From Proper Scoring Rules to Max-Min Optimal Forecast Aggregation

Published Online:https://doi.org/10.1287/opre.2022.2414

References

  • Abbas EA (2009) A Kullback-Leibler view of linear and log-linear pools. Decision Anal. 6(1):25–37.LinkGoogle Scholar
  • Abernethy JD, Chen Y, Vaughan JW (2013) Efficient market making via convex optimization, and a connection to online learning. ACM Trans. Econom. Comput. 1(2):12:1–12:39.CrossrefGoogle Scholar
  • Aczél J (1948) On mean values. Bull. Amer. Math. Soc. (New Ser.) 54(4):392–400.CrossrefGoogle Scholar
  • Aczél J, Wagner C (1980) A characterization of weighted arithmetic means. SIAM J. Algebraic Discrete Methods 1(3):259–260.CrossrefGoogle Scholar
  • Adamčík M (2014) Collective reasoning under uncertainty and inconsistency. PhD thesis, University of Manchester, Manchester, UK.Google Scholar
  • Allard D, Comunian A, Renard P (2012) Probability aggregation methods in geoscience. Math. Geosci. 44(5):545–581.CrossrefGoogle Scholar
  • Archer A, Kleinberg R (2014) Truthful germs are contagious: A local-to-global characterization of truthfulness. Games Econom. Behav. 86(C):340–366.CrossrefGoogle Scholar
  • Arieli I, Babichenko Y, Smorodinsky R (2018) Robust forecast aggregation. Proc. National Acad. Sci. USA 115(52):E12135–E12143.CrossrefGoogle Scholar
  • Ashlagi I, Braverman M, Hassidim A, Monderer D (2010) Monotonicity and implementability. Econometrica 78(5):1749–1772.CrossrefGoogle Scholar
  • Azagra D, Mudarra C (2015) Whitney extension theorems for convex functions of the classes C1 and C1,ω. Proc. London Math. Soc. 114:133–158.Google Scholar
  • Bauschke HH, Combettes PL (2011) Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 1st ed. (Springer, Berlin).CrossrefGoogle Scholar
  • Boyd SP, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Brier GW (1950) Verification of forecasts expressed in terms of probability. Monthly Weather Rev. 78:1–3.CrossrefGoogle Scholar
  • Carvalho A (2016) An overview of applications of proper scoring rules. Decision Anal. 13(4):223–242.LinkGoogle Scholar
  • Carvalho A, Larson K (2013) A consensual linear opinion pool. Rossi R, ed. Proc. 23rd Internat. Joint Conf. on Artificial Intelligence (AAAI Press, Palo Alto, CA), 2518–2524.Google Scholar
  • Cesa-Bianchi N, Lugosi G (2006) Prediction, Learning, and Games (Cambridge University Press, Cambridge, UK).Google Scholar
  • Chambers CP, Healy PJ, Lambert NS (2019) Proper scoring rules with general preferences: A dual characterization of optimal reports. Games Econom. Behav. 117:322–341.CrossrefGoogle Scholar
  • Chen Y, Pennock DM (2007) A utility framework for bounded-loss market makers. Parr R, van der Gaag L, eds. Proc. 23rd Conf. on Uncertainty in Artificial Intelligence (AUAI Press), 49–56.Google Scholar
  • Chen Y, Vaughan JW (2010) A new understanding of prediction markets via no-regret learning. Parkes DC, Dellarocas C, Tennenholtz M, eds. Proc. 11th ACM Conf. on Electronic Commerce (ACM, New York), 189–198.Google Scholar
  • Chen Y, Devanur NR, Pennock DM, Vaughan JW (2014) Removing arbitrage from wagering mechanisms. Babaioff M, Conitzer V, Easley DA, eds. Proc. ACM Conf. on Econom. and Comput. (ACM, New York), 377–394.Google Scholar
  • Chun S, Shachter RD (2011) Strictly proper mechanisms with cooperating players. Cozman FG, Pfeffer A, eds. Proc. 27th Conf. on Uncertainty in Artificial Intelligence (AUAI Press), 125–134.Google Scholar
  • Clemen RT, Winkler RL (2007) Aggregating probability distributions. Edwards W, Miles Jr. R, Von Winterfeldt D, eds. Advances in Decision Analysis: From Foundations to Applications (Cambridge University Press, Cambridge, UK), 154–176.CrossrefGoogle Scholar
  • Dawid A, Musio M (2014) Theory and applications of proper scoring rules. METRON 72:169–183.CrossrefGoogle Scholar
  • Dietrich F, List C (2014) Probabilistic opinion pooling. Accessed December 15, 2022, http://philsci-archive.pitt.edu/11349/.Google Scholar
  • Feldbacher-Escamilla CJ, Schurz G (2020) Optimal probability aggregation based on generalized Brier scoring. Annals Math. Artificial Intelligence 88:717–734.CrossrefGoogle Scholar
  • Frongillo R, Kash I (2014) General truthfulness characterizations via convex analysis. Tie-Yan QQ, Ye Y, eds. Web and Internet Economics (Springer International Publishing, Cham, Switzerland), 354–370.CrossrefGoogle Scholar
  • Frongillo RM, Kash IA (2015) Vector-valued property elicitation. Grünwald P, Hazan E, Kale S, eds. Proc. 28th Conf. on Learn. Theory, vol. 40. JMLR Workshop and Conference Proceedings, 710–727.Google Scholar
  • Frongillo RM, Chen Y, Kash IA (2015) Elicitation for aggregation. Bonet B, Koenig S, eds. Proc. 29th AAAI Conf. on Artificial Intelligence (AAAI Press, Palo Alto, CA), 900–906.Google Scholar
