scholarly journals Proportional Belief Merging

2020 ◽  
Vol 34 (03) ◽  
pp. 2822-2829 ◽  
Author(s):  
Adrian Haret ◽  
Martin Lackner ◽  
Andreas Pfandler ◽  
Johannes P. Wallner
Keyword(s):  
Social Choice ◽  
Complexity Analysis ◽  
The Other ◽  
Belief Merging ◽  
Rationality Postulates

In this paper we introduce proportionality to belief merging. Belief merging is a framework for aggregating information presented in the form of propositional formulas, and it generalizes many aggregation models in social choice. In our analysis, two incompatible notions of proportionality emerge: one similar to standard notions of proportionality in social choice, the other more in tune with the logic-based merging setting. Since established merging operators meet neither of these proportionality requirements, we design new proportional belief merging operators. We analyze the proposed operators against established rationality postulates, finding that current approaches to proportionality from the field of social choice are, at their core, incompatible with standard rationality postulates in belief merging. We provide characterization results that explain the underlying conflict, and provide a complexity analysis of our novel operators.

scholarly journals Belief Merging Operators as Maximum Likelihood Estimators

2020 ◽  
Author(s):  
Patricia Everaere ◽  
Sebastien Konieczny ◽  
Pierre Marquis
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Noise Model ◽  
Belief Merging ◽  
The World ◽  
Natural Noise ◽  
True State ◽  
Merging Process ◽  
Rationality Postulates ◽  
Noise Models

We study how belief merging operators can be considered as maximum likelihood estimators, i.e., we assume that there exists a (unknown) true state of the world and that each agent participating in the merging process receives a noisy signal of it, characterized by a noise model. The objective is then to aggregate the agents' belief bases to make the best possible guess about the true state of the world. In this paper, some logical connections between the rationality postulates for belief merging (IC postulates) and simple conditions over the noise model under consideration are exhibited. These results provide a new justification for IC merging postulates. We also provide results for two specific natural noise models: the world swap noise and the atom swap noise, by identifying distance-based merging operators that are maximum likelihood estimators for these two noise models.

scholarly journals Belief Merging and Judgment Aggregation in Fuzzy Setting

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Ismat Beg ◽  
Nabeel Butt
Keyword(s):  
Fuzzy Logic ◽  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Judgment Aggregation ◽  
Belief Merging ◽  
Aggregation Functions ◽  
Fuzzy Aggregation ◽  
Doctrinal Paradox ◽  
Fuzzy Setting

We explore how judgment aggregation and belief merging in the framework of fuzzy logic can help resolve the “Doctrinal Paradox.” We also illustrate the use of fuzzy aggregation functions in social choice theory.

Social choice theory, belief merging, and strategy-proofness

2006 ◽  
Vol 7 (1) ◽  
pp. 61-79 ◽  
Author(s):  
Samir Chopra ◽  
Aditya Ghose ◽  
Thomas Meyer
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Belief Merging ◽  
Strategy Proofness

scholarly journals Consolidation via Tacit Culpability Measures: Between Explicit and Implicit Degrees of Culpability

2021 ◽  
Author(s):  
Jandson S. Ribeiro ◽  
Matthias Thimm
Keyword(s):  
Fixed Point ◽  
Knowledge Base ◽  
Special Class ◽  
Belief Change ◽  
Minimal Change ◽  
The Other ◽  
Preference Relations ◽  
Other Hand ◽  
The One ◽  
Rationality Postulates

Restoring consistency of a knowledge base, known as consolidation, should preserve as much information as possible of the original knowledge base. On the one hand, the field of belief change captures this principle of minimal change via rationality postulates. On the other hand, within the field of inconsistency measurement, culpability measures have been developed to assess how much a formula participates in making a knowledge base inconsistent. We look at culpability measures as a tool to disclose epistemic preference relations and build rational consolidation functions. We introduce tacit culpability measures that consider semantic counterparts between conflicting formulae, and we define a special class of these culpability measures based on a fixed-point characterisation: the stable tacit culpability measures. We show that the stable tacit culpability measures yield rational consolidation functions and that these are also the only culpability measures that yield rational consolidation functions.

The Jenkins Commission and the Implications of Electoral Reform for the UK Constitution

1999 ◽  
Vol 34 (2) ◽  
pp. 143-160 ◽  
Author(s):  
Iain McLean
Keyword(s):  
Social Choice ◽  
Democratic Theory ◽  
Electoral Systems ◽  
Electoral System ◽  
Electoral Reform ◽  
The Other ◽  
Choice Sets ◽  
The Uk

THERE ARE TWO MAIN CONCEPTIONS OF ‘REPRESENTATION’ IN democratic theory, and they are not wholly compatible. All democratic electoral systems implicitly appeal to one or the other conception of representation. Therefore, the nature of an ideal electoral system is an essentially contested question. Furthermore, the mathematics of social choice sets severe limits on what an electoral system — any electoral system — can achieve. Though the implications of social choice are not so nihilistic as some would have us believe, they are relevant and serious.

scholarly journals Joint desirability foundations of social choice and opinion pooling

2021 ◽  
Author(s):  
Arianna Casanova ◽  
Enrique Miranda ◽  
Marco Zaffalon
Keyword(s):  
Social Choice ◽  
Sufficient Conditions ◽  
The Other ◽  
Incomplete Preferences ◽  
Inherent Limitation ◽  
Uncertainty Model ◽  
The Status ◽  
Opinion Pooling ◽  
New Perspective ◽  
The One

