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Documents authored by Hartline, Jason

Document
DOI: 10.4230/LIPIcs.ITCS.2024.59
Equivocal Blends: Prior Independent Lower Bounds

Authors: Jason Hartline and Aleck Johnsen

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
The prior independent framework for algorithm design considers how well an algorithm that does not know the distribution of its inputs approximates the expected performance of the optimal algorithm for this distribution. This paper gives a method that is agnostic to problem setting for proving lower bounds on the prior independent approximation factor of any algorithm. The method constructs a correlated distribution over inputs that can be described both as a distribution over i.i.d. good-for-algorithms distributions and as a distribution over i.i.d. bad-for-algorithms distributions. We call these two descriptions equivocal blends. Prior independent algorithms are upper-bounded by the optimal algorithm for the latter distribution even when the true distribution is the former. Thus, the ratio of the expected performances of the Bayesian optimal algorithms for these two decompositions is a lower bound on the prior independent approximation ratio. We apply this framework to give new lower bounds on canonical prior independent mechanism design problems. For one of these problems, we also exhibit a near-tight upper bound. Towards solutions for general problems, we give distinct descriptions of two large classes of correlated-distribution "solutions" for the technique, depending respectively on an order-statistic separability property and a paired inverse-distribution property. We exhibit that equivocal blends do not generally have a Blackwell ordering, which puts this paper outside of standard information design.
Cite as

Jason Hartline and Aleck Johnsen. Equivocal Blends: Prior Independent Lower Bounds. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 59:1-59:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hartline_et_al:LIPIcs.ITCS.2024.59,
  author =	{Hartline, Jason and Johnsen, Aleck},
  title =	{{Equivocal Blends: Prior Independent Lower Bounds}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{59:1--59:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.59},
  URN =		{urn:nbn:de:0030-drops-195878},
  doi =		{10.4230/LIPIcs.ITCS.2024.59},
  annote =	{Keywords: prior independent algorithms, lower bounds, correlated decompositions, minimax, equivocal blends, mechanism design, blackwell ordering}
}
Document
DOI: 10.4230/LIPIcs.FORC.2023.6
Screening with Disadvantaged Agents

Authors: Hedyeh Beyhaghi, Modibo K. Camara, Jason Hartline, Aleck Johnsen, and Sheng Long

Published in: LIPIcs, Volume 256, 4th Symposium on Foundations of Responsible Computing (FORC 2023)

Abstract
Motivated by school admissions, this paper studies screening in a population with both advantaged and disadvantaged agents. A school is interested in admitting the most skilled students, but relies on imperfect test scores that reflect both skill and effort. Students are limited by a budget on effort, with disadvantaged students having tighter budgets. This raises a challenge for the principal: among agents with similar test scores, it is difficult to distinguish between students with high skills and students with large budgets. Our main result is an optimal stochastic mechanism that maximizes the gains achieved from admitting "high-skill" students minus the costs incurred from admitting "low-skill" students when considering two skill types and n budget types. Our mechanism makes it possible to give higher probability of admission to a high-skill student than to a low-skill, even when the low-skill student can potentially get higher test-score due to a higher budget. Further, we extend our admission problem to a setting in which students uniformly receive an exogenous subsidy to increase their budget for effort. This extension can only help the school’s admission objective and we show that the optimal mechanism with exogenous subsidies has the same characterization as optimal mechanisms for the original problem.
Cite as

Hedyeh Beyhaghi, Modibo K. Camara, Jason Hartline, Aleck Johnsen, and Sheng Long. Screening with Disadvantaged Agents. In 4th Symposium on Foundations of Responsible Computing (FORC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 256, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{beyhaghi_et_al:LIPIcs.FORC.2023.6,
  author =	{Beyhaghi, Hedyeh and Camara, Modibo K. and Hartline, Jason and Johnsen, Aleck and Long, Sheng},
  title =	{{Screening with Disadvantaged Agents}},
  booktitle =	{4th Symposium on Foundations of Responsible Computing (FORC 2023)},
  pages =	{6:1--6:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-272-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{256},
  editor =	{Talwar, Kunal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2023.6},
  URN =		{urn:nbn:de:0030-drops-179274},
  doi =		{10.4230/LIPIcs.FORC.2023.6},
  annote =	{Keywords: screening, strategic classification, budgeted mechanism design, fairness, effort-incentives, subsidies, school admission}
}
Document
DOI: 10.4230/LIPIcs.FORC.2023.7
Fair Grading Algorithms for Randomized Exams

