Papers
2025
- The Price of Processing: Information Frictions and Market Efficiency in DeFiPablo D. Azar, Sergio Olivas, and Nish D. SinhaApr 2025
This paper investigates the speed of price discovery when information becomes publicly available but requires costly processing to become common knowledge. We exploit the unique institutional setting of hacks on decentralized finance (DeFi) protocols. Public blockchain data provides the precise time a hack’s transactions are recorded—becoming public information—while subsequent social media disclosures mark the transition to common knowledge. This empirical design allows us to isolate the price impact occurring during the interval characterized by information asymmetry driven purely by differential processing capabilities. Our central empirical finding is that substantial price discovery precedes common knowledge: approximately 36 percent of the total 24-hour price decline (∼27 percent) materializes before the public announcement. This evidence suggests sophisticated traders rapidly exploit their ability to process complex, publicly available on-chain data, capturing informational rents. We develop a theoretical model of informed trading under processing costs which predicts strategic, slow information revelation, consistent with our empirical findings. Our results quantify the limits imposed by information processing costs on market efficiency, demonstrating that transparency alone does not guarantee immediate information incorporation into prices.
- Natural Centralization in Decentralized FinancePablo D. Azar, Adrian Casillas, and Maryam FarboodiMay 2025
The decentralized nature of blockchain markets has given rise to a complex and highly heterogeneous market structure, gaining increasing importance as traditional and decentralized finance become more interconnected. This paper introduces the DeFi intermediation chain and provides theoretical and empirical evidence for private infor- mation as a key determinant of intermediation rents. We propose a repeated bargain- ing model that predicts that profit share of Ethereum market participants is positively correlated with their private information, and employ a novel instrumental variable approach to show that a 1% increase in the value of intermediaries’ private information leads to a 1.4% increase in their profit share.
- The Financial Stability Implications of Tokenized Money Market FundsPablo D. Azar, Francesca Carapella, and Alexandros VardoulakisMay 2025
The market for repurchase agreements (repo) is central to short-term funding and monetary policy transmission, relying critically on high-quality collateral, typically sovereign debt. While the exchanged security serves as the primary collateral, cash is commonly posted to cover haircuts or variation margin, ensuring the transaction remains adequately collateralized against market fluctuations. This paper examines the financial stability implications of substituting tokenized Money Market Fund (MMF) shares for cash in this crucial margining function. We argue that while technologically feasible, this substitution introduces novel systemic risks. Tokenized MMFs inherit the run propensity of traditional MMFs and add unique technological vulnerabilities (blockchain finality, smart contract risk). Embedding these instruments within the repo margining process creates a new transmission channel for shocks from both the MMF sector and the digital asset ecosystem into the core of the traditional financial system, potentially amplifying procyclicality and systemic fragility. We draw parallels to the information sensitivity of private debt used as collateral, suggesting tokenized MMFs may be insufficiently robust to serve the role typically played by cash margin in mitigating counterparty risk during stress.
- Banking on the BlockchainPablo D. Azar, and Will F. DiamondMay 2025
The ability of banks to transform maturities creates economic value but also inherent fragility, potentially leading to inefficient runs and liquidations, as shown by Diamond and Dybvig (1983). Traditional solutions like deposit insurance or suspension of convertibility mitigate runs but introduce other distortions. This paper asks whether banks can achieve efficient liquidity transformation without runs, relying solely on market mechanisms augmented by modern cryptographic tools, thereby potentially reaching a constrained first-best outcome. We develop a model where banks face idiosyncratic depositor liquidity shocks and where revealing liquidity stress publicly incurs stigma, triggering runs. We argue that cryptographic primitives require verifiable on-chain representations of bank state, achievable via specific blockchain architectures (e.g., Bowe, Gabizon, and Miers 2020) or trusted auditors. Our core analysis shows that anonymous funding mechanisms, enabled by cryptography and verifiable state, allow solvent-but-stressed banks to access liquidity without incurring stigma, thus eliminating inefficient runs. Under conditions where such funding is sufficiently available, the equilibrium allocation approaches the constrained first-best, characterized by minimal precautionary liquidity hoarding and the absence of belief-driven runs. We also analyze the complementary role of Zero-Knowledge Proofs for state verification and, in an extension, Verifiable Random Functions for mitigating adverse selection in liquidations. The paper provides a micro-founded analysis of how specific cryptographic tools, underpinned by verifiable state information, can address fundamental informational frictions in banking.
