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1. Fairness through Equality of Effort

   https://doi.org/10.1145/3366424.3383558  

   Huang, Wen; Wu, Yongkai; Zhang, Lu; Wu, Xintao (April 2020, Companion of The 2020 Web Conference)
2. Effort or outcome? Children’s meritorious decisions

   https://doi.org/10.1016/j.jecp.2018.09.005  

   Noh, Jee Young; D'Esterre, Alexander; Killen, Melanie (February 2019, Journal of Experimental Child Psychology)
3. High-Effort Crowds: Limited Liability via Tournaments

   https://doi.org/10.1145/3543507.3583334  

   Zhang, Yichi; Schoenebeck, Grant (April 2023, ACM)

   We consider the crowdsourcing setting where, in response to the assigned tasks, agents strategically decide both how much effort to exert (from a continuum) and whether to manipulate their reports. The goal is to design payment mechanisms that (1) satisfy limited liability (all payments are non-negative), (2) reduce the principal’s cost of budget, (3) incentivize effort and (4) incentivize truthful responses. In our framework, the payment mechanism composes a performance measurement, which noisily evaluates agents’ effort based on their reports, and a payment function, which converts the scores output by the performance measurement to payments. Previous literature suggests applying a peer prediction mechanism combined with a linear payment function. This method can achieve either (1), (3) and (4), or (2), (3) and (4) in the binary effort setting. In this paper, we suggest using a rank-order payment function (tournament). Assuming Gaussian noise, we analytically optimize the rank-order payment function, and identify a sufficient statistic, sensitivity, which serves as a metric for optimizing the performance measurements. This helps us obtain (1), (2) and (3) simultaneously. Additionally, we show that adding noise to agents’ scores can preserve the truthfulness of the performance measurements under the non-linear tournament, which gives us all four objectives. Our real-data estimated agent-based model experiments show that our method can greatly reduce the payment of effort elicitation while preserving the truthfulness of the performance measurement. In addition, we empirically evaluate several commonly used performance measurements in terms of their sensitivities and strategic robustness. 

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4. Optimal Scoring Rules for Multi-dimensional Effort

   Hartline, Jason; Shan, Liren; Li, Yingkai; Wu, Yifan (November 2023, Proceedings of Thirty Sixth Conference on Learning Theory)

   Neu, Gergely; Rosasco, Lorenzo (Ed.)

   This paper develops a framework for the design of scoring rules to optimally incentivize an agent to exert a multi-dimensional effort. This framework is a generalization to strategic agents of the classical knapsack problem (cf. Briest, Krysta, and Vocking, 2005; Singer, 2010) and it is foundational to applying algorithmic mechanism design to the classroom. The paper identifies two simple families of scoring rules that guarantee constant approximations to the optimal scoring rule. The truncated separate scoring rule is the sum of single dimensional scoring rules that is truncated to the bounded range of feasible scores. The threshold scoring rule gives the maximum score if reports exceed a threshold and zero otherwise. Approximate optimality of one or the other of these rules is similar to the bundling or selling separately result of Babaioff, Immorlica, Lucier, and Weinberg (2014). Finally, we show that the approximate optimality of the best of those two simple scoring rules is robust when the agent’s choice of effort is made sequentially. 

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5. An Effort to Reconcile Electron-Broadening Theories

   Gomez, T. A.; Nagayama, T.; Fones, C. J.; Kilcrease, D. P.; Montgomery, M. H.; Winget, D. E. (April 2019, International Conference on Atomic Processes in Plasmas)

   Calculations of line broadening are important for many different applications including plasma diagnostics and opacity calculations. One concern is that line-shape models employ many approximations that are not experimentally validated for most element conditions due to challenges with high-fidelity line-shape benchmark experiments. Until such experiments become available, we need to test approximations with ab-initio line-shape calculations. There are three primary formalisms to derive an electron-broadening operator: the impact theory (Baranger, Griem), relaxation theory (Fano), and kinetic theories (Zwanzig, Hussey), all of which give different expressions for electron broadening. The impact and relaxation theories approximate the density matrix as factorizeable while the kinetic theory has a more general density matrix. The impact and kinetic theories relate the electron broadening operator to collision amplitudes, while the relaxation theory has a more complicated formula using projection operators. Each theory has a different prediction for the width and shift of spectral lines, which will become apparent in strongly-coupled plasmas. We have made an effort to better understand the approximations and limitations of all of these approaches and to try to reconcile the differences between them. Here, we present the current status of our understanding of the electron-broadening theories and our preliminary attempt to unify the various formulae. Currently, we have found the projection operator to be necessary part of line broadening. We will be showing (for the first time) how the projection operator broadens spectral lines. 

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