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Social Choice and Welfare

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14.09.2015 | Original Paper

Jury voting without objective probability

Erschienen in: Social Choice and Welfare | Ausgabe 2/2016

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Abstract

Unlike in the standard jury voting experiment, the voting environment in practice has no explicit signal structure. Voters then need to conceptualize the information structure in order to update their beliefs based on “pivotal reasoning”. This paper investigates whether voters can play a strategic voting under a “detail-free” environment. We obtain non-parametric predictions in terms of the differences in voting behaviors under majority and unanimity rule. Our experimental results suggest that voters can still play the strategic voting as in the existing experiments.

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Nächster Artikel The contribution of improved joint survival conditions to living standards: an equivalent consumption approach

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Battaglini et al. (2010) also tested another type of pivotal voting model called “swing voter’s curse” and confirmed their predictions.

Voter i’s cognitive ability should be a major determinant of \(p_{i}\), while voter i’s cognitive ability is determined before the experiment. Thus, the assumption that \(p_{i}\) is drawn from a distribution might not be very natural if i is interpreted as a subject’s identity. However, if i is interpreted as a seat number in the session, the assumption is natural as the subjects were randomly assigned to seats.

For more detail, see Appendix.

Since the subjects have different cognitive abilities, one might think that it is unnatural to consider an equilibrium in which the strategy profile is independent of i. However, as we mentioned in the earlier footnote, if i is interpreted as a seat number in the session instead of a subject’s identity, it is natural to consider an equilibrium in which two voters in seat i and j choose the same action if \(p_{i}=p_{j}\) as the subjects were randomly assigned to seats.

Since the proposer’s payoff is independent of a group decision, there is no reason that the quality of proposals depends on a voting rule. Then, since the subjects were assigned to four treatments randomly, \(f(p|\omega )\) should be independent of voting rules.

To obtain testable predictions at the group level, we need to specify the parameters of the model, which contradicts the purpose of our experiment, a detail-free experiment.

We appreciate one of the referees for pointing out this possibility.

For example, Caplin et al. (2011) tested a rational inattention model of individual decision making. In their experiment, the value of each choice is represented by a simple algebraic expression so that the subjects fail to choose the best choice when they are inattentive.

There are some experimental papers that investigate voting games with costly information acquisition, e.g., Großer and Seebauer (2013) and Elbittar et al. (2014). However, unlike in our experiment, the cost of information acquisition in their experiments is explicit in the sense that it directly reduces the payoff.

We can compute the average probability of being pivotal from the frequency of approval/rejection votes. In the logic treatment, the probability of being pivotal was around 16.78 % under unanimity rule while it was 37.23 % under majority rule. In the math treatment, it was 6.25 and 26.46 % respectively.

For more detail, see Persico (2004) and Elbittar et al. (2014).

Wilson (1987) emphasizes the theoretical aspect whereas our paper focuses on the empirical aspect.

Austen-Smith D, Banks JS (1996) Information aggregation, rationality, and the Condorcet Jury Theorem. Am Polit Sci Rev 90(1):34–45CrossRef

Battaglini M, Morton R, Palfrey T (2010) The swing voter’s curse in the laboratory. Rev Econ Stud 77:61–89

Caplin A, Dean M, Martin D (2011) Search and satisficing. Am Econ Rev 101(7):2899–2922

Condorcet M (1785) Essai sur l application de l analyse a la probabilite des decisions rendues a la probabilite des voix. In: Baker KM (ed) Paris: De l imprimerie royale. Translated in 1976 to essay on the application of mathematics to the theory of decision-making, condorcet: selected writings. Bobbs–Merrill, Indianapolis, IN

Elbittar A, Gomberg A, Martinelli C, Palfrey T (2014) Ignorance and bias in collective decision: theory and experiments. In: Working Papers 1401, Centro de Investigacion Economica, ITAM

Feddersen T, Pesendorfer W (1998) Convicting the innocent: the inferiority of unanimous Jury verdicts under strategic voting. Am Polit Sci Rev 92(1):23–25

Goeree JK, Yariv L (2011) An experimental study of collective deliberation. Econometrica 79:893–921

Großer J, Seebauer M (2013) The curse of uninformed voting: an experimental study. University of Cologne, Department of Economics Working Paper Series in Economics 64

Guarnaschelli S, McKelvey RP, Palfrey TR (2000) An experimental study of Jury decision rules. Am Polit Sci Rev 94(2):407–423

Kruger J, Dunning D (1999) Unskilled and unaware of it: how difficulties in recognizing one’s own incompetence lead to inflated self-assessments. J Person Soc Psychol 77(6):1121–1134

Persico N (2004) Committee design with endogenous information. Rev Econ Stud 71(1):165–191

Wason PC (1966) Reasoning. In: New horizons in psychology, vol. 1. Penguin Books, Harmondsworth

Wilson R (1987) Game-theoretic approaches to trading processes. In: Bewley T (ed) Advances in economic theory, chap. 2. Cambridge University Press, Cambridge, pp 33–77

Titel: Jury voting without objective probability
Publikationsdatum: 14.09.2015
Erschienen in: Social Choice and Welfare / Ausgabe 2/2016
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-015-0918-z

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