- Computation, Misallocation and GrowthPablo D. AzarMay 2025
This paper develops a novel economic growth model where computational capacity serves as a fundamental constraint on allocation efficiency. We model an economy facing an infinite sequence of resource allocation problems with varying dimensionality, where finding optimal solutions requires exponentially increasing computational resources as problem complexity grows. Using results from computational complexity theory—specifically the hardness of the Closest Vector Problem—we derive the optimal allocation of computational resources across problems and characterize the steady state. Our model demonstrates that computational investment represents a critical channel for economic growth, particularly as economies become more complex. The framework provides new insights into the diminishing returns to computational advancement observed in mature sectors and establishes conditions for sustainable growth paths that balance computational capacity with increasing economic complexity.
- Blockchain Breakdown: Causal Evidence that Proof of Work is not StrategyproofPablo D. AzarMay 2025
Digital assets, increasingly integrated into finance via ETFs and tokenized products, rely on consensus protocols like Proof-of-Work (PoW) for security. However, whether these PoW protocols truly incentivize honest participation or allow strategic deviation (selfish mining) remains debated. Exploiting high-frequency Ethereum data and a novel instrumental variables strategy, we causally demonstrate PoW’s manipulability. We find that higher mining rewards—-driven by exogenous shocks such as crypto hacks and crises—-significantly increase stolen and uncle blocks—proxies for consensus instability linked to selfish mining. Quantitatively, a one percent increase in average hourly transaction fee revenue leads to approximately 1.23 additional stolen blocks per hour. We explain these empirical findings with a model where selfish miners can adjust their hashing rate at the intensive margin by renting computational power from mining pools. This reveals a fundamental tension: the very incentives designed for blockchain security can degrade stability, posing systemic risks and highlighting critical market design challenges for decentralized financial infrastructure as these assets become more interconnected with traditional financial institutions.
2024
- The Financial Stability Implications of Digital AssetsPablo D. Azar, Garth Baughman, Francesca Carapella, and 8 more authorsEconomic Policy Review, May 2024
The value of assets in the digital ecosystem has grown rapidly amid periods of high volatility. Does the digital financial system create new potential challenges to financial stability? This paper explores this question using the Federal Reserve’s framework for analyzing vulnerabilities in the traditional financial system. The digital asset ecosystem has recently proven itself to be highly fragile. However, adverse digital asset market shocks have had limited spillovers to the traditional financial system. Currently, the digital asset ecosystem does not provide significant financial services outside the ecosystem, and it exhibits limited interconnections with the traditional financial system. The paper describes emerging vulnerabilities that could present risks to financial stability in the future if the digital asset ecosystem becomes more systemic, including run risks among large stablecoins, valuation pressures in crypto-assets, fragilities of DeFi platforms, growing interconnectedness, and a general lack of regulation.
2023
- Runs and Flights to Safety: Are Stablecoins the New Money Market Funds?Kenechukwu Anadu, Pablo D. Azar, Marco Cipriani, and 7 more authorsSep 2023Revise and Resubmit at JFQA
Similar to the more traditional money market funds (MMFs), stablecoins aim to provide investors with safe, money-like assets. We investigate similarities and differences between these two investment products. Like MMFs, stablecoins suffer from "flight-to-safety" dynamics: we document net flows from riskier to safer stablecoins on days of crypto-market stress and estimate a discrete "break-the-buck" threshold of $1, below which stablecoin redemptions accelerate. We then focus on two specific stablecoin runs, in 2022 and 2023, showing that the same flight-to-safety dynamics also characterized these episodes. Finally, as flight-to-safety flows occur within MMF families, stablecoin flows tend to happen within blockchains.
