Affecting Distributions of Opinions with Evidence

Jimenez Martinez, Antonio and Melguizo Lopez, Isabel (2026): Affecting Distributions of Opinions with Evidence.

Abstract

We investigate evidence acquisition and disclosure by a communicator who cares about the distribution of the opinions of an audience. Uncertainty about whether evidence can be obtained allows for selective disclosure. We consider two alternativemotivations for the communicator: (i) to shift the average opinion towards her preferred one and (ii) to raise the dispersion of opinions. Under general structures for evidence provision, we characterize the unique equilibrium disclosure strategy for both motivations. The communicator’s return in equilibrium is linear in a measure of the extent to which the evidence-provision structure could favor her preferred state conditional on a given obtained piece of evidence. In this context, we analyze how certain features of the evidence-provision structure and of the distribution of initial opinions of the audience influence the communicator’s return. The relation between thewelfare of the audience and the acquisition effort depends critically on which of the two motivations yields higher returns to the communicator, an insight useful for policy recommendations. Minimum limits on evidence acquisition benefit audiences only when communicators seek to raise the dispersion of opinions, not when they seek to shift the average opinion.

• Item Type: MPRA Paper
• Language: English
• Keywords: Distributions of Opinions; Evidence Acquisition; Strategic Disclosure; Sanitization Strategies; Hazard Rates
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D72 - Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D84 - Expectations ; Speculations

References

Adams, J., M. Clark, E. Lawrence, and G. Glasgow (2004): “Understanding Change and Stability in Party Ideologies: Do Parties Respond to Public Opinion or to Past Election Results?” British Journal of Political Science, 34, 589–610.

Alesina, A., A. Miano, and S. Stantcheva (2023): “Immigration and Redistribution,” Review of Economic Studies, 90, 1–41.

Ali, S. N., N. Haghpanah, X. Lin, and R. Siegel (2022): “How to Sell Hard Information,” The Quarterly Journal of Economics, 619–678. 40

Ali, S. N., G. Lewis, and S. Vasserman (2023): “Voluntary Disclosure and Personalized Pricing,” Review of Economic Studies, 90, 538–571.

Alonso, R. and O. Camara (2016): “Bayesian Persuasion with Heterogeneous Priors,” Journal of Economic Theory, 165, 672–706.

Bäck, H., R. Carroll, E. Renström, and A. Ryan (2023): “Elite Communication and Affective Polarization among Voters,” Electoral Studies, 84.

Bernhardt, D., J. Duggan, and F. Squintani (2009): “The Case for Responsible Parties,”American Political Science Review, 103, 570–587.

Billingsley, P. (1995): Probability and Measure, John Wiley and Sons.

Blackwell, D. (1951): “Comparison of Experiments,” in Proceedings of the Second Berkelely Symposium on Mathematical Statistics and Probability, ed. by J. Neyman, UC Berkeley, University of California Press, vol. 1.

———(1953): “Equivalent Comparisons of Experiments,” Annals of Mathematical Statistics, 24, 265–272.

Brier, G. W. (1950): “Verification of Forecasts Expressed in Terms of Probability,” Monthly Weather Review, 78, 1–3.

Bullock, J. G. (2011): “Elite Influence on Public Opinion in an Informed Electorate,” American Political Science Review, 105, 496–515.

Bulow, J. and J. Roberts (1989): “The Simple Economics of Optimal Auctions,” Journal of Political Economy, 5, 1060–1090.

Che, Y.-K. and N. Kartik (2009): “Opinions as Incentives,” Journal of Political Economy, 117, 815–860.

Chew, S. H. (1983): “A Generalization of the Quasilinear Mean with Applications to the Measurament of Income Inequality and Decision Theory Resolving the Allais Paradox,” Econometrica, 51, 1065–1092.

Diamond, P. and Stiglitz (1974): “Increases in Risk and in Risk Aversion,” journal of Economic Theory, 8, 337–360.

Duffie, D. and K. J. Singleton (1999): “Modeling Term Structures of Defaultable Bonds,” The Review of Financial Studies, 12, 687–720.

Durovic, A. and T. Schnatterer (2025): “Why Governments Want to Learn about Citizens’ Preferences. Explaining the Representational Logic behind Government Polling,”

European Journal of Political Research, 64, 1039–1067. Dye, R. A. (1985): “Disclosure of Nonproprietary Information,” Journal of Accounting Research, 23, 124–145. 41

Gentzkow, M. and E. Kamenica (2017): “Bayesian Persuasion with Multiple Senders and Rich Signal Spaces,” Games and Economic Behavior, 104, 411–429.

Glaeser, E. L., G. A. M. Ponzetto, and J. M. Shapiro (2005): “Strategic Extremism: Why Republicans and Democrats Divide on Religious Values,” Quartely Journal of Economics, 120, 1283–1330.

Grossman, S. J. (1981): “The Informational Role ofWarranties and Private Disclosure about Product Quality,” Journal of Law and Economics, 24, 461–483.

Grossman, S. J. and O. D. Hart (1983): “An Analyis of the Principal-Agent Problem,” Econometrica, 51, 7–45.