  • Freeman R, Pennock DM, Peters D, Waggoner B (2020) Preventing arbitrage from collusion when eliciting probabilities. Proc. 34th AAAI Conf. on Artificial Intelligence, 32nd Innovative Applications of Artificial Intelligence Conf., 10th AAAI Sympos. on Edu. Adv. in Artificial Intelligence (AAAI Press, Palo Alto, CA), 1958–1965.Google Scholar
  • Genest C (1984) A characterization theorem for externally Bayesian groups. Ann. Statist. 12(3):1100–1105.CrossrefGoogle Scholar
  • Genest C, Zidek JV (1986) Combining probability distributions: A critique and an annotated bibliography. Statist. Sci. 1(1):114–135.CrossrefGoogle Scholar
  • Gneiting T, Raftery AE (2007) Strictly proper scoring rules, prediction, and estimation. J. Amer. Statist. Assoc. 102(477):359–378.CrossrefGoogle Scholar
  • Good IJ (1952) Rational decisions. J. Royal Statist. Soc. Ser. B Methodological 14(1):107–114.Google Scholar
  • Grabisch M, Marichal J-L, Mesiar R, Pap E (2011) Aggregation functions: Means. Inform. Sci. 181(1):1–22.CrossrefGoogle Scholar
  • Grünwald PD, Philip Dawid A (2004) Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory. Annals Statist. 32(4):1367–1433.CrossrefGoogle Scholar
  • Hanson R (2003) Combinatorial information market design. Inform. Systems Frontiers 5(1):107–119.CrossrefGoogle Scholar
  • Hazan E (2022) Introduction to Online Convex Optimization. 2nd ed. Adaptive Computation and Machine Learning Series (MIT Press, London).Google Scholar
  • Heidari H, Lahaie S, Pennock DM, Vaughan JW (2018) Integrating market makers, limit orders, and continuous trade in prediction markets. ACM Trans. Econom. Comput. 6:3–4.Google Scholar
  • Kascha C, Ravazzolo F (2010) Combining inflation density forecasts. J. Forecast 29:231–250.Google Scholar
  • Kolmogorov AN (1930) Sur la Notion de la Moyenne Atti R. Accad. Naz. Lincei, vol. 12, 388.Google Scholar
  • Lambert NS, Pennock DM, Shoham Y (2008) Eliciting properties of probability distributions. Fortnow L, Riedl J, Sandholm T, eds. Proc. 9th ACM Conf. on Electronic Commerce (ACM, New York), 129–138.Google Scholar
  • Lavi R, Swamy C (2007) Truthful mechanism design for multi-dimensional scheduling via cycle monotonicity. Proc. 8th ACM Conf. Electronic Commerce (Association for Computing Machinery, New York), 252–261.Google Scholar
  • Nagumo M (1930) Über eine Klasse der Mittelwerte. Japanese J. Math. Trans. Abstracts 7:71–79.CrossrefGoogle Scholar
  • Nesterov YE (2009) Primal-dual subgradient methods for convex problems. Math. Programming 120(1):221–259.CrossrefGoogle Scholar
  • Neyman E, Roughgarden T (2022) No-regret learning with unbounded losses: The case of logarithmic pooling. Preprint, submitted February 22, https://arxiv.org/abs/2202.11219.Google Scholar
  • Pettigrew R (2019) Aggregating incoherent agents who disagree. Synthese 196:2737–2776.CrossrefGoogle Scholar
  • Poole D, Raftery AE (2000) Inference for deterministic simulation models: The Bayesian melding approach. J. Amer. Statist. Assoc. 95(452):1244–1255.CrossrefGoogle Scholar
  • Ranjan R, Gneiting T (2010) Combining probability forecasts. J. Royal Statist. Soc. Ser. B Statist. Methodology 72(1):71–91.CrossrefGoogle Scholar
  • Rockafellar RT (1970a) Convex Analysis (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Rockafellar RT (1970b) On the maximal monotonicity of subdifferential mappings. Pacific J. Math. 33(1):209–216.CrossrefGoogle Scholar
  • Saks M, Yu L (2005) Weak monotonicity suffices for truthfulness on convex domains. Proc. ACM Conf. Electronic Commerce(ACM), 286–293.Google Scholar
  • Satopää V, Baron J, Foster D, Mellers B, Tetlock P, Ungar L (2014) Combining multiple probability predictions using a simple logit model. Internat. J. Forecasting 30:344–356.CrossrefGoogle Scholar
  • Savage LJ (1971) Elicitation of personal probabilities and expectations. J. Amer. Statist. Assoc. 66(336):783–801.CrossrefGoogle Scholar
  • Shuford E, Albert A, Edward Massengill H (1966) Admissible probability measurement procedures. Psychometrika 31(2):125–145.CrossrefGoogle Scholar
  • Vohra RV (2007) Paths, cycles and mechanism design. Technical report, Kellogg School of Management.Google Scholar
  • Waggoner B (2021) Linear functions to the extended reals. Preprint, February 18, https://arxiv.org/abs/2102.09552.Google Scholar
  • Winkler RL, Grushka-Cockayne Y, Lichtendahl KC, Jose VR (2018) Averaging probability forecasts: Back to the future. Preprint, submitted October 1, https://dx.doi.org/10.2139/ssrn.3258627.Google Scholar
  • Xiao L (2010) Dual averaging methods for regularized stochastic learning and online optimization. J. Machine Learn. Res. 11:2543–2596.Google Scholar
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