Authors: Jiale Chen, Jason Hartline, and Onno Zoeter

Published in: LIPIcs, Volume 256, 4th Symposium on Foundations of Responsible Computing (FORC 2023)

Abstract
This paper studies grading algorithms for randomized exams. In a randomized exam, each student is asked a small number of random questions from a large question bank. The predominant grading rule is simple averaging, i.e., calculating grades by averaging scores on the questions each student is asked, which is fair ex-ante, over the randomized questions, but not fair ex-post, on the realized questions. The fair grading problem is to estimate the average grade of each student on the full question bank. The maximum-likelihood estimator for the Bradley-Terry-Luce model on the bipartite student-question graph is shown to be consistent with high probability when the number of questions asked to each student is at least the cubed-logarithm of the number of students. In an empirical study on exam data and in simulations, our algorithm based on the maximum-likelihood estimator significantly outperforms simple averaging in prediction accuracy and ex-post fairness even with a small class and exam size.
Cite as

Jiale Chen, Jason Hartline, and Onno Zoeter. Fair Grading Algorithms for Randomized Exams. In 4th Symposium on Foundations of Responsible Computing (FORC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 256, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chen_et_al:LIPIcs.FORC.2023.7,
  author =	{Chen, Jiale and Hartline, Jason and Zoeter, Onno},
  title =	{{Fair Grading Algorithms for Randomized Exams}},
  booktitle =	{4th Symposium on Foundations of Responsible Computing (FORC 2023)},
  pages =	{7:1--7:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-272-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{256},
  editor =	{Talwar, Kunal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2023.7},
  URN =		{urn:nbn:de:0030-drops-179282},
  doi =		{10.4230/LIPIcs.FORC.2023.7},
  annote =	{Keywords: Ex-ante and Ex-post Fairness, Item Response Theory, Algorithmic Fairness in Education}
}
Document
Extended Abstract
DOI: 10.4230/LIPIcs.ITCS.2021.84
Non-Quasi-Linear Agents in Quasi-Linear Mechanisms (Extended Abstract)

Authors: Moshe Babaioff, Richard Cole, Jason Hartline, Nicole Immorlica, and Brendan Lucier

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
Mechanisms with money are commonly designed under the assumption that agents are quasi-linear, meaning they have linear disutility for spending money. We study the implications when agents with non-linear (specifically, convex) disutility for payments participate in mechanisms designed for quasi-linear agents. We first show that any mechanism that is truthful for quasi-linear buyers has a simple best response function for buyers with non-linear disutility from payments, in which each bidder simply scales down her value for each potential outcome by a fixed factor, equal to her target return on investment (ROI). We call such a strategy ROI-optimal. We prove the existence of a Nash equilibrium in which agents use ROI-optimal strategies for a general class of allocation problems. Motivated by online marketplaces, we then focus on simultaneous second-price auctions for additive bidders and show that all ROI-optimal equilibria in this setting achieve constant-factor approximations to suitable welfare and revenue benchmarks.
Cite as

Moshe Babaioff, Richard Cole, Jason Hartline, Nicole Immorlica, and Brendan Lucier. Non-Quasi-Linear Agents in Quasi-Linear Mechanisms (Extended Abstract). In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, p. 84:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{babaioff_et_al:LIPIcs.ITCS.2021.84,
  author =	{Babaioff, Moshe and Cole, Richard and Hartline, Jason and Immorlica, Nicole and Lucier, Brendan},
  title =	{{Non-Quasi-Linear Agents in Quasi-Linear Mechanisms}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{84:1--84:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.84},
  URN =		{urn:nbn:de:0030-drops-136230},
  doi =		{10.4230/LIPIcs.ITCS.2021.84},
  annote =	{Keywords: Return on investment, Non-quasi-linear agents, Transferable Welfare, Simultaneous Second-Price Auctions}
}
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