Ontology Merging as Social Choice

The problem of merging several ontologies has important applications in the Semantic Web, medical ontology engineering and other domains where information from several distinct sources needs to be integrated in a coherent manner.We propose to view ontology merging as a problem of social choice, i.e. as a problem of aggregating the input of a set of individuals into an adequate collective decision. That is, we propose to view ontology merging as ontology aggregation. As a first step in this direction, we formulate several desirable properties for ontology aggregators, we identify the incompatibility of some of these properties, and we define and analyse several simple aggregation procedures. Our approach is closely related to work in judgment aggregation, but with the crucial difference that we adopt an open world assumption, by distinguishing between facts not included in an agent’s ontology and facts explicitly negated in an agent’s ontology

Group deliberation and the transformation ofjudgments: an impossibility result

While a large social-choice-theoretic literature discusses the aggregation ofindividual judgments into collective ones, there is relatively little formalwork on the transformation of individual judgments in group deliberation. Idevelop a model of judgment transformation and prove a baselineimpossibility result: Any judgment transformation function satisfying someinitially plausible condition is the identity function, under which no opinionchange occurs. I identify escape routes from this impossibility result andargue that successful group deliberation must be 'holistic': individualscannot generally revise their judgments on a proposition based on judgmentson that proposition alone but must take other propositions into account too. Idiscuss the significance of these findings for democratic theory.group deliberation, judgment aggregation, judgmenttransformation, belief revision

Beliefs in Repeated Games

Consider a two-player discounted infinitely repeated game. A player's belief is a probability distribution over the opponent's repeated game strategies. This paper shows that, for a large class of repeated games, there are no beliefs that satisfy three conditions, learnability, consistency, and a diversity condition, CS. This impossibility theorem generalizes results in Nachbar (1997).

The Present and Future of Judgement Aggregation Theory. A Law and Economics Perspective

This chapter briefly reviews the present state of judgment aggregation theory and tentatively suggests a future direction for that theory. In the review, we start by emphasizing the difference between the doctrinal paradox and the discursive dilemma, two idealized examples which classically serve to motivate the theory, and then proceed to reconstruct it as a brand of logical theory, unlike in some other interpretations, using a single impossibility theorem as a key to its technical development. In the prospective part, having mentioned existing applications to social choice theory and computer science, which we do not discuss here, we consider a potential application to law and economics. This would be based on a deeper exploration of the doctrinal paradox and its relevance to the functioning of collegiate courts. On this topic, legal theorists have provided empirical observations and theoretical hints that judgment aggregation theorists would be in a position to clarify and further elaborate. As a general message, the chapter means to suggest that the future of judgment aggregation theory lies with its applications rather than its internal theoretical development

The Discursive Dilemma and Probabilistic Judgement Aggregation

Let S be a set of logically related propositions, and suppose a jury must decide the truth/falsehood of each member of S. A `judgement aggregation rule' (JAR) is a rule for combining the truth valuations on S from each juror into a collective truth valuation on S. Recent work has shown that there is no reasonable JAR which always yields a logically consistent collective truth valuation; this is referred to as the `Doctrinal Paradox' or the `Discursive Dilemma'. In this paper we will consider JARs which aggregate the subjective probability estimates of the jurors (rather than Boolean truth valuations) to produce a collective probability estimate for each proposition in S. We find that to properly aggregate these probability estimates, the JAR must also utilize information about the private information from which each juror generates her own probability estimate.discursive dilemma; doctrinal paradox; judgement aggregation; statistical opinion pool; interactive epistemology; common knowledge; epistemic democracy; deliberative democracy

Aggregation theory and the relevance of some issues to others

I propose a general collective decision problem consisting in many issues that are interconnected in two ways: by mutual constraints and by connections of relevance. Aggregate decisions should respect the mutual constraints, and be based on relevant information only. This general informational constraint has many special cases, including premise-basedness and Arrow''s independence condition; they result from special notions of relevance. The existence and nature of (non-degenerate) aggregation rules depends on both types of connections. One result, if applied to the preference aggregation problem and adopting Arrow''s notion of (ir)relevance, becomes Arrow''s Theorem, without excluding indifferences unlike in earlier generalisations.mathematical economics;

Strategy-proof judgment aggregation.

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy.

Lack of Finite Characterizations for the Distance-based Revision

Lehmann, Magidor, and Schlechta developed an approach to belief revision based on distances between any two valuations. Suppose we are given such a distance D. This defines an operator |D, called a distance operator, which transforms any two sets of valuations V and W into the set V |D W of all elements of W that are closest to V. This operator |D defines naturally the revision of K by A as the set of all formulas satisfied in M(K) |D M(A) (i.e. those models of A that are closest to the models of K). This constitutes a distance-based revision operator. Lehmann et al. characterized families of them using a loop condition of arbitrarily big size. An interesting question is whether this loop condition can be replaced by a finite one. Extending the results of Schlechta, we will provide elements of negative answer. In fact, we will show that for families of distance operators, there is no "normal" characterization. Approximatively, a normal characterization contains only finite and universally quantified conditions. These results have an interest of their own for they help to understand the limits of what is possible in this area. Now, we are quite confident that this work can be continued to show similar impossibility results for distance-based revision operators, which suggests that the big loop condition cannot be simplified