Belief-consistent Pareto dominance
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Belief-consistent Pareto dominance Xiangyu Qu1,2 Received: 11 October 2018 / Accepted: 17 September 2019 © Society for the Advancement of Economic Theory 2019
Abstract The classic Pareto criterion claims that all voluntary trades, even on the grounds of heterogeneous beliefs, should be encouraged. I argue that a trade without hope for Pareto improvement remains controversial. I introduce and characterize a notion of belief-consistent Pareto dominance to formalize this argument, which, in addition to unanimity of preferences, requires all rankings in a trade to be supported by some common beliefs that must coincide with the agents’ beliefs about the events on which all agents agree. Keywords Heterogeneous beliefs · Belief consistent · Pareto condition · Speculation JEL Classification D80
1 Introduction For years, free Pareto-improving trades have received almost faithful respect from economists. In a democratic society, why should traders be denied their mutual desire to trade? In recent years, this principle has gained much less support in the face of uncertainty, particularly when the involved traders possess different beliefs upon which the trade hinges. The examples provided by Weyl (2007) and Kreps (2012) demonstrated that when traders have different beliefs, fair trade is impaired.1 Guided by similar observations, Gilboa et al. (2014), Brunnermeier et al. (2014), Posner and 1 In advance, preference aggregation with heterogeneous beliefs has a similar flavor. Gilboa et al. (2004)
offered an example in which two parties do not receive mutual gains from a duel, but each party is expecting to benefit at the expense of the other party. Because both parties cannot be correct, Mongin (1997) argued that such unanimity is spurious. I thank Anotine Billot, Itzhak Gilboa, Marcus Pivato, and David Schmeidler for discussions. I especially appreciate helpful comments from a referee.
B
Xiangyu Qu [email protected]
1
CNRS, Centre d’Economie de la Sorbonne, Paris, France
2
School of Management, Wuhan University of Technology, Wuhan, China
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X. Qu Table 1 Pillow bet s1 = classic feather
s2 = polyester
s3 = goose down
Alice belief
0.1
0.7
0.2
Bob belief
0.7
0.1
0.2
Alice payoff
− $100
$10
$30
Bob payoff
$10
− $100
$30
Weyl (2013), Blume et al. (2014), etc., claim that society may be improved by restrictions that prevent such malicious trades from occurring. This paper proposes a belief-consistent Pareto criterion, which can somehow justify benevolent paternalism when traders holding heterogeneous beliefs engage in controversial trades. To illustrate the basic idea, consider the following adaptation of an example provided by Kreps (2012).2 There are two agents, Alice and Bob, who argue about the contents of a pillow. Suppose this pillow only has the following three possible types of content: classic feather, polyester and goose down. Both Alice and Bob know that the goose down pillow is a limited edition and, therefore, they share the belief that the probability that the pillow has goose down fi
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