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Disagreement behind the veil of ignorance


In this paper we argue that there is a kind of moral disagreement that survives the Rawlsian veil of ignorance. While a veil of ignorance eliminates sources of disagreement stemming from self-interest, it does not do anything to eliminate deeper sources of disagreement. These disagreements not only persist, but transform their structure once behind the veil of ignorance. We consider formal frameworks for exploring these differences in structure between interested and disinterested disagreement, and argue that consensus models offer us a solution concept for disagreements behind the veil of ignorance.

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Fig. 1


  1. Of course, Rawls saw a version of this problem, which he called the ‘burdens of judgment.’ This motivated him to switch to the idea of the overlapping consensus in Political Liberalism (Rawls 2005).

  2. Note that these personal preferences need not be selfish: an altruist may fiercely pursue the well-being of those who are more disadvantaged than her. In such situations, an agreement on moral questions is transformed into a settlement of competing, position-dependent interests.

  3. The definition below is easily generalizable to more than three players.

  4. Consensus models were originally developed with factual disagreements in mind, but recent work on the topic has suggested that these models have wider applications (Steele et al. 2007; Martini et al. 2012).

  5. Formally, this amounts to matrix multiplication of the opinion vector by the weights matrix.

  6. Besides, an agent who refused to be rational and listen to her peers in the Original Position would surely violate the spirit of Rawls’ thought experiment in a fundamental way.

  7. These weights need not depend on how close the agents are to each other with regard to their respective estimates. Using distance between estimates as a measure of respect was advocated by Regan et al. (2006) for pragmatic reasons and also by Hegselmann and Krause (2002). The model permits us to assign relative weights as a function of the difference of opinion, if this is desired, but it is not required.


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The authors wish to thank Samuel Freeman, Douglas Paletta, Gerald Gaus, and the audience of the Conference ‘New Directions in the Philosophy of Science’ held at the Bertinoro Conference Centre (University of Bologna) for their useful comments on earlier versions of the manuscript. The usual exculpations apply. Part of this work was funded by a Dutch Science Foundation Internationalisation Grant.

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Correspondence to Ryan Muldoon.



Summary of the Lehrer–Wagner model

Let \(G = \{1, \ldots N\}\) be a group of agents. The Lehrer–Wagner model is concerned with the problem of estimating an unknown quantity x from the individual estimates x i of every group member i. This quantity x is thought of as objective and independent of the group members’ cognitive states.

Lehrer and Wagner’s central idea consists in ascribing the agents beliefs about each other’s expertise, or in other words, mutual degrees of respect for the issue at hand. These weights w ij represent the respect that agent i has for agent j, relative to the subject matter in question, and describe the proportion to which j’s opinion affects i’s revised opinion. The mutual respect assignments are in an N × N matrix W:

$$ W = \left( \begin{array}{llll} w_{11} & w_{12} & \dots & w_{1N} \\ w_{21} & w_{22} & \dots & w_{2N} \\ \dots & \dots & \dots & \dots \\ w_{N1} & w_{N2} & \dots & w_{NN} \end{array}\right). $$

An important mathematical constraint is that the values in each row are nonnegative and normalized so as to sum to 1: ∑ N j=1 w ij  = 1. Then, W is multiplied with a vector \(\vec{x} = (x_{1}, \ldots, x_{N})\) that contains the agents’ individual estimates of x, obtaining a novel updated value for \(\vec{x}\):

$$ W \cdot \vec{x} = \left( \begin{array}{l} w_{11} x_{1} + w_{12} x_2+ \ldots + w_{1N} x_N\\ w_{21} x_{1} + w_{22} x_2 + \ldots + w_{2N} x_N \\ \dots \\ w_{N1} x_{1} + w_{N2} x_2 + \ldots + w_{NN} x_N \end{array}\right). $$

In general, however, this procedure will not directly lead to consensus, since the entries of \(W \cdot \vec{x}\) differ: \((W\vec{x})_{i} \neq (W\vec{x})_{j}\). However, it can be shown that the iterated application of the pooling procedure represented by WW n, converges to the so-called “consensus matrix” \(W^{\infty}\). It can also be shown that the individual entries of \(W^{\infty} \cdot \vec{x}\) are equal to each other. Thus, repeating the pooling procedure leads to (rational) consensus.

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Muldoon, R., Lisciandra, C., Colyvan, M. et al. Disagreement behind the veil of ignorance. Philos Stud 170, 377–394 (2014).

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  • Rawls
  • Veil of ignorance
  • Disagreement
  • Consensus modeling
  • Bargaining