The doctrinal paradox, the discursive dilemma, and some problems of deliberative capabilities in multi-agents systems

Deliberative capabilities of multi-agents systems do not necessarily emerge from their individual members' deliberative capabilities alone. Although, we don’t need any kind of telepathy (wireless direct communication between robots) or collective consciousness in order to conceptualize those capabilities. Pettit (2004) helps understanding the problem, leading us from the doctrinal paradox, identified in jurisprudence, to a generalized discursive dilemma most deliberative collectives may face.

This is an example of the doctrinal paradox.
A three-judge court has to decide a tort case and judge the defendant liable if and only if the defendant’s negligence was causally responsible for the injury to the plaintiff and the defendant has a duty of care toward the plaintiff. Now, which decision has been taken when judges voted as follows?

	Cause of harm? (Premise 1)	Duty of care? (Premise 2)	Liable? (Conclusion)
Judge A	Yes	No	No
Judge B	No	Yes	No
Judge C	Yes	Yes	Yes

With a conclusion-centered procedure, the court decides “No”. With a premise-centered procedure, the court decides “Yes”, the conclusion following deductively from the conjunction of positive answers to both premises. The doctrinal paradox consists in having different outcomes to the same case with the same votes but different procedures. The same paradox can arise with a conclusion linked to a disjunction of premises. For example, when an appellant should be given a retrial either if inadmissible evidence has been used or a forced confession has taken place.

	Inadmissible evidence?	Forced confession?	Retrial?
Judge A	Yes	No	Yes
Judge B	No	Yes	Yes
Judge C	No	No	No

The paradox in not confined to courts and legal domain. It can arise within many groups, like appointment and promotion committees or committees deciding who is to win a certain contract or a prize. “It will arise whenever a group of people discourse together with a view to forming an opinion on a certain matter that rationally connects, by the lights of all concerned, with other issues” (Pettit 2004:170).

In a generalized version, the paradox is named the discursive dilemma. Purposive groups (organizations with a specific function or goal, like states, political parties or business corporations) will almost inevitably confront the discursive dilemma in an especially interesting version. They have to take a series of decisions over a period of time in a consistent and coherent way.
Take as an example a political party that takes each major decision by a majority vote. It announces in March it will not increase taxes if it gets into government and announces in June it will increase defence spending. In September it must announce whether it will increase spending in other policy areas. The following matrix (where A, B, C stands for voting behaviour patterns) shows the dilemma’s structure.

	Increase taxes?	Increase defence spending?	Increase other spending?
A	No	No	No (reduce)
B	No	No (reduce)	Yes
C	Yes	Yes	Yes

If the party allows a majority vote on last issue, it risks incoherence and, so, discredit.

This kind of situations can occur partly because in ordinary social life people (even within organizations) do not show preferences and take decisions on the basis of complete information and deep theoretical basis. So, collectives prone to achieve their own goals, involving the outside world and/or their own members, must adopt some kind of collective reason, some mechanism to sustain coherent global behaviour towards those goals. Collective reason does not necessarily emerges from individuals’ reason alone.


REFERENCE

(Pettit 2004) PETTIT, Philip, “Groups with Minds of their Own”, in SCHMITT, Frederick (Ed.), Socializing Metaphysics, New York, Rowman and Littlefield, 2004 pp. 167-193 (click to get the paper in pdf file)

More information at the Philip Pettit's Web Page