Judgment aggregation by quota rules

It is known that majority voting among several individuals on logically interconnected propositions may generate 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 some (proposition-specific) threshold. After characterizing quota rules, we prove necessary and sufficient conditions under which their outcomes satisfy various rationality conditions. We also consider sequential quota rules, which adjudicate propositions sequentially, letting earlier judgments constrain later ones. While ensuring rationality, sequential rules may be path-dependent. We characterize path-independence and prove its equivalence to strategy- proofness under mild conditions. Our results generalize earlier (im)possibility theorems.Judgment aggregation, quota rules, collective rationality, path-dependence, strategy-proofness, formal logic

Aggregation and the relevance of some issues for others

A general collective decision problem is analysed. It consists in many issues that are interconnected in two ways: by mutual constraints and by connections of relevance. The goal is to decide on the issues by respecting the mutual constraints and by aggregating in accordance with an informational constraint given by the relevance connections. Whether this is possible in a non-degenerate way depends on both types of connections and their interplay. One result, if applied to the preference aggregation problem and adopting Arrow''s notion of (ir)relevance, gives Arrow''s Theorem, without excluding indifferences unlike in the existing general aggregation literature.mathematical economics;

A non-proposition-wise variant of majority voting for aggregating judgments

Majority voting is commonly used in aggregating judgments. The literature to date on judgment aggregation (JA) has focused primarily on proposition-wise majority voting (PMV). Given a set of issues on which a group is trying to make collective judgments, PMV aggregates individual judgments issue by issue, and satisfies a salient property of JA rules—independence. This paper introduces a variant of majority voting called holistic majority voting (HMV). This new variant also meets the condition of independence. However, instead of aggregating judgments issue by issue, it aggregates individual judgments en bloc. A salient and straightforward feature of HMV is that it guarantees the logical consistency of the propositions expressing collective judgments, provided that the individual points of view are consistent. This feature contrasts with the known inability of PMV to guarantee the consistency of the collective outcome. Analogously, while PMV may present a set of judgments that have been rejected by everyone in the group as collectively accepted, the collective judgments returned by HMV have been accepted by a majority of individuals in the group and, therefore, rejected by a minority of them at most. In addition, HMV satisfies a large set of appealing properties, as PMV also does. However, HMV may not return any complete proposition expressing the judgments of the group on all the issues at stake, even in cases where PMV does. Moreover, demanding completeness from HMV leads to impossibility results similar to the known impossibilities on PMV and on proposition-wise JA rules in genera

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;

Uncertainty Analysis of the Adequacy Assessment Model of a Distributed Generation System

Due to the inherent aleatory uncertainties in renewable generators, the reliability/adequacy assessments of distributed generation (DG) systems have been particularly focused on the probabilistic modeling of random behaviors, given sufficient informative data. However, another type of uncertainty (epistemic uncertainty) must be accounted for in the modeling, due to incomplete knowledge of the phenomena and imprecise evaluation of the related characteristic parameters. In circumstances of few informative data, this type of uncertainty calls for alternative methods of representation, propagation, analysis and interpretation. In this study, we make a first attempt to identify, model, and jointly propagate aleatory and epistemic uncertainties in the context of DG systems modeling for adequacy assessment. Probability and possibility distributions are used to model the aleatory and epistemic uncertainties, respectively. Evidence theory is used to incorporate the two uncertainties under a single framework. Based on the plausibility and belief functions of evidence theory, the hybrid propagation approach is introduced. A demonstration is given on a DG system adapted from the IEEE 34 nodes distribution test feeder. Compared to the pure probabilistic approach, it is shown that the hybrid propagation is capable of explicitly expressing the imprecision in the knowledge on the DG parameters into the final adequacy values assessed. It also effectively captures the growth of uncertainties with higher DG penetration levels

Computerized Classification Testing and Its Relationship to the Testing Goal

Assessment can serve different goals. If the aim of testing is to classify respondents into one of multiple levels instead of obtaining a precise estimate of the respondent’s ability, computerized classification testing can be used. This type of testing requires algorithms for item selection and making the classification decision. The result of the test administration is provided in a report about the decision with sometimes additional feedback. The design of all these components of the test should be in line with the testing goal. Several goals have been defined for assessment which make a judgment about: pupils, the learning process, groups of students and schools, and the quality of education. The possibilities for use of computerized classification testing for different testing goals are investigated in the current pape

The possibility of judgment aggregation for network agendas

Within social choice theory, the new field of judgment aggregation aims at reaching collective judgments on a set of logically interconnected propositions. I investigate decision problems, in which the agenda is a network, composed of atomic propositions and connection rules between them. Networks can represent various realistic decision problems, including most concrete examples given in the literature. Nevertheless, networks are unexplored so far due to problems when modelling connection rules in standard propositional logic. By extending the logic, I prove that, for any network, decision rules satisfying the common conditions always exist, in contrast to the literature's emphasis on impossibilities. I also characterise the class of such decision rules, and propose a simple way to select a decision rule.judgment aggregation, collective inconsistency, possibility theorems, network, connection rule, formal logic, material conditional, subjunctive conditional

Green visions and democratic constraints: the possibility and design of democratic institutions for environmental decision-making

This thesis addresses a recurrent question of our time – whether democracy can secure environmental sustainability – by drawing on literatures in the normative theory of democracy, social choice theory and environmental politics. I propose a basic, yet substantial organising principle, the ‘dilemma of green democracy’, which maps out the possibility of realising green outcomes under democratic constraints. Interdisciplinary ideas from neighbouring disciplines are also imported for the purpose of studying the design of good environmental-democratic institutions. The analytical framework is an integrated one, comprising formal choice theory and normative democratic theory. The first part of the thesis focuses on the possibility of environmentaldemocratic institutions. Chapter 1 introduces the dilemma of green democracy – a conflict between three plausible desiderata for environmental democracy – and suggests several proposals for avoiding the dilemma. It concludes that, as long as the dilemma is resolved, it is logically possible to construct environmental-democratic institutions. Chapters 2, 3 and 4 assess the desirability of the different proposals in terms of procedure and outcome. The general conclusion is that whether these proposals are desirable depends on a number of conditions and/or contextual factors. The second part of the thesis examines the substantive issues in designing environmental-democratic institutions. Chapter 5 discusses how the discursive dilemma in social choice theory and the normative ends of deliberation constrain the inputs of such institutions. Chapter 6 demonstrates how the concept of distributed cognition, drawn from cognitive/computer science, reconciles the tension between technocracy and democracy. Chapter 7 suggests how the theory of cognitive dissonance, drawn from psychology, challenges the epistemic performance of practicable (environmental-) deliberative-democratic institutions. The overall conclusion is two-fold. First, democracy can, at least in principle, secure environmental sustainability, provided that the dilemma of green democracy is resolved. Second, interdisciplinary ideas are useful for designing good democratic institutions for collective environmental decision-making. This conclusion has implications not only for intellectual enquiry, but also for institutional design in practice

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