In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using "systematicity" and "independence" conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we thereby (...) provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model. JEL Classi…cation: D70, D71.. (shrink)

The new field of judgment aggregation aims to merge many individual sets of judgments on logically interconnected propositions into a single collective set of judgments on these propositions. Judgment aggregation has commonly been studied using classical propositional logic, with a limited expressive power and a problematic representation of conditional statements ("if P then Q") as material conditionals. In this methodological paper, I present a simple unified model of judgment aggregation in general logics. I show how many realistic decision problems can (...) be represented in it. This includes decision problems expressed in languages of classical propositional logic, predicate logic (e.g. preference aggregation problems), modal or conditional logics, and some multi-valued or fuzzy logics. I provide a list of simple tools for working with general logics, and I prove impossibility results that generalise earlier theorems. (shrink)

Philosophically, one of the most important questions in the enterprise termed confirmation theory is this: Why should one stick to well confirmed theories rather than to any other theories? This paper discusses the answers to this question one gets from absolute and incremental Bayesian confirmation theory. According to absolute confirmation, one should accept ''absolutely well confirmed'' theories, because absolute confirmation takes one to true theories. An examination of two popular measures of incremental confirmation suggests the view that one should stick (...) to incrementally well confirmed theories, because incremental confirmation takes one to (the most) informative (among all) true theories. However, incremental confirmation does not further this goal in general. I close by presenting a necessary and sufficient condition for revealing the confirmational structure in almost every world when presented separating data. (shrink)

Degrees of belief are familiar to all of us. Our confidence in the truth of some propositions is higher than our confidence in the truth of other propositions. We are pretty confident that our computers will boot when we push their power button, but we are much more confident that the sun will rise tomorrow. Degrees of belief formally represent the strength with which we believe the truth of various propositions. The higher an agent’s degree of belief for a particular (...) proposition, the higher her confidence in the truth of that proposition. For instance, Sophia’s degree of belief that it will be sunny in Vienna tomorrow might be .52, whereas her degree of belief that the train will leave on time might be .23. The precise meaning of these statements depends, of course, on the underlying theory of degrees of belief. These theories offer a formal tool to measure degrees of belief, to investigate the relations between various degrees of belief in different propositions, and to normatively evaluate degrees of belief. (shrink)

I propose a relevance-based independence axiom on how to aggregate individual yes/no judgments on given propositions into collective judgments: the collective judgment on a proposition depends only on people’s judgments on propositions which are relevant to that proposition. This axiom contrasts with the classical independence axiom: the collective judgment on a proposition depends only on people’s judgments on the same proposition. I generalize the premise-based rule and the sequential-priority rule to an arbitrary priority order of the propositions, instead of a (...) dichotomous premise/conclusion order resp. a linear priority order. I prove four impossibility theorems on relevance-based aggregation. One theorem simultaneously generalizes Arrow’s Theorem (in its general and indifference-free versions) and the well-known Arrow-like theorem in judgment aggregation. (shrink)

Several recent results on the aggregation of judgments over logically connected propositions show that, under certain conditions, dictatorships are the only propositionwise aggregation functions generating fully rational (i.e., complete and consistent) collective judgments. A frequently mentioned route to avoid dictatorships is to allow incomplete collective judgments. We show that this route does not lead very far: we obtain oligarchies rather than dictatorships if instead of full rationality we merely require that collective judgments be deductively closed, arguably a minimal condition of (...) rationality, compatible even with empty judgment sets. We derive several characterizations of oligarchies and provide illustrative applications to Arrowian preference aggregation and Kasher and Rubinsteinís group identification problem. (shrink)

The widely discussed "discursive dilemma" shows that majority voting in a group of individuals on logically connected propositions may produce irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds a given threshold, where different thresholds may be used for different propositions. After characterizing quota rules, we prove necessary and sufficient conditions on the required thresholds for various collective rationality requirements. We also consider sequential (...) quota rules, which ensure collective rationality by adjudicating propositions sequentially and letting earlier judgments constrain later ones. Sequential rules may be path-dependent and strategically manipulable. We characterize path-independence and prove its essential equivalence to strategy-proofness. Our results shed light on the rationality of simple-, super-, and sub-majoritarian decision-making. (shrink)

