Abstract
We introduce an electoral pollster in the canonical pivotal voting model and show that the misreporting of pre-election poll results can happen even in the absence of partisan motives, as long as reputational concerns are present. By underreporting the expected number of supporters of the most preferred candidate in society, the pollster can induce an election result more likely to be in line with its report. By doing so, not only victory chances of the most preferred candidate rise above 50%, thus breaking the unrealistic neutrality result of the pivotal voting model, but also total election costs are reduced, thus yielding welfare gains and partially offsetting the expected negative effect of polls on welfare (see Goeree and Großer in Econ Theory 31:51–68, 2007; Taylor and Yildirim in Games Econ Behav 68:353–375, 2010). Our model also allows for the simultaneous accommodation of the underdog effect (a feature of pivotal voting models) and the apparently inconsistent bandwagon effect, in the sense that the latter can actually be understood as an illusion due to the possibility of misreporting being overlooked. All of these results hold even as the electorate size grows without bound.
Similar content being viewed by others
References
Börgers, T.: Costly voting. Am. Econ. Rev. 94, 57–66 (2004)
Brier, G.W.: Verification of forecasts expressed in terms of probability. Mon. Weather Rev. 78, 1–3 (1950)
Campbell, C.: Large electorates and decisive minorities. J. Polit. Econ. 107, 1199–1217 (1999)
Faravelli, M., Man, P.: Generalized majority rules: utilitarian welfare in large but finite populations. Econ. Theory 72, 21–48 (2021)
Goeree, J.K., Großer, J.: Welfare reducing polls. Econ. Theory 31, 51–68 (2007)
Good, I.J.: Rational decisions. J. R. Stat. Soc. 14B, 107–114 (1952)
Grillo, A.: Risk aversion and bandwagon effect in the pivotal voter model. Public Choice 172, 465–482 (2017)
Hossain, T., Okui, R.: The binarized scoring rule. Rev. Econ. Stud. 80, 984–1001 (2013)
Johnson, N.L., Kotz, S., Balakrishnan, L.: Discrete Multivariate Distributions. Wiley, New York (1997)
Krasa, S., Polborn, M.K.: Is mandatory voting better than voluntary voting? Games Econ. Behav. 66, 275–291 (2009)
Ledyard, J.O.: The pure theory of large two-candidate elections. Public Choice 44, 7–41 (1984)
Morton, R.B., Ou, K.: What motivates bandwagon voting behavior: Altruism or a desire to win? Eur. J. Polit. Econ. 40B, 224–241 (2015)
Palfrey, T.R., Rosenthal, H.: A strategic calculus of voting. Public Choice 41, 7–53 (1983)
Palfrey, T.R., Rosenthal, H.: Voter participation and strategic uncertainty. Am. Polit. Sci. Rev. 79, 62–78 (1985)
Roby, T.B.: Belief states: a preliminary empirical study. Decis. Sci. Lab. 64, 1–34 (1964)
Rudin, W.: Principles of Mathematical Analysis, 3rd edn. McGraw-Hill, New York (1976)
Savage, L.: Elicitation of personal probabilities and expectations. J. Am. Stat. Assoc. 66, 783–801 (1971)
Schochetman, I.E.: Pointwise versions of the maximum theorem with applications in optimization. Appl. Math. Lett. 3, 89–92 (1990)
Selten, R.: Axiomatic characterization of the quadratic scoring rule. Exp. Econ. 1, 43–62 (1998)
Shi, P., Conitzer, V., Guo, M.: Prediction mechanisms that do not incentivize undesirable actions. In: Leonardi, S. (ed.) Internet and Network Economics, pp. 89–100. Springer, Berlin (2009)
Skellam, J.G.: The frequency distribution of the difference between two Poisson variates belonging to different populations. J. R. Stat. Soc. 109, 296 (1946)
Tarnaud, R.: Convergence within binary market scoring rules. Econ. Theory 68, 1017–1050 (2019)
Taylor, C.R., Yildirim, H.: Public information and electoral bias. Games Econ. Behav. 68, 353–375 (2010a)
Taylor, C.R., Yildirim, H.: A unified analysis of rational voting with private values and group-specific costs. Games Econ. Behav. 70, 457–471 (2010b)
Wadsworth, G.P., Bryan, J.G.: Applications of Probability and Random Variables, 2nd edn. McGraw-Hill, New York (1974)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Durazzo, F.R., Turchick, D. Welfare-improving misreported polls. Econ Theory 75, 523–565 (2023). https://doi.org/10.1007/s00199-022-01413-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00199-022-01413-9