- Central bank digital currency (CBDC) information security and operational risks to central banksCBDC Task Force AmericasNov 2023
Introducing a central bank digital currency (CBDC) will have far-reaching implications for the operations of the issuing central bank and the risk it faces. Both will depend mainly on the particular design adopted and on a large range of factors internal and external to the central bank. This report analyses the operating, technology, thirdparty and business continuity risks for the issuing central bank. It therefore provides a useful complement to other work on CBDCs, which tends to focus on their implications for financial stability, monetary policy and the wider economy. The report proposes an integrated risk-management framework that can be applied to the entire life cycle of a CBDC, from the research and design stages to implementation and operation. It discusses the implications of many of the design choices that a central bank needs to take and suggests tools and processes to identify and mitigate the risks that a CBDC poses to the issuing institution. For CBDCs to be a reliable means of payments, central banks also need to address, among others, the risks of interruptions or disruptions and ensure integrity and confidentiality. A key risk are the potential gaps in central banks’ internal capabilities and skills. While many of the CBDC-related activities could in principle be outsourced, doing so requires adequate capacity to select and supervise vendors. The report is the outcome of the work conducted by BIS member central banks in the Americas within the Consultative Group on Risk Management (CGRM), which brings together representatives of the central banks of Brazil, Canada, Chile, Colombia, Mexico, Peru and the United States. The task force was led by Diego Ballivián from the Central Bank of Chile; subgroups were led by Antonieta Campa from the Bank of Mexico, María Jesús Orellana from the Central Bank of Chile and David Whyte from the BIS. The BIS Americas Office acted as the secretariat.
2021
- Moore’s Law and Economic GrowthPablo D. AzarMay 2021Revised October 2022
Over the past sixty years, semiconductor sizes have decreased by 50 percent every eighteen months, a trend known as Moore’s Law. Moore’s Law has increased productivity in virtually every industry, both by increasing the computational and storage power of electronic devices, and by allowing the incorporation of electronics into existing products such as vehicles and industrial machinery. In this paper, I examine the physical channel through which Moore’s Law affects GDP growth. A new model incorporates physical constraints on firms’ production functions and allows for new types of spillovers from the physical characteristics of products. I use the model, and a new data set of product weights, to estimate the effect of the electronic miniaturization channel on productivity growth. The results show that between 11.74 and 18.63 percent of productivity growth during 1960 to 2019 can be attributed to physical changes in the size of electronic components. This effect is highest during the 1990s and early 2000s.
2020
- Endogenous Production NetworksDaron Acemoglu, and Pablo D. AzarEconometrica, May 2020
We develop a tractable model of endogenous production networks. Each one of a number of products can be produced by combining labor and an endogenous subset of the other products as inputs. Different combinations of inputs generate (prespecified) levels of productivity and various distortions may affect costs and prices. We establish the existence and uniqueness of an equilibrium and provide comparative static results on how prices and endogenous technology/input choices (and thus the production network) respond to changes in parameters. These results show that improvements in technology (or reductions in distortions) spread throughout the economy via input–output linkages and reduce all prices, and under reasonable restrictions on the menu of production technologies, also lead to a denser production network. Using a dynamic version of the model, we establish that the endogenous evolution of the production network could be a powerful force towards sustained economic growth. At the root of this result is the fact that the arrival of a few new products expands the set of technological possibilities of all existing industries by a large amount—that is, if there are n products, the arrival of one more new product increases the combinations of inputs that each existing product can use from 2n−1 to 2n, thus enabling significantly more pronounced cost reductions from choice of input combinations. These cost reductions then spread to other industries via lower input prices and incentivize them to also adopt additional inputs.
2019
- Prior-Independent Mechanisms via Prophet Inequalities with Limited InformationPablo D. Azar, Robert Kleinberg, and S. Matthew WeinbergGames and Economic Behavior, May 2019
Prophet inequalities have recently become a fundamental tool in the design of sequential and multi-dimensional mechanisms in Bayesian settings. However, existing mechanisms—as well as the underlying prophet inequalities behind their analysis—require sophisticated information about the distribution from which inputs are drawn. Our goal in this work is to design prior-independent sequential and multi-dimensional mechanisms. To this end, we first design prophet inequalities that require knowing only a single sample from the input distribution. These results come in two forms: the first is via a reduction from single-sample prophet inequalities to secretary algorithms. The second is via novel single-sample prophet inequalities for k-uniform matroids. Leveraging our new prophet inequalities, we construct the first prior-independent sequential mechanisms where the seller does not know the order in which buyers arrive, and buyers may have asymmetric value distributions. We also construct the first prior-independent multi-dimensional mechanism where buyers may have asymmetric value distributions.
