncertainty. We introduce a model synthesizing simultaneous multi-issue voting with Meir, Lev, and Rosenschein (2014)'s local dominance theory 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 and endowing agents with less uncertainty about issues they are modifying than others. Our empirical studies demonstrate that although cycles are common when agents have no uncertainty, introducing uncertainty makes convergence almost guaranteed in practice.

cs.GT↗

arXiv2022

Frustratingly Easy Truth Discovery

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.

cs.AI↗

arXiv2022

Beyond the Worst Case: Semi-Random Complexity Analysis of Winner Determination

The computational complexity of winner determination is a classical and important problem in computational social choice. Previous work based on worst-case analysis has established NP-hardness of winner determination for some classic voting rules, such as Kemeny, Dodgson, and Young. In this paper, we revisit the classical problem of winner determination through the lens of semi-random analysis, which is a worst average-case analysis where the preferences are generated from a distribution chosen by the adversary. Under a natural class of semi-random models that are inspired by recommender systems, we prove that winner determination remains hard for Dodgson, Young, and some multi-winner rules such as the Chamberlin-Courant rule and the Monroe rule. Under another natural class of semi-random models that are extensions of the Impartial Culture, we show that winner determination is hard for Kemeny, but is easy for Dodgson. This illustrates an interesting separation between Kemeny and Dodgson.

cs.GT↗

arXiv2022

Differentially Private Condorcet Voting

Designing private voting rules is an important and pressing problem for trustworthy democracy. In this paper, under the framework of differential privacy, we propose a novel famliy of randomized voting rules based on the well-known Condorcet method, and focus on three classes of voting rules in this family: Laplacian Condorcet method ($\CMLAP_λ$), exponential Condorcet method ($\CMEXP_λ$), and randomized response Condorcet method ($\CMRR_λ$), where $λ$ represents the level of noise. We prove that all of our rules satisfy absolute monotonicity, lexi-participation, probabilistic Pareto efficiency, approximate probabilistic Condorcet criterion, and approximate SD-strategyproofness. In addition, $\CMRR_λ$ satisfies (non-approximate) probabilistic Condorcet criterion, while $\CMLAP_λ$ and $\CMEXP_λ$ satisfy strong lexi-participation. Finally, we regard differential privacy as a voting axiom, and discuss its relations to other axioms.

cs.GT↗

arXiv2022

Semi-Random Impossibilities of Condorcet Criterion

The Condorcet criterion (CC) is a classical and well-accepted criterion for voting. Unfortunately, it is incompatible with many other desiderata including participation (Par), half-way monotonicity (HM), Maskin monotonicity (MM), and strategy-proofness (SP). Such incompatibilities are often known as impossibility theorems, and are proved by worst-case analysis. Previous work has investigated the likelihood for these impossibilities to occur under certain models, which are often criticized of being unrealistic. We strengthen previous work by proving the first set of semi-random impossibilities for voting rules to satisfy CC and the more general, group versions of the four desiderata: for any sufficiently large number of voters $n$, any size of the group $1\le B\le \sqrt n$, any voting rule $r$, and under a large class of {\em semi-random} models that include Impartial Culture, the likelihood for $r$ to satisfy CC and Par, CC and HM, CC and MM, or CC and SP is $1-Ω(\frac{B}{\sqrt n})$. This matches existing lower bounds for CC and Par ($B=1$) and CC and SP ($B\le \sqrt n$), showing that many commonly-studied voting rules are already asymptotically optimal in such cases.

econ.TH↗

arXiv2022

Learning Mixtures of Random Utility Models with Features from Incomplete Preferences

Random Utility Models (RUMs), which subsume Plackett-Luce model (PL) as a special case, are among the most popular models for preference learning. In this paper, we consider RUMs with features and their mixtures, where each alternative has a vector of features, possibly different across agents. Such models significantly generalize the standard PL and RUMs, but are not as well investigated in the literature. We extend mixtures of RUMs with features to models that generate incomplete preferences and characterize their identifiability. For PL, we prove that when PL with features is identifiable, its MLE is consistent with a strictly concave objective function under mild assumptions, by characterizing a bound on root-mean-square-error (RMSE), which naturally leads to a sample complexity bound. We also characterize identifiability of more general RUMs with features and propose a generalized RBCML to learn them. Our experiments on synthetic data demonstrate the effectiveness of MLE on PL with features with tradeoffs between statistical efficiency and computational efficiency. Our experiments on real-world data show the prediction power of PL with features and its mixtures.

cs.LG↗

arXiv2022

Favoring Eagerness for Remaining Items: Designing Efficient, Fair, and Strategyproof Mechanisms

In the assignment problem, the goal is to assign indivisible items to agents who have ordinal preferences, efficiently and fairly, in a strategyproof manner. In practice, first-choice maximality, i.e., assigning a maximal number of agents their top items, is often identified as an important efficiency criterion and measure of agents' satisfaction. In this paper, we propose a natural and intuitive efficiency property, favoring-eagerness-for-remaining-items (FERI), which requires that each item is allocated to an agent who ranks it highest among remaining items, thereby implying first-choice maximality. Using FERI as a heuristic, we design mechanisms that satisfy ex-post or ex-ante variants of FERI together with combinations of other desirable properties of efficiency (Pareto-efficiency), fairness (strong equal treatment of equals and sd-weak-envy-freeness), and strategyproofness (sd-weak-strategyproofness). We also explore the limits of FERI mechanisms in providing stronger efficiency, fairness, or strategyproofness guarantees through impossibility results.

cs.GT↗