Community detection based on modularity maximization is one of the most widely used approaches for uncovering mesoscale structures in complex networks. However, it is well known that the modularity function exhibits a highly degenerate optimization landscape: a large number of structurally distinct partitions attain close modularity values. This degeneracy raises issues of instability, reproducibility, and interpretability of the detected communities. We propose a simple and user-friendly post-processing method to address this problem by selecting a representative partition among the set of high-modularity solutions. The proposed approach is model-agnostic and can be applied a posteriori to the output of any modularity-based community detection algorithm. Rather than seeking the optimal partition in terms of modularity, our method aims to identify a solution that best represents the structural features shared across degenerate partitions. We compare our approach with consensus clustering methods, which pursue a similar objective, and show that the resulting partitions are highly consistent, while being obtained through a substantially simpler procedure that does not require additional optimization steps or external software packages. Moreover, unlike standard consensus clustering techniques, the proposed method can be applied to networks with both positive and negative edge weights, making it suitable for a wide range of applications involving signed networks and correlation-based systems, such as social, financial, and neuroscience networks. Overall, the method provides a practical and robust tool for handling degeneracy in modularity-based community detection, combining simplicity with broad applicability across different types of networks and real-world problems.

For millennia, human cognition was the primary engine of progress on Earth. As AI decouples cognition from biology, the marginal cost of measurable execution falls to zero, absorbing any labor capturable by metrics--including creative, analytical, and innovative work. The binding constraint on growth is no longer intelligence but human verification bandwidth: the capacity to validate, audit, and underwrite responsibility when execution is abundant. We model the AGI transition as the collision of two racing cost curves: an exponentially decaying Cost to Automate and a biologically bottlenecked Cost to Verify. This structural asymmetry widens a Measurability Gap between what agents can execute and what humans can afford to verify. It also drives a shift from skill-biased to measurability-biased technical change. Rents migrate to verification-grade ground truth, cryptographic provenance, and liability underwriting--the ability to insure outcomes rather than merely generate them. The current human-in-the-loop equilibrium is unstable: eroded from below as apprenticeship collapses (Missing Junior Loop) and from within as experts codify their obsolescence (Codifier's Curse). Unverified deployment becomes privately rational--a Trojan Horse externality. Unmanaged, these forces pull toward a Hollow Economy. Yet by scaling verification alongside agentic capabilities, the forces that threaten collapse become the catalyst for unbounded discovery and experimentation--an Augmented Economy. We derive a practical playbook for individuals, companies, investors, and policymakers. Today's defining challenge is not the race to deploy the most autonomous systems; it is the race to secure the foundations of their oversight. Only by scaling our bandwidth for verification alongside our capacity for execution can we ensure that the intelligence we have summoned preserves the humanity that initiated it.

As LLMs become embedded in research workflows and organizational decision processes, their effect on analytical reliability remains uncertain. We distinguish two dimensions of analytical reliability -- intelligence (the capacity to reach correct conclusions) and integrity (the stability of conclusions when analytically irrelevant cues about desired outcomes are introduced) -- and ask whether frontier LLMs possess both. Whether these dimensions trade off is theoretically ambiguous: the sophistication enabling accurate analysis may also enable responsiveness to non-evidential cues, or alternatively, greater capability may confer protection through better calibration and discernment. Using synthetically generated data with embedded ground truth, we evaluate fourteen models on a task simulating empirical analysis of hospital merger effects. We find that intelligence and integrity trade off: frontier models most likely to reach correct conclusions under neutral conditions are often most susceptible to shifting conclusions under motivated framing. We extend work on sycophancy by introducing goal-conditioned analytical sycophancy: sensitivity of inference to cues about desired outcomes, even when no belief is asserted and evidence is held constant. Unlike simple prompt sensitivity, models shift conclusions away from objective evidence in response to analytically irrelevant framing. This finding has important implications for empirical research and organizations. Selecting tools based on capability benchmarks may inadvertently select against the stability needed for reliable and replicable analysis.

This paper introduces OccCANINE, an open-source tool that maps occupational descriptions to HISCO codes. Manual coding is slow and error-prone; OccCANINE replaces weeks of work with results in minutes. We fine-tune CANINE on 15.8 million description-code pairs from 29 sources in 13 languages. The model achieves 96 percent accuracy, precision, and recall. We also show that the approach generalizes to three systems - OCC1950, OCCICEM, and ISCO-68 - and release them open source. By breaking the "HISCO barrier," OccCANINE democratizes access to high-quality occupational coding, enabling broader research in economics, economic history, and related disciplines.

We develop a model of social media in which users produce different types of content and choose whom to follow. Even when abstracting from algorithmic bias, linking costs shape networks and polarization. In the welfare-maximizing equilibrium, lower linking costs can raise welfare but also increase exposure to extreme content, while very low costs reduce welfare and heighten polarization by discouraging moderate contributors. Policies that incentivize content provision can generate large welfare gains by changing who produces information, whereas link subsidies or attention reallocation mainly affect exposure and have limited welfare impact. These insights help explain why exposure-based interventions on social media platforms often yield ambiguous effects on polarization.

We analyze how frequently instant runoff voting (IRV) selects the weakest (or least popular) candidate in three-candidate elections. We consider four definitions of ``weakest candidate'': the Borda loser, the Bucklin loser, the candidate with the most last-place votes, and the candidate with minimum social utility. We determine the probability that IRV selects the weakest candidate under the impartial anonymous culture and impartial culture models of voter behavior, and use Monte Carlo simulations to estimate these probabilities under several spatial models. We also examine this question empirically using a large dataset of real elections. Our results show that IRV can select the weakest candidates under each of these definitions, but such outcomes are generally rare. Across most models, the probability that IRV elects a given type of weakest candidate is at most 5\%. Larger probabilities arise only when the electorate is extremely polarized.

