ditions: (i) Anonymity: all individuals play the same role; (ii) Respect for unanimity: if every individual strictly prefers x to y , then the collective ranking strictly prefers also x to y ; (iii) Independence of irrelevant alternatives:
the collective preference about two alternatives x and y depends only on the individual preferences about x and y . According to Arrow's theorem, such a rule does not exist, except in the case where there are only two alternatives.

The doctrinal paradox has motivated the question of extending Arrow's theorem to the general problem of constrained judgment aggregation. Analogously to the preceding paragraph, one would be interested in rules that, besides keeping consistency with the doctrine in question, comply also with the following conditions: (i) Anonymity; (ii) Respect for unanimity: if a particular proposition is accepted by every individual, then it is also accepted by the collective judgment; (iii) Issue-by-issue aggregation (or independence): the collective judgment about each issue depends only on the individual judgments about it. In the present context, the possibility or impossibility of a rule satisfying these conditions clearly depends on the structure of the doctrine under consideration. For instance, the majority rule will always do for an empty doctrine, i. e. several propositions without any logical connection between them. Accordingly, the existing impossibility results, for which we refer to [*21, 22, 7, 17, 8*], specify certain conditions to be met by the doctrine.

1.4 In practice, one is bound to make decisions, even for doctrines that are included in the above-mentioned impossibility results. The purpose of this article is to put forward a general rule for making such decisions in consistency with the doctrine. This rule will not comply with the property of issue-by-issue aggregation. However, it will be anonymous and it will respect unanimity about any particular issue whenever the individual beliefs are consistent with the doctrine.

The proposed method generalizes two other ones that are already known in certain particular areas: In fact, when the doctrine corresponds to the notion of an equivalence relation on a certain set of items, then one of the variants of our method yields the so-called single-link method of cluster analysis [13]. On the other hand, when the doctrine corresponds to the notion of a total order, then the proposed method corresponds essentially to the one that was introduced in 1997 by Markus Schulze [24 , 25 ; 27 : p. 228–232; 4 , 5 ].

The problem considered in this article should be distinguished from a related but different one that is often referred to as 'belief revision'. This subject is reviewed for instance in [11]. In contrast to the present work, where the doctrine remains fixed, there one allows for the possibility of revising it.