2018
- Momentum, Mean-Reversion and Social-Media: Evidence from StockTwits and TwitterPablo D. Azar, Shreyash Agrawal, Andrew W. Lo, and 1 more authorThe Journal of Portfolio Management, May 2018
We analyze the relation between stock market liquidity and real-time measures of sentiment obtained from the social-media platforms StockTwits and Twitter. Linear regression analysis shows that extreme sentiment corresponds to higher demand and lower supply of liquidity, with negative sentiment having a much larger effect on demand and supply than positive sentiment. An intraday event study shows that booms and panics end when bullish and bearish sentiment reach extreme levels, respectively. After extreme sentiment, prices become more mean-reverting and spreads narrow. To quantify the magnitudes of these effects, we conduct a historical simulation of a market-neutral mean-reversion strategy that uses social-media information to determine its portfolio allocations. Our results suggest that the demand and supply of liquidity are influenced by investor sentiment, and that market makers who can keep their transaction costs to a minimum are able to profit by using extreme bullish and bearish emotions in social media as a real-time barometer for the end of momentum and a return to mean reversion.
- Computational Principal-Agent ProblemsPablo D. Azar, and Silvio MicaliTheoretical Economics, May 2018
Collecting and processing large amounts of data is becoming increasingly crucial in our society. We model this task as evaluating a function f over a large vector x = (x_1, \ldots, x_n), which is unknown, but drawn from a publicly known distribution X. In our model, learning each component of the input x is costly, but computing the output f(x) has zero cost once x is known. We consider the problem of a principal who wishes to delegate the evaluation of f to an agent whose cost of learning any number of components of x is always lower than the corresponding cost of the principal. We prove that, for every continuous function f and every ε> 0, the principal can—by learning a single component x_i of x—incentivize the agent to report the correct value f(x) with accuracy ε.
2016
- The Wisdom of Twitter Crowds: Predicting Stock Market Reactions to FOMC Meetings via Twitter FeedsPablo D. Azar, and Andrew W. LoThe Journal of Portfolio Management, May 2016
With the rise of social media, investors have a new tool to measure sentiment in real time. However, the nature of these sources of data raises serious questions about its quality. Since anyone on social media can participate in a conversation about markets – whether they are informed or not – it is possible that this data may have very little information about future asset prices. In this paper, we show that this is not the case by analyzing a recurring event that has a high impact on asset prices: Federal Open Market Committee (FOMC) meetings. We exploit a new dataset of tweets referencing the Federal Reserve and shows that the content of tweets can be used to predict future returns, even after controlling for common asset pricing factors. To gauge the economic magnitude of these predictions, the authors construct a simple hypothetical trading strategy based on this data. They find that a tweet-based asset-allocation strategy outperforms several benchmarks, including a strategy that buys and holds a market index as well as a comparable dynamic asset allocation strategy that does not use Twitter information.
- How to Incentivize Data-Driven Collaboration Among Competing PartiesPablo D. Azar, Shafi Goldwasser, and Sunoo ParkIn 7th Innovations in Theoretical Computer Science conference (ITCS 2016), May 2016
The availability of vast amounts of data is changing how we can make medical discoveries, predict global market trends, save energy, and develop educational strategies. In some settings such as Genome Wide Association Studies or deep learning, sheer size of data seems critical. When data is held distributedly by many parties, they must share it to reap its full benefits. One obstacle to this revolution is the lack of willingness of different parties to share data, due to reasons such as loss of privacy or competitive edge. Cryptographic works address privacy aspects, but shed no light on individual parties’ losses/gains when access to data carries tangible rewards. Even if it is clear that better overall conclusions can be drawn from collaboration, are individual collaborators better off by collaborating? Addressing this question is the topic of this paper. * We formalize a model of n-party collaboration for computing functions over private inputs in which participants receive their outputs in sequence, and the order depends on their private inputs. Each output "improves" on preceding outputs according to a score function. * We say a mechanism for collaboration achieves collaborative equilibrium if it ensures higher reward for all participants when collaborating (rather than working alone). We show that in general, computing a collaborative equilibrium is NP-complete, yet we design efficient algorithms to compute it in a range of natural model settings. Our collaboration mechanisms are in the standard model, and thus require a central trusted party; however, we show this assumption is unnecessary under standard cryptographic assumptions. We show how to implement the mechanisms in a decentralized way with new extensions of secure multiparty computation that impose order/timing constraints on output delivery to different players, as well as privacy and correctness.
