Friday, October 15, 2010

Morals by Agreement (Part 4): Bargaining and Impartiality

This post is part of my series on David Gauthier's Morals by Agreement. For an index, see here.

In the two previous entries we have looked at Gauthier's proposed solution to the bargaining problem, namely: minimax relative concession (MRC). According to this solution, when rational players have to reach some agreement on how to distribute a cooperative surplus, they should initially claim as much of the surplus as they could possibly have, and then agree on the distribution that minimises the maximum relative concessions they have to make from this initial claim.

If that summarisation is in any way confusing, I advise you to go back and read parts two and three. If it's not confusing, we can proceed to consider the moral implications of this theory.

1. What is it that Gauthier wants to do again?
As mentioned in part one, the goal of Gauthier's book is to find the deep connection between morality and rationality. Knowing when we have found the deep connection will depend on how we understand the terms "rationality" and "morality".

For Gauthier, "rationality" means what it means to economists, decision theorists, and game theorists: people should do what they most want to do. In slightly more formal terms, this means that rational agents should choose actions that maximise their utility. (Utility is simply the worth of an action or outcome to an agent -- the utility scale is calculated on a strictly individualistic basis). So, if there is such a thing as morality, it will have to be compatible with the utility-maximising conception of rationality.

But what is morality? For Gauthier, the distinctive feature of moral behaviour is its impartial nature. In other words, a moral act or a moral outcome is notable in that it treats agent's in an equal manner (no favour or bias is shown to particular agents).

It follows that if Gauthier's project of finding the deep connection between morality and rationality is to succeed, he must show how impartiality is possible for a utility-maximising agent. The theory of minimax relative concession is part (but only part!) of his attempt to do this.

In the remainder of this entry, three issues will be addressed: (i) why the MRC-solution is something to which utility-maximising agents can agree; (ii) why the MRC-solution allows us to realise impartial outcomes; and (iii) why the MRC-solution is only part of the complete picture.

2. Why is the MRC-solution Rational?
The bargaining process arises when there is some value to be obtained from cooperation that goes over and above what can be obtained from independent action. As such, there is the opportunity for every agent to increase their utility by cooperating. The problems arise when deciding how exactly the cooperative surplus should be distributed.

Gauthier identifies the following four conditions of rational bargaining (remember: a concession is an offer by a prospective cooperator for less than their initial claim; a concession point is the outcome that would result from a given set of concessions, one from each cooperator):

  • (1) Rational Claim: every player should claim the cooperative surplus that yields them the maximum utility, with the sole caveat being that they cannot claim the surplus if they would not be party to the cooperative interaction required to create it. In other words, they can't claim or demand something from the other rational players in order to secure cooperation, if they themselves wouldn't agree to that claim or demand.
  • (2) Concession Point: Given claims satisfying condition (1), every player must suppose that there is a feasible concession point that every rational player is willing to entertain (since they want the benefit of the cooperative surplus, but they know they can't each get their maximum claim, they must suppose there is some concession point that they can agree upon).
  • (3) Willingness to Concede: Each player must be willing to entertain a concession in relation to a feasible concession point, if its relative magnitude is no greater than that of the greatest concession that he supposes some other rational player is willing to entertain.
  • (4) Limits of Concession: No person is willing to entertain a concession in relation to a concession point if he is not required to do so by conditions (2) and (3).

I think conditions (1) and (2) are relatively straightforward. (1) is simply the application of the utility maximising model of rationality to the specific context of a bargaining problem; and (2) merely draws out from this the fact that if cooperation is to be possible at all, there must be a concession point that all can agree upon. Otherwise, there would be no point to cooperation.

Condition (3) highlights the equal rationality of the players. Since each player is seeking to maximise their utility (and by correlation minimise their concessions) no player can expect another player to make a concession unless they would be willing to make a similar concession.

Condition (4) is saying that no utility maximising player will be willing to entertain a concession unless: (i) there is a feasible concession point that all could agree upon and (ii) he/she is not being asked to make unnecessary, or unnecessarily large, concessions.

These conditions of rational bargaining -- which are compatible with the utility-maximising conception of rationality -- combine to show that the MRC-solution is one on which rational actors can be expected to agree. How so? Well, conditions (2), (3) and (4) imply that every rational agent should be willing to entertain a concession point up to and including (but no greater than) the minimax relative concession. At the same time, if the proposed outcome is not the MRC-point, it would mean that some player is being asked to concede more than they can be expected to concede. Consequently, no rational player is going to agree to an outcome that is different from the MRC-point.

3. Why is the MRC-solution Impartial?
Gauthier's argument for the impartiality of the MRC-solution is slightly more complicated and, as it's late enough as I'm writing this, I'm going to skimp on the details and give a pretty cursory summary. Basically, Gauthier argues that a solution is impartial if it gives the same relative treatment to people, whenever similar treatment is possible.

There are two cases to consider. The first is where the surplus produced by cooperation is a fully transferable good (i.e. can be easily transferred between the parties). In this case, equal relative shares should be distributed between the parties as they contribute equally to the creation of the surplus.*

The second case is that of the non-fully-transferable good. In this case, it will not be possible to equally distribute the entire surplus, only the transferable portion can be so distributed.

The MRC-solution covers both scenarios: when it is possible to fully transfer the good, an equal relative share will coincide with the MRC; likewise, in the non-transferable case, the MRC-solution will allow for equal relative shares of the transferable portion with the non-transferable portion going to whoever accrues it. It is the best that any rational player can expect to obtain, and it also affords them equal relative treatment.

4. What more needs to be done?
Although the MRC-solution is a significant step along the road to showing the deep connection between rationality and morality, it does not bring us all the way to our desired destination. Two additional things need to be done.

First, the MRC-solution only shows the impartiality of the agreement reached through rational bargaining. It does not show the rationality of complying with that agreement in the long run. Gauthier's theory of constrained maximisation tries to deal with this problem.

Second, the impartiality of the MRC-solution is relative to the initial bargaining position (IBP) of the parties. If this IBP is seriously partial or unequal, it will be reflected in the final outcome. Hence, some restrictions may need to be placed on what counts as an IBP. Gauthier tries to specify those restrictions in a later chapter.

I will be looking into the idea of constrained maximisation in due course. I have no intentions to look at the stuff on the IBP.

* Gauthier has an argument covering cases where the initial contribution seems to be unequal. In those cases he shows how the MRC-solution leads to a distribution which is equal, but proportionate to the contribution. I won't explain that here, it occurs on pp. 140-141 of the book.

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