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Many voting rules are based on minimization or maximization principle. Likewise, in the field of logic-based knowledge representation and reasoning, many belief change or inconsistency handling operators make use of minimization. Surprisingly, minimization has not played a major role in the field of judgment aggregation, in spite of its proximity to voting theory and logic-based knowledge representation and reasoning. Here we make a first step in the study of judgment aggregation rules based on minimization, and propose a classification of judgment aggregation rules based on some minimization or maximization principle. We distinguish four families. The rules of the first family compute the collective judgment for each issue, using proposition-wise majoritarian aggregation, and then restore consistency using some minimal change principle. The rules of the second family proceed in a similar way but take into account the strength of the majority on each issue. Those of the third family consist in restoring the consistency of the majoritarian judgment by removing or changing some individual judgments in a minimal way. Finally, those of the fourth family are based on some predefined distance between judgment sets, and look for a consistent collective judgment minimizing the overall distance to the individual judgment sets. For each family we propose a few typical rules. While most of these rules are new, a few ones correspond to rules * A preliminary version of this paper appeared in the

The literature on judgment aggregation is moving from studying impossibility results regarding aggregation rules towards studying specific judgment aggregation rules. Here we give a structured list of most rules that have been proposed and studied recently in the literature, together with various properties of such rules. We first focus on the majoritypreservation property, which generalizes Condorcet-consistency, and identify which of the rules satisfy it. We study the inclusion relationships that hold between the rules. Finally, we consider two forms of unanimity, monotonicity, homogeneity, and reinforcement, and we identify which of the rules satisfy these properties.

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Several recent articles have defined and studied judgment aggregation rules based on some minimization principle. Although some of them are defined by analogy with some voting rules, the exact connection between these rules and voting rules is not always obvious. We explore these connections and show how several well-known voting rules such as the top cycle, Copeland, maximin, Slater or ranked pairs, are recovered as specific cases of judgment aggregation rules.