2015
- Law is Code: A Software Engineering Approach to Analyzing the United States CodePablo D. Azar, William Li, David Larochelle, and 2 more authorsJournal of Business and Technology Law, May 2015
The agglomeration of rules and regulations over time has produced a body of legal code that no single individual can fully comprehend. This complexity produces inefficiencies, makes the processes of understanding and changing the law difficult, and frustrates the fundamental principle that the law should provide fair notice to the governed. In this Article, we take a quantitative, unbiased, and softwareengineering approach to analyze the evolution of the United States Code from 1926 to today. Software engineers frequently face the challenge of understanding and managing large, structured collections of instructions, directives, and conditional statements, and we adapt and apply their techniques to the U.S. Code over time. Our work produces insights into the structure of the U.S. Code as a whole, its strengths and vulnerabilities, and new ways of thinking about individual laws. For example, we identify the first appearance and spread of important terms in the U.S. Code like "whistleblower" and "privacy." We also analyze and visualize the network structure of certain substantial reforms, including the Patient Protection and Affordable Care Act and the Dodd-Frank Wall Street Reform and Consumer Protection Act, and show how the interconnections of references can increase complexity and create the potential for unintended consequences. Our work is a timely illustration of computational approaches to law as the legal profession embraces technology for scholarship in order to increase efficiency and to improve access to justice.
2014
- Prophet Inequalities With Limited InformationPablo D. Azar, Robert Kleinberg, and S. Matthew WeinbergIn Symposium on Discrete Algorithms (SODA 2014), May 2014
In the classical prophet inequality, a gambler observes a sequence of stochastic rewards V_1, \ldots, V_n and must decide, for each reward V_i, whether to keep it and stop the game or to forfeit the reward forever and reveal the next value V_i. The gambler’s goal is to obtain a constant fraction of the expected reward that the optimal offline algorithm would get. Recently, prophet inequalities have been generalized to settings where the gambler can choose k items, and, more generally, where he can choose any independent set in a matroid. However, all the existing algorithms require the gambler to know the distribution from which the rewards V_1, \ldots, V_n are drawn. The assumption that the gambler knows the distribution from which V_1, \ldots, V_n are drawn is very strong. Instead, we work with the much simpler assumption that the gambler only knows a few samples from this distribution. We construct the first single-sample prophet inequalities for many settings of interest, whose guarantees all match the best possible asymptotically, \empheven with full knowledge of the distribution. Specifically, we provide a novel single-sample algorithm when the gambler can choose any k elements whose analysis is based on random walks with limited correlation. In addition, we provide a black-box method for converting specific types of solutions to the related \emphsecretary problem to single-sample prophet inequalities, and apply it to several existing algorithms. Finally, we provide a constant-sample prophet inequality for constant-degree bipartite matchings. In addition, we apply these results to design the first posted-price and multi-dimensional auction mechanisms with limited information in settings with asymmetric bidders. Connections between prophet inequalities and posted-price mechanisms are already known, but applying the existing framework requires knowledge of the underlying distributions, as well as the so-called “virtual values” even when the underlying prophet inequalities do not. We therefore provide an extension of this framework that bypasses virtual values altogether, allowing our mechanisms to take full advantage of the limited information required by our new prophet inequalities.
- The Query Complexity of Scoring RulesPablo D. Azar, and Silvio MicaliACM Transactions on Economics and Computation, May 2014
Proper scoring rules are crucial tools to elicit truthful information from experts. A scoring rule maps X, an expert-provided distribution over the set of all possible states of the world, and ω, a realized state of the world, to a real number representing the expert’s reward for his provided information. To compute this reward, a scoring rule queries the distribution X at various states. The number of these queries is thus a natural measure of the complexity of the scoring rule. We prove that any bounded and strictly proper scoring rule that is deterministic must make a number of queries to its input distribution that is a quarter of the number of states of the world. When the state space is very large, this makes the computation of such scoring rules impractical. We also show a new stochastic scoring rule that is bounded, strictly proper, and which makes only two queries to its input distribution. Thus, using randomness allows us to have significant savings when computing scoring rules.