If a group is modelled as a single Bayesian agent, what should its beliefs be? I propose an axiomatic model that connects group beliefs to beliefs of group members, who are themselves modelled as Bayesian agents, possibly with different priors and different information. Group beliefs are proven to take a simple multiplicative form if people’s information is independent, and a more complex form if information overlaps arbitrarily. This shows that group beliefs can incorporate all information spread over the individuals without (...) the individuals having to communicate their (possibly complex and hard-to-describe) private information; communicating prior and posterior beliefs sufices. JEL classification: D70, D71.. (shrink)

In the framework of judgment aggregation, we assume that some formulas of the agenda are singled out as premisses, and that both Independence (formula-wise aggregation) and Unanimity Preservation hold for them. Whether premiss-based aggregation thus defined is compatible with conclusion-based aggregation, as defined by Unanimity Preservation on the non-premisses, depends on how the premisses are logically connected, both among themselves and with other formulas. We state necessary and sufficient conditions under which the combination of both approaches leads to dictatorship (resp. (...) oligarchy), either just on the premisses or on the whole agenda. This framework is inspired by the doctrinal paradox of legal theory and arguably relevant to this field as well as political science and political economy. When the set of premisses coincides with the whole agenda, a limiting case of our assumptions, we obtain several existing results in judgment aggregation theory. (shrink)

In this paper, we identify a new and mathematically well-defined sense in which the coherence of a set of hypotheses can be truth-conducive. Our focus is not, as usual, on the probability but on the confirmation of a coherent set and its members. We show that, if evidence confirms a hypothesis, confirmation is “transmitted” to any hypotheses that are sufficiently coherent with the former hypothesis, according to some appropriate probabilistic coherence measure such as Olsson’s or Fitelson’s measure. Our findings have (...) implications for scientific methodology, as they provide a formal rationale for the method of indirect confirmation and the method of confirming theories by confirming their parts. (shrink)

The new …eld of judgment aggregation aims to …nd collective judgments on logically interconnected propositions. Recent impossibility results establish limitations on the possibility to vote independently on the propositions. I show that, fortunately, the impossibility results do not apply to a wide class of realistic agendas once propositions like “if a then b” are adequately modelled, namely as subjunctive implications rather than material implications. For these agendas, consistent and complete collective judgments can be reached through appropriate quota rules (which decide (...) propositions using acceptance thresholds). I characterise the class of these quota rules. I also prove an abstract result that characterises consistent aggregation for arbitrary agendas in a general logic. (shrink)

The Spohnian paradigm of ranking functions is in many respects like an order-of-magnitude reverse of subjective probability theory. Unlike probabilities, however, ranking functions are only indirectly—via a pointwise ranking function on the underlying set of possibilities W —defined on a field of propositions A over W. This research note shows under which conditions ranking functions on a field of propositions A over W and rankings on a language L are induced by pointwise ranking functions on W and the set of (...) models for L, ModL, respectively. (shrink)

In judgment aggregation, unlike preference aggregation, not much is known about domain restrictions that guarantee consistent majority outcomes. We introduce several conditions on individual judgments su¢ - cient for consistent majority judgments. Some are based on global orders of propositions or individuals, others on local orders, still others not on orders at all. Some generalize classic social-choice-theoretic domain conditions, others have no counterpart. Our most general condition generalizes Sen’s triplewise value-restriction, itself the most general classic condition. We also prove a (...) new characterization theorem: for a large class of domains, if there exists any aggregation function satisfying some democratic conditions, then majority voting is the unique such function. Taken together, our results provide new support for the robustness of majority rule. (shrink)

All existing impossibility theorems on judgment aggregation require individual and collective judgment sets to be consistent and complete, arguably a demanding rationality requirement. They do not carry over to aggregation functions mapping profiles of consistent individual judgment sets to consistent collective ones. We prove that, whenever the agenda of propositions under consideration exhibits mild interconnections, any such aggregation function that is "neutral" between the acceptance and rejection of each proposition is dictatorial. We relate this theorem to the literature.