We ask when a normal-form game yields a single equilibrium prediction, even if players can coordinate by delegating play to an intermediary such as a platform or a cartel. Delegation outcomes are modeled via coarse correlated equilibria (CCE) when the intermediary cannot punish deviators, and via the set of individually rational correlated profiles (IRCP) when it can. We characterize games in which the IRCP or the CCE is unique, uncovering a structural link between these solution concepts. Our analysis also provides new conditions for the uniqueness of classical correlated and Nash equilibria that do not rely on the existence of dominant strategies. The resulting equilibria are robust to players' information about the environment, payoff perturbations, pre-play communication, equilibrium selection, and learning dynamics. We apply these results to collusion-proof mechanism design.

We study spillover effects in corporate toxic emissions using a heterogeneous panel network of U.S. industrial facilities from 2000-2023. Rather than imposing a network structure a priori, we uncover an unobserved web of influence directly from the data using recent advances in high-dimensional network econometrics. Indirect effects transmitted through the estimated network account for about 28% of the total impact of key firm balance-sheet characteristics. By contrast, distance-based networks generate no statistically discernible spillovers, while a priori firm- or industry-based networks substantially overstate within-group spillins relative to the data-driven network. These findings show that who is linked to whom, and with what strength, matters critically for assessing systemic environmental risk and for designing targeted regulation. Methodologically, the paper provides a flexible framework for quantifying facility-level emissions spillovers and their consequences in financial and policy settings.

In practice, auction data are often endogenously censored and anonymous, revealing only limited outcome statistics rather than full bid profiles. We study robust auction design when the seller observes only aggregated, anonymous order statistics and seeks to maximize worst-case expected revenue over all product distributions consistent with the observed statistic. We show that simple and widely used mechanisms are robustly optimal. Specifically, posted pricing is robustly optimal given the distribution of the highest value; the Myerson auction designed for the unique consistent i.i.d. distribution is robustly optimal given the lowest value distribution; and the second-price auction with an optimal reserve is robustly optimal when an intermediate order statistic is observed and the implied i.i.d. distribution is regular above its reserve. More generally, for a broad class of monotone symmetric mechanisms depending only on the top k order statistics, including multi-unit and position auctions, the worst-case revenue is attained under the i.i.d. distribution consistent with the observed k-th order statistic. Our results provide a tractable foundation for non-discriminatory auction design, where fairness and privacy are intrinsic consequences of the information structure rather than imposed constraints.

We develop an overlapping generations model where each agent observes a verifiable private signal about the state and, with positive probability, also receives signals disclosed by his predecessor. The agent then takes an action and decides which signals to pass on. Each agent's action has a positive externality on his predecessor and his optimal action increases in his belief about the state. We show that as the probability that messages reach the next generation approaches one, agents become increasingly selective in disclosing information. In the limit, all signals except for the most favorable ones will be concealed.

This article develops a continuous-time asymptotic framework for analyzing adaptive experiments -- settings in which data collection and treatment assignment evolve dynamically in response to incoming information. A key challenge in analyzing fully adaptive experiments, where the assignment policy is updated after each observation, is that the sequence of policy rules often lack a well-defined asymptotic limit. To address this, we focus instead on the empirical allocation process, which captures the fraction of observations assigned to each treatment over time. We show that, under general conditions, any adaptive experiment and its associated empirical allocation process can be approximated by a limit experiment defined by Gaussian diffusions with unknown drifts and a corresponding continuous-time allocation process. This limit representation facilitates the analysis of optimal decision rules by reducing the dimensionality of the state-space and leveraging the tractability of Gaussian diffusions. We apply the framework to derive optimal estimators, analyze in-sample regret for adaptive experiments, and construct e-processes for anytime-valid inference. Notably, we introduce the first definition of any-time and any-experiment valid inference for multi-treatment settings.

Mean Field Game (MFG) models implicitly assume "rational expectations", meaning that the heterogeneous agents being modeled correctly know all relevant transition probabilities for the complex system they inhabit. When there is common noise, it becomes necessary to solve the "Master equation", in which the infinite-dimensional density of agents is a state variable. The rational expectations assumption and the implication that agents solve Master equations is unrealistic in many applications. We show how to instead formulate MFGs with non-rational expectations. Departing from rational expectations is particularly relevant in "MFGs with a low-dimensional coupling", i.e. MFGs in which agents' running reward function depends on the density only through low-dimensional functionals of this density. This happens, for example, in most macroeconomics MFGs in which these low-dimensional functionals have the interpretation of "equilibrium prices." In MFGs with a low-dimensional coupling, departing from rational expectations allows for completely sidestepping the Master equation and for instead solving much simpler finite-dimensional HJB equations. We introduce an adaptive learning model as a particular example of non-rational expectations and discuss its properties.

Synthetic control methods (SCMs) are a canonical approach used to estimate treatment effects from panel data in the internet economy. We shed light on a frequently overlooked but ubiquitous assumption made in SCMs of "overlap": a treated unit can be written as some combination -- typically, convex or linear -- of the units that remain under control. We show that if units select their own interventions, and there is sufficiently large heterogeneity between units that prefer different interventions, overlap will not hold. We address this issue by proposing a recommender system which incentivizes units with different preferences to take interventions they would not normally consider. Specifically, leveraging tools from information design and online learning, we propose an SCM that incentivizes exploration in panel data settings by providing incentive-compatible intervention recommendations to units. We establish this estimator obtains valid counterfactual estimates without the need for an a priori overlap assumption. We extend our results to the setting of synthetic interventions, where the goal is to produce counterfactual outcomes under all interventions, not just control. Finally, we provide two hypothesis tests for determining whether unit overlap holds for a given panel dataset.