2013
- Super-Efficient Rational ProofsPablo D. Azar, and Silvio MicaliIn 14th ACM Conference on Electronic Commerce (EC 2013), May 2013
Information asymmetry is a central problem in both computer science and economics. In many fundamental problems, an uninformed principal wants to obtain some knowledge from an untrusted expert. This models several real-world situations, such as a manager’s relation with her employees, or the delegation of computational tasks in mechanical turk. Because the expert is untrusted, the principal needs some guarantee that the provided knowledge is correct. In computer science, this guarantee is usually provided via a proof, which the principal can verify. Thus, a dishonest expert will get caught and penalized (with very high probability). In many economic settings, the guarantee that the knowledge is correct is usually provided via incentives. That is, a game is played between expert and principal such that the expert maximizes her utility by being honest. A rational proof is an interactive proof where the prover, Merlin, is neither honest nor malicious, but rational. That is, Merlin acts in order to maximize his own utility. Rational proofs have been previously studied when the verifier, Arthur, is a probabilistic polynomial-time machine \citeAzarMicali. In this paper, we study super efficient rational proofs, that is, rational proofs where Arthur runs in logarithmic time. Our new rational proofs are very practical. Not only are they much faster than their classical analogues, but they also provide very tangible incentives for the expert to be honest. Arthur only needs a polynomial-size budget, yet he can penalize Merlin by a large quantity if he deviates from the truth. We give the following characterizations of which problems admit super-efficient rational proofs. (1)Uniform TC0 coincides with the set of languages L that admit a rational proof using O(log n) time, O(log n) communication, a constant number of rounds and a polynomial size budget. P║NPcoincides with the set of languages having a rational proof using O(log n) time, poly(n) communication, one round and a polynomial-size budget. Furthermore, we show that when Arthur is restricted to have a polynomial-size budget, the set of languages which admit rational proofs with polynomial time verification, polynomial communication and one round is P║MA
- Parametric Digital AuctionsPablo D. Azar, and Silvio MicaliIn 4th Innovations in Theoretical Computer Science Conference (ITCS 2013), May 2013
We study revenue maximization for digital auctions, where there are infinitely many copies of a good for sale. There are n buyers, each of whom is interested in obtaining one copy of the good. The buyers’ private valuations are drawn from a joint distribution vecF. The seller does not know this distribution. The only information that she has are the mean ui and variance σi2 of each buyer i’s marginal distribution Fi. We call such auctions parametric auctions. We construct a deterministic parametric auction that, for a wide class of distributions, guarantees a constant fraction of the optimal revenue achievable when the seller precisely knows the distribution F. Furthermore, our auction is a posted price mechanism and it is maximin optimal among all such mechanisms. That is, it is the posted price mechanism that maximizes revenue in the worst case over an adversarial choice of the distribution.
- Optimal and Efficient Parametric AuctionsPablo D. Azar, Costantinos Daskalakis, Silvio Micali, and 1 more authorIn Symposium on Discrete Algorithms (SODA 2013), May 2013
Consider a seller who seeks to provide service to a collection of interested parties, subject to feasibility constraints on which parties may be simultaneously served. Assuming that a distribution is known on the value of each party for service—arguably a strong assumption—Myerson’s seminal work provides revenue optimizing auctions [12]. We show instead that, for very general feasibility constraints, only knowledge of the median of each party’s value distribution, or any other quantile of these distributions, or approximations thereof, suffice for designing simple auctions that simultaneously approximate both the optimal revenue and the optimal welfare. Our results apply to all downward-closed feasibility constraints under the assumption that the underlying, unknown value distributions are monotone hazard rate, and to all matroid feasibility constraints under the weaker assumption of regularity of the underlying distributions. Our results jointly generalize the single-item results obtained by Azar and Micali [2] on parametric auctions, and Daskalakis and Pierrakos [6] for simultaneously approximately optimal and efficient auctions.