Bayesianism is the position that scientific reasoning is probabilistic and that probabilities are adequately interpreted as an agent's actual subjective degrees of belief, measured by her betting behaviour. Confirmation is one important aspect of scientific reasoning. The thesis of this paper is the following: if scientific reasoning is at all probabilistic, the subjective interpretation has to be given up in order to get right confirmation—and thus scientific reasoning in general. The Bayesian approach to scientific reasoning Bayesian confirmation theory The example (...) The less reliable the source of information, the higher the degree of Bayesian confirmation Measure sensitivity A more general version of the problem of old evidence Conditioning on the entailment relation The counterfactual strategy Generalizing the counterfactual strategy The desired result, and a necessary and sufficient condition for it Actual degrees of belief The common knock-down feature, or ‘anything goes’ The problem of prior probabilities. (shrink)

Erstmals 1951 publiziert, bilden die Vorlesungen über die Grundlagen und den Aufbau der Ethik ein geschlossenes und harmonisches Ganzes. Der Band geht zurück auf ein im Wintersemester 1876 niedergeschriebenes Manuskript, das Brentano 1894 als Kolleg an der Universität Wien vortrug.

Standard impossibility theorems on judgment aggregation over logically connected propositions either use a controversial systematicity condition or apply only to agendas of propositions with rich logical connections. Are there any serious impossibilities without these restrictions? We prove an impossibility theorem without requiring systematicity that applies to most standard agendas: Every judgment aggregation function (with rational inputs and outputs) satisfying a condition called unbiasedness is dictatorial (or effectively dictatorial if we remove one of the agenda conditions). Our agenda conditions are tight. (...) When applied illustratively to (strict) preference aggregation represented in our model, the result implies that every unbiased social welfare function with universal domain is effectively dictatorial. (shrink)

Den 1905 gefaßten Plan einer Gesamtdarstellung der Aristotelischen Lehre brachte Brentano nicht mehr zur Ausführung. Die hier erstmals veröffentlichten Vorarbeiten aus den Jahren 1908 bis 1911 für die Abhandlung »Aristoteles und seine Weltanschauung« bieten einen detaillierten Einblick in das Aristoteles-Bild des späten Brentano.

Zusammenfassung Der dargelegte Befund deutet darauf hin, daß es in Konstantinopel wie in Rom und anderen Provinzmetropolen zahlreiche Statuen hoher Beamter und Würdenträger gab. Allerdings fehlt ein entsprechender Befund für die Regierungszeit Konstantins d. Gr.; erst unter der Regierung Konstantius' II. lassen sich die ersten Beamtenstatuen feststellen. Das mag am Zufall der Überlieferung liegen, deckt sich aber immerhin damit, daß erst unter diesem Kaiser der Rahmen für eine breite magistratische Repräsentation gegeben war. Unter Konstantius II. wurde der Konstantinopler Senat zahlenmäßig (...) beträchtlich erweitert, zudem gleichberechtigt neben den römischen Senat gestellt, wurde das Amt des Stadtpräfekten eingeführt und, wie Paul Speck gezeigt hat, zugleich die Allpräsenz des Gründerkaisers Konstantin im Stadtbild relativiert, so daß überhaupt erst die Grundlagen für die öffentliche Repräsentation der Senatsaristokratie gegeben waren. Hatte Konstantin die nach ihm benannte Stadt zunächst als Residenzstadt errichtet, deren Bauten und Ausstattung ganz auf seine Person ausgerichtet waren, so schuf sein Sohn Konstantius die Voraussetzungen für die Entwicklung einer selbstbewußten Senatsaristokratie und einer entsprechenden Präsenz im Stadtbild. Die wenigen Indizien deuten darauf hin, daß sich die Statuen dieser Würdenträger, sofern es sich um senatorische Beamte handelte, beim Senat am Augusteion befanden. Stets dürfte es sich dabei um ‚einfache’ Statuen gehandelt haben, die allenfalls vergoldet waren, um bronzene Statuen oder um solche aus Marmor, die den Beamten in der Toga mit seinen Insignien zeigten. Seit dem fünften Jahrhundert läßt sich beobachten, daß eine kleine Gruppe einflußreicher Beamter und Heerführer entweder durch eine Vielzahl verschiedener Bildnisse an verschiedenen Orten oder aber durch die wesentlich aufwendigere Denkmalform eines Reiterstandbilds an prominenten Orten geehrt wird. Nie jedoch fand sich die Statue eines Nichtkaisers auf einem Ehrenbogen oder einer Säule, von denen es in Konstantinopel so viele gab. Diese blieben dem Kaiser und seiner Familie vorbehalten, der so im Denkmal den Abstand zu den aufwendigen Monumenten einflußreicher Personen wahren und auch erhöhen konnte. Doch beschränkte sich das kaiserliche Denkmal nicht nur auf einfache Ehrensäulen. Mehrfach sind Gruppen von Ehrensäulen überliefert, die städtebaulich an zentralen Stellen plaziert wurden. Zudem begegnet in der Spätantike zum erstenmal die Reiterstatue auf einem Säulenmonument, werden also zwei zunächst verschiedene Monumentformen miteinander verbunden (Abb. 7). Diese für die Spätantike typische Potenzierung der Wirkungsstrukturen und die Kombination bislang verschiedener Repräsentationsformen des imperialen Monuments ist wohl auch Folge des Konkurrenzdrucks durch allmächtige Militärs, die ihrerseits solche Selbstdarstellungsmodi aufgriffen. Die Kaiserdenkmäler bestimmen bis heute unser Bild von der Stadt Konstantinopel und lassen bisweilen vergessen, daß sie vor dem Hintergrund zahlreicher kleinerer Denkmäler hochrangiger Beamter errichtet wurden, unter denen einige so aufwendig waren, daß sie den Kaiser zum Aufgriff neuer, bislang noch nicht dagewesener Monumentformen zwangen. (shrink)

