Contribution to a public good under subjective uncertainty

• DOI: http://doi.org/10.1111/jpet.12423
• Published date: 01 June 2020
• Author: Nicolas Gravel,Anwesha Banerjee
• Date: 01 June 2020

J Public Econ Theory. 2020;22:473–500. wileyonlinelibrary.com/journal/jpet © 2019 Wiley Periodicals, Inc.

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473

Received: 24 August 2018

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Accepted: 7 December 2019

DOI: 10.1111/jpet.12423

ORIGINAL ARTICLE

Contribution to a public good under subjective

uncertainty

Anwesha Banerjee

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Nicolas Gravel

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1

Aix‐Marseille Université, CNRS, EHESS,

ECM, AMSE, Marseille, France

2

Centre de Sciences Humaines &

Aix‐Marseille Université, CNRS, EHESS,

ECM, AMSE, Delhi, India

Correspondence

Nicolas Gravel, Centre de Sciences

Humaines & Aix‐Marseille Université,

CNRS, EHESS, ECM, AMSE, 2, Dr. Abdul

Kalam Road, Delhi 110011, India.

Email: Nicolas.gravel@csh-delhi.com

Funding information

Agence Nationale de la Recherche,

Grant/Award Number: ANR‐16‐CE41‐

0005

Abstract

This paper examines how voluntary contributions to

a public good are affected by the contributors’

heterogeneity in beliefs about the uncertain impact

of their contributions. It assumes that contributors

have Savagian preferences that are represented by a

two‐state‐dependent expected utility function and

different beliefs about the benefit that will result

from the sum of their contributions. We establish

general comparative statics results regarding the

effect of specific changes in the distribution of beliefs

on the (unique) Nash equilibrium provision of the

public good, under certain conditions imposed on the

preferences. We specifically show that the equili-

brium public good provision is increasing with

respect to both first‐and second‐order stochastic

dominance changes in the distribution of beliefs.

Hence, increasing the contributors’optimism about

the uncertain benefit of their contributions increases

aggregate public good provision, as does any homo-

genization of these beliefs around their mean.

“The debate’s over. The people who dispute the international consensus on global

warming are in the same category now with the people who think the moon landing

was staged on a movie lot in Arizona.”(Al Gore)

“Whether global warming or climate change. The fact is we didn’t cause it. We cannot

change it.”(Donald J. Trump)

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INTRODUCTION

There are many situations where agents are uncertain about the benefit they get from

contributing to a public good. The fight against global warming through carbon emission

reductions is an example of such a situation. As shown in Figure 1, borrowed from Millner,

Dietz, and Heal (2013), there is considerable scientific uncertainty about the impact of carbon

accumulation on the Earth’s temperature at the 2050 horizon. Moreover, as is also apparent in

the picture, there is significant heterogeneity amongst scientists themselves regarding the

probability that they assign to increases in the Earth’s temperature associated with specific

scenarios of carbon accumulation (such as the “business as usual”one in Figure 1). This

heterogeneity in beliefs about the impact of carbon emissions is also reflected in the variety of

(less scientific) opinions on this matter found in public debate, and illustrated by the polarized

views of the two leading American political figures quoted above. There is little doubt that a

person’s belief about the impact of carbon emissions on global warming will affect this person’s

propensity to make costly efforts to prevent climate change (see, e.g., Roser‐Renouf, Maibach,

Leiserowitz, & Zhao, 2014). After all, had he been the US president, Al Gore would have

certainly not taken the same decision vis‐à‐vis the Paris agreement on global climate change as

that taken by Donald J. Trump. Other examples of contributions to a public good under

subjective uncertainty include contributions to charities or philanthropic institutions by agents

who are uncertain about their reliability or effectiveness, individuals’decisions to vaccinate

(see, e.g., Brewer, Chapman, Gibbons, Gerrard, & McCaul, 2007) or, in developing countries, to

defecate in the open rather than in toilets (see, e.g., Clasen et al., 2014).

FIGURE 1 Estimated distributions of increase in the Earth’s temperature (in celsius) by 2050 under a

business as usual scenario (Source: Millner et al., 2013)

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BANERJEE AND GRAVEL