- Using Algorithmic Attribution Techniques to Determine Authorship in Unsigned Judicial OpinionsPablo D. Azar, William Li, David Larochelle, and 3 more authorsStanford Technology Law Review, May 2013
This Article proposes a novel and provocative analysis of judicial opinions that are published without indicating individual authorship. Our approach provides an unbiased, quantitative, and computer scientific answer to a problem that has long plagued legal commentators. United States courts publish a shocking number of judicial opinions without divulging the author. Per curiam opinions, as traditionally and popularly conceived, are a means of quickly deciding uncontroversial cases in which all judges or justices are in agreement. Today, however, unattributed per curiam opinions often dispose of highly controversial issues, frequently over significant disagreement within the court. Obscuring authorship removes the sense of accountability for each decision’s outcome and the reasoning that led to it. Anonymity also makes it more difficult for scholars, historians, practitioners, political commentators, and—in the thirty-nine states with elected judges and justices—the electorate, to glean valuable information about legal decisionmakers and the way they make their decisions. The value of determining authorship for unsigned opinions has long been recognized but, until now, the methods of doing so have been cumbersome, imprecise, and altogether unsatisfactory. Our work uses natural language processing to predict authorship of judicial opinions that are unsigned or whose attribution is disputed. Using a dataset of Supreme Court opinions with known authorship, we identify key words and phrases that can, to a high degree of accuracy, predict authorship. Thus, our method makes accessible an important class of cases heretofore inaccessible. For illustrative purposes, we explain our process as applied to the Obamacare decision, in which the authorship of a joint dissent was subject to significant popular speculation. We conclude with a chart predicting the author of every unsigned per curiam opinion during the Roberts Court.
2012
- Rational ProofsPablo D. Azar, and Silvio MicaliIn 44th ACM Symposium on Theory of Computing (STOC 2012), May 2012
We study a new type of proof system, where an unbounded prover and a polynomial time verifier interact, on inputs a string x and a function f, so that the Verifier may learn f(x). The novelty of our setting is that there no longer are "good" or "malicious" provers, but only rational ones. In essence, the Verifier has a budget c and gives the Prover a reward r ∈ [0,c] determined by the transcript of their interaction; the prover wishes to maximize his expected reward; and his reward is maximized only if he the verifier correctly learns f(x). Rational proof systems are as powerful as their classical counterparts for polynomially many rounds of interaction, but are much more powerful when we only allow a constant number of rounds. Indeed, we prove that if f ∈ #P, then f is computable by a one-round rational Merlin-Arthur game, where, on input x, Merlin’s single message actually consists of sending just the value f(x). Further, we prove that CH, the counting hierarchy, coincides with the class of languages computable by a constant-round rational Merlin-Arthur game. Our results rely on a basic and crucial connection between rational proof systems and proper scoring rules, a tool developed to elicit truthful information from experts.
- Crowdsourced Bayesian AuctionsPablo D. Azar, Jing Chen, and Silvio MicaliIn 3rd Innovations in Theoretical Computer Science Conference (ITCS 2012), May 2012
We investigate the problem of optimal mechanism design, where an auctioneer wants to sell a set of goods to buyers, in order to maximize revenue. In a Bayesian setting the buyers’ valuations for the goods are drawn from a prior distribution D, which is often assumed to be known by the seller. In this work, we focus on cases where the seller has no knowledge at all, and "the buyers know each other better than the seller knows them". In our model, D is not necessarily common knowledge. Instead, each buyer individually knows a posterior distribution associated with D. Since the seller relies on the buyers’ knowledge to help him set a price, we call these types of auctions crowdsourced Bayesian auctions. For this crowdsourced Bayesian model and many environments of interest, we show that, for arbitrary valuation distributions D (in particular, correlated ones), it is possible to design mechanisms matching to a significant extent the performance of the optimal dominant-strategy-truthful mechanisms where the seller knows D. To obtain our results, we use two techniques: (1) proper scoring rules to elicit information from the players; and (2) a reverse version of the classical Bulow-Klemperer inequality. The first lets us build mechanisms with a unique equilibrium and good revenue guarantees, even when the players’ second and higher-order beliefs about each other are wrong. The second allows us to upper bound the revenue of an optimal mechanism with n players by an n/n–1 fraction of the revenue of the optimal mechanism with n – 1 players. We believe that both techniques are new to Bayesian optimal auctions and of independent interest for future work.