Assuming that votes are independent, the epistemically optimal procedure in a binary collective choice problem is known to be a weighted supermajority rule with weights given by personal log-likelihood-ratios. It is shown here that an analogous result holds in a much more general model. Firstly, the result follows from a more basic principle than expected-utility maximisation, namely from an axiom (Epistemic Monotonicity) which requires neither utilities nor prior probabilities of the ‘correctness’ of alternatives. Secondly, a person’s input need not be (...) a vote for an alternative, it may be any type of input, for instance a subjective degree of belief or probability of the correctness of one of the alternatives. The case of a profile of subjective degrees of belief is particularly appealing, since here no parameters such as competence parameters need to be known. (shrink)

There has been much discussion on the two-envelope paradox. Clark and Shackel (2000) have proposed a solution to the paradox, which has been refuted by Meacham and Weisberg (2003). Surprisingly, however, the literature still contains no axiomatic justification for the claim that one should be indifferent between the two envelopes before opening one of them. According to Meacham and Weisberg, "decision theory does not rank swapping against sticking [before opening any envelope]" (p. 686). To fill this gap in the literature, (...) we present a simple axiomatic justification for indifference, avoiding any expectation reasoning, which is often considered problematic in infinite cases. Although the two-envelope paradox assumes an expectation-maximizing agent, we show that analogous paradoxes arise for agents using different decision principles such as maximin and maximax, and that our justification for indifference before opening applies here too. (shrink)

New production concepts rely on the active (co-) shaping of planning, control and organisation processes on the shop floor level. Established CAPM technologies (CAPM =Computer Aided Production Management) only provide insufficient support, and a complete automation of the production management is not suited to close this gap. This is why new principles of system design have to be developed which meet various requirements: from taking into account a multidimensionality and contradiction of planning targets and the integration of learning opportunities with (...) the use of systems up to the promotion of work process knowledge. (shrink)

In this paper we are primarily concerned with political expertise, interest, and agreement as factors that might accelerate the flow of information between citizens. We examine dyadic exchanges of information as a function of two primary sets of factors: the characteristics of the citizens in the dyadic relationship and the characteristics of the larger network within which the dyad is located. Moreover, we compare political communication within dyads across several different national contexts: Germany, Japan, and the United States. We assume (...) that citizens are more likely to obtain information from people they trust, but why do they trust some individuals more than others? Is the frequency of communication predicated on shared political preferences? Or is it based on one citizen's assessment regarding the political expertise of another? The answers to these questions have important implications for whether social communication and social capital create added value in the collective deliberations of democratic politics. (shrink)

This article discusses the characteristics of analytic philosophy and the relationship between these characteristics and Whitehead’s philosophy. In particular,Whitehead’s metaphysical theory building is treated in relation to analytic philosophy and is seen as compatible with the tradition of analytic philosophy as it has developed in recent decades.