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equivalent to accepting its negation :B , then, even if individual opinions are each
logically coherent, the collective set A , A ! B , and :B is inconsistent.
Again, doctrinal paradoxes apply to any aggregation procedure that respects
some basic fairness desiderata, this is the meaning of the theorem proven by
Christian List and Philip Pettit ( 2002 ). It is important to stress once again that
the case of doctrinal paradoxes, far from being a curious example envisaged
by means of some thought experiment, has actually occurred in the deliberative
practice of judicial courts. In particular, the paradox has been perceived as a
serious threat to the legitimacy of the decision of the Court by the judges of the
Court themselves. A contradictory outcome, in that case, amounts to providing an
inconsistent sentence that can be contested by the defendant who is being charged
on that ground. Thus, it is important to provide a conceptual characterization of what
type of conflict the doctrinal paradox exhibits, as the problem of understanding to
which agent the conflict can be ascribed is not of immediate solution.
Summing up the content of this section, we have seen how SCT allows for
individuating and formalizing an important form of group conflict that applies in
normative settings and that is the specific notion of conflict that we want to analyze
in this paper.
2.3
A Model of Judgment Aggregation
We present the main elements of the formal approach of judgment aggregation (JA).
The reason why we focus on JA is twofold: on the one hand, it has been taken to
be more general than preference aggregation (List and Puppe 2009 ), on the other
hand, it has been claimed that JA can provide a general theory of aggregation of
propositional attitudes (Dietrich and List 2009 ). Therefore, JA provides the proper
level of abstraction for our abstract model of types of conflict. The content of this
section is based on List and Puppe ( 2009 ) and Endriss et al. ( 2012 ) and builds upon
them.
Let P be a set of propositional variables that represent the contents of the matter
under discussion by a number of agents. The language L P is the set of propositional
formulas built from P by using the usual logical connectives : , ^ , _ , ! , $ .
Definition 2.1. An agenda is a finite nonempty set ˚ L P that is closed under
(non-double) negations if A 2 ˚ then :A 2 ˚ .
An agenda is the set of propositions that are evaluated by the agent in a given
situation. In the examples of the previous section, the agenda is given by A , B , A !
B , :A , :B , :.A ! B/ . The fact that, given a proposition, the agenda must contain
also its negation aims to model the fact that agents may approve or reject a given
matter. The rejection of a matter A is then modeled by an agent accepting :A .Inthis
model, for the sake of simplicity, we do not present the case of abstention, however
it is possible to account for such cases by slightly generalizing our framework.
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