AbstractWe develop joint foundations for the fields of social choice and opinion pooling using coherent sets of desirable gambles, a general uncertainty model that allows to encompass both complete and incomplete preferences. This leads on the one hand to a new perspective of traditional results of social choice (in particular Arrow’s theorem as well as sufficient conditions for the existence of an oligarchy and democracy) and on the other hand to using the same framework to analyse opinion pooling. In particular, we argue that weak Pareto (unanimity) should be given the status of a rationality requirement and use this to discuss the aggregation of experts’ opinions based on probability and (state-independent) utility, showing some inherent limitation of this framework, with implications for statistics. The connection between our results and earlier work in the literature is also discussed.

scholarly journals Algorithmic Information Distortions in Node-Aligned and Node-Unaligned Multidimensional Networks

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 835
Author(s):  
Felipe S. Abrahão ◽  
Klaus Wehmuth ◽  
Hector Zenil ◽  
Artur Ziviani
Keyword(s):  
Extra Dimensions ◽  
Complexity Analysis ◽  
The Other ◽  
Multidimensional Space ◽  
Case Scenario ◽  
Logarithmic Order ◽  
Algorithmic Information Theory ◽  
Worst Case ◽  
Algorithmic Information ◽  
Uniform Case

In this article, we investigate limitations of importing methods based on algorithmic information theory from monoplex networks into multidimensional networks (such as multilayer networks) that have a large number of extra dimensions (i.e., aspects). In the worst-case scenario, it has been previously shown that node-aligned multidimensional networks with non-uniform multidimensional spaces can display exponentially larger algorithmic information (or lossless compressibility) distortions with respect to their isomorphic monoplex networks, so that these distortions grow at least linearly with the number of extra dimensions. In the present article, we demonstrate that node-unaligned multidimensional networks, either with uniform or non-uniform multidimensional spaces, can also display exponentially larger algorithmic information distortions with respect to their isomorphic monoplex networks. However, unlike the node-aligned non-uniform case studied in previous work, these distortions in the node-unaligned case grow at least exponentially with the number of extra dimensions. On the other hand, for node-aligned multidimensional networks with uniform multidimensional spaces, we demonstrate that any distortion can only grow up to a logarithmic order of the number of extra dimensions. Thus, these results establish that isomorphisms between finite multidimensional networks and finite monoplex networks do not preserve algorithmic information in general and highlight that the algorithmic information of the multidimensional space itself needs to be taken into account in multidimensional network complexity analysis.

scholarly journals Impossibility in Belief Merging (Extended Abstract)

2018 ◽  
Author(s):  
Amilcar Mata Diaz ◽  
Ramon Pino Perez
Keyword(s):  
Social Choice ◽  
Propositional Logic ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Impossibility Theorem ◽  
General Version ◽  
Representation Theorems ◽  
Belief Merging ◽  
Epistemic States ◽  
Standard Domain

With the aim of studying social properties of belief merging and having a better understanding of impossibility, we extend in three ways the framework of logic-based merging introduced by Konieczny and Pino Perez. First, at the level of representation of the information, we pass from belief bases to complex epistemic states. Second, the profiles are represented as functions of finite societies to the set of epistemic states (a sort of vectors) and not as multisets of epistemic states. Third, we extend the set of rational postulates in order to consider the epistemic versions of the classical postulates of social choice theory: standard domain, Pareto property, independence of irrelevant alternatives and absence of dictator. These epistemic versions of social postulates are given, essentially, in terms of the finite propositional logic. We state some representation theorems for these operators. These extensions and representation theorems allow us to establish an epistemic and very general version of Arrow's impossibility theorem. One of the interesting features of our result, is that it holds for different representations of epistemic states; for instance conditionals, ordinal conditional functions and, of course, total preorders.

scholarly journals Voting method based on approval voting and arithmetic mean

2020 ◽  
Vol 9 (1) ◽  
pp. 1
Author(s):  
Zoïnabo Savadogo ◽  
Blaise Somé
Keyword(s):  
Decision Making ◽  
Social Choice ◽  
Vital Role ◽  
Arithmetic Mean ◽  
The Other ◽  
New Method ◽  
Approval Voting ◽  
Voting Methods ◽  
General Opinion ◽  
Voting Method

Voting plays a vital role in any society. Indeed the votes involve decision making especially and the more in the decision of group. Thanks to the opinions expressed by a group of people, an opinion representing the preference of the group is determined. But most often some voting methods seem to distance the result from a vote of the general opinion. The study of voting methods is based on the theory of social choice. For several years, in the literature on the theory of social choice, many theorists have contributed trying to find a representative voting method.It seems that there is no totally satisfactory way of voting.Thus we have tried, through this article, to design a voting method based on approval voting and the arithmetic mean that leads to goodcompromise results.In contrast to the other methods, the new method takes into account the choice of each voter and allows to obtain a result which represents the choice of the majority of the voters.

scholarly journals Set and revealed preference axioms for multi-valued choice

2020 ◽  
Author(s):  
Hans Peters ◽  
Panos Protopapas
Keyword(s):  
Social Choice ◽  
Preference Relation ◽  
Revealed Preference ◽  
The Other ◽  
Social Choice Correspondence ◽  
Other Hand ◽  
Independence Of Irrelevant Alternatives ◽  
Choice Correspondence ◽  
Infinite Set ◽  
Weak Axiom

Abstract We consider choice correspondences that assign a subset to every choice set of alternatives, where the total set of alternatives is an arbitrary finite or infinite set. We focus on the relations between several extensions of the condition of independence of irrelevant alternatives on one hand, and conditions on the revealed preference relation on sets, notably the weak axiom of revealed preference, on the other hand. We also establish the connection between the condition of independence of irrelevant alternatives and so-called strong sets; the latter characterize a social choice correspondence satisfying independence of irrelevant alternatives.

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