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Bets on Hats - On Dutch Books Against Groups, Degrees of Belief as Betting Rates, and Group-Reflection

Rabinowicz, Wlodek LU and Luc, Bovens (2011) In Episteme 8(3). p.281-300
Abstract (Swedish)
Abstract in Undetermined

The aim was to use Todd Ebert's Hats puzzle to devise a Dutch Book showing that individual rationality could add up to collective irrationality even if the players aim to promote common goals. Situations in which this happens involve violations of what might be called the Group-Reflection Principle. The Dutch book that can be set up against groups that violate Group-Reflection is a version of van Fraassen’s Dutch book against individual agents who violate the standard individual version of Reflection.

Unfortunately, as it turned out, the argument leading to the paradox is flawed, but it is flawed in interesting ways. It was based on the betting interpretation of the subjective... (More)
Abstract in Undetermined

The aim was to use Todd Ebert's Hats puzzle to devise a Dutch Book showing that individual rationality could add up to collective irrationality even if the players aim to promote common goals. Situations in which this happens involve violations of what might be called the Group-Reflection Principle. The Dutch book that can be set up against groups that violate Group-Reflection is a version of van Fraassen’s Dutch book against individual agents who violate the standard individual version of Reflection.

Unfortunately, as it turned out, the argument leading to the paradox is flawed, but it is flawed in interesting ways. It was based on the betting interpretation of the subjective probabilities, but ignored the fact that this interpretation does not take into account the strategic, i.e. game-theoretic, considerations that might influence an agent’s betting behavior. If such considerations are taken into account, as they clearly should, then the Dutch book construction crumbles.

Thus, the argument that individual rationality in pursuing a common objective can add up to collective irrationality does not go through after all. Instead, the lesson to be learned concerns the interpretation of probabilities in terms of fair bets and, more generally, the role of game-theoretic considerations in epistemic contexts. Another lesson concerns Group-Reflection, which in its unrestricted form is a highly counter-intuitive principle. We consider how this principle of social epistemology should be formulated so as to make it tenable. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
puzzle of the hats, dutch book, rationality, collective rationality, subjective probabilities, reflection, betting interprettation, game theory, Nash equilibria
in
Episteme
volume
8
issue
3
pages
281 - 300
publisher
Edinburgh University Press
external identifiers
  • scopus:85010699984
ISSN
1750-0117
language
English
LU publication?
yes
id
360ce249-14c1-4718-bb61-ae3ed840c447 (old id 2295454)
date added to LUP
2012-01-17 16:56:49
date last changed
2017-04-02 03:15:52
@article{360ce249-14c1-4718-bb61-ae3ed840c447,
  abstract     = {<b>Abstract in Undetermined</b><br/><br>
The aim was to use Todd Ebert's Hats puzzle to devise a Dutch Book showing that individual rationality could add up to collective irrationality even if the players aim to promote common goals. Situations in which this happens involve violations of what might be called the Group-Reflection Principle. The Dutch book that can be set up against groups that violate Group-Reflection is a version of van Fraassen’s Dutch book against individual agents who violate the standard individual version of Reflection.<br/><br>
Unfortunately, as it turned out, the argument leading to the paradox is flawed, but it is flawed in interesting ways. It was based on the betting interpretation of the subjective probabilities, but ignored the fact that this interpretation does not take into account the strategic, i.e. game-theoretic, considerations that might influence an agent’s betting behavior. If such considerations are taken into account, as they clearly should, then the Dutch book construction crumbles. <br/><br>
Thus, the argument that individual rationality in pursuing a common objective can add up to collective irrationality does not go through after all. Instead, the lesson to be learned concerns the interpretation of probabilities in terms of fair bets and, more generally, the role of game-theoretic considerations in epistemic contexts. Another lesson concerns Group-Reflection, which in its unrestricted form is a highly counter-intuitive principle. We consider how this principle of social epistemology should be formulated so as to make it tenable.},
  author       = {Rabinowicz, Wlodek and Luc, Bovens},
  issn         = {1750-0117},
  keyword      = {puzzle of the hats,dutch book,rationality,collective rationality,subjective probabilities,reflection,betting interprettation,game theory,Nash equilibria},
  language     = {eng},
  number       = {3},
  pages        = {281--300},
  publisher    = {Edinburgh University Press},
  series       = {Episteme},
  title        = {Bets on Hats - On Dutch Books Against Groups, Degrees of Belief as Betting Rates, and Group-Reflection},
  volume       = {8},
  year         = {2011},
}