Haaland, I. and C. Roth (2020): “Labor Market Concerns and Support for Immigration,” Journal of Public Economics, 191, 1–10.

Holmström, B. (1979): “Moral Hazard and Observability,” The Bell Journal of Economics, 10, 74–91.

Iyengar, S., S. Gaurav, and L. Yphtach (2012): “Affect, Not Ideology: a Social Identity Perspective on Polarization,” Public Opinon Quarterly, 76, 405–431.

Iyengar, S., Y. Lelkes, M. Levendusky, N. Malhotra, and S. J. Westwood (2019): “The Origins and Consequences of Affective Polarization in the United States,” Annual Review of Political Science, 22, 129–146.

Iyengar, S. and S. J. Westwood (2015): “Fear and Loathing across Party Lines: New Evidence on Group Polarization,” American Journal of Political Science, 59, 690–707.

Jarrow, R. A. and S. M. Turnbull (1995): “Pricing Derivatives on Financial Securities subject to Credit Risk,” The Journal of Finance, 50, 53–85.

Jung,W.-O. and Y. K. Kwon (1988): “Disclosure when the Market is Unsure of Information Endowment of Managers,” Journal of Accounting Research, 26, 146–153.

Kamenica, E. and M. Gentzkow (2011): “Bayesian Persuasion,” American Economic Review, 101, 2590–2615.

Karni, E. and D. Schmeidler (1991): “Utility Theory with Uncertainty,” in Handbook of Mathematical Economics, ed. by W. Hildenbrand and H. Sonnenschein, Amsterdam: Elsevier, vol. 4, 1763–1831.

Kartik, N., F. X. Lee, and W. Suen (2017): “Investment in Concealable Information by Biased Experts,” RAND Journal of Economics, 48, 24–43.

Koessler, F. and V. Skreta (2023): “Informed Information Design,” Journal of Political Economy, 131, 3186–3232. 42

Kuklinski, J. H., P. J. Quirk, J. Jerit, D. Schweider, and R. F. Rich (2000): “Misinformation and the Currency of Democratic Citizenship,” The Journal of Politics, 62, 790–816s.

Lawrence, E., C. D. Vries, M. Sttenbergen, and E. Edwards (2011): “Mean Voter Representation and Partisian Constituency Representation: Do Parties Respond to the Mean Voter Position or to their Supporters,” Party Politics, 17, 275–301.

Lizzeri, A. (1999): “Information Revelation and Certification Intermediaries,” The RAND Journal of Economics, 30.

Manili, J. (2024): “Disclosure to an Heterogeneous Auudience: The Role of Motivated Beliefs,” Tech. rep., Northwestern University.

Milgrom, P. and J. Roberts (1986): “Relying on the Information of Interested Parties,” RAND Journal of Economics, 17, 18–32.

Milgrom, P. R. (1981): “Good News and Bad News: Representation Theorems and Applications,” The Bell Journal of Economics, 12, 380–391.

Monroe, A. D. (1998): “Public Opinon and Public Policy,” Public Opinon Quarterly, 62, 6–28.

Mussa, M. and S. Rosen (1978): “Monopoly and Product Quality,” Journal of Economic Theory, 18, 301–317.

Myerson, R. B. (1981): “Optimal Auction Design,” Mathematics of Operations Research, 6, 58–73.

Pereira, M. M. (2019): “Do Parties Respond Strategically to Opinion Polls? Evidence from Campaign Statements,” Electoral Studies, 59, 78–86.

Perez-Richet, E. (2014): “Interim Bayesian Persuasion: First Steps,” American Economic Review, 5, 469–474.

Poblete, J. and D. Spulber (2012): “The Form of Incentive Contracts: Agency with Moral Hazard, Risk Neutrality, and Limited Liability,” The RAND Journal of Economics, 43, 215–234.

Rayo, L. and I. R. Segal (2010): “Optimal Information Disclosure,” Journal of Political Economy, 118, 949–987.

Reiljan, A., D. Garzia, F. F. D. Silva, and A. H. Trechsel (2024): “Pattern of Affective Polarization toward Parties and Leaders accross the DemocraticWorld,” American Political Science Review, 118, 654–670.

Shin, H. S. (1994): “News Management and the Value of Firms,” The RAND Journal of Economics, 25, 58–71. 43

Somer-Topcu, Z. (2009): “Timely Decisions: the Effects of Past National Elections on Party Policy Change,” Journal of Politics, 71, 238–248.

Stagnaro, M. N. and E. Amsalem (2025): “Factual Knowledge Can Reduce Attitude Polarization,” Nature Communications, 16.

Walgrave, S., S. Soroka, P. Loewen, T. Sheafer, and K. Soontjens (2022): “Revisiting Elite Perceptions as Mediator of Elite Responsiveness to Public Opinion,” Political Studies, 72, 364–379.

Wang, T. and E. Lehrer (2024): “Weighted Utility and Optimisim/Pessimism: A Decision-Theoretic Foundation of Various Stochastic Dominance Orders,” American Economic Journal: Microeconomics, 16, 210–223.

Zapechelnyuk, A. (2023): “On the Equivalence of Information Design by Uninformed and Informed Principals,” Economic Theory, 76, 1051–1067.