scholarly journals The median rule in judgement aggregation

2021 ◽  
Author(s):  
Klaus Nehring ◽  
Marcus Pivato
Keyword(s):  
Average Distance ◽  
Aggregation Rule ◽  
Preference Aggregation ◽  
Regularity Conditions ◽  
Judgement Aggregation ◽  
Input And Output ◽  
Median Rule ◽  
Special Case

AbstractA judgement aggregation rule takes the views of a collection of voters over a set of interconnected issues and yields a logically consistent collective view. The median rule is a judgement aggregation rule that selects the logically consistent view which minimizes the average distance to the views of the voters (where the “distance” between two views is the number of issues on which they disagree). In the special case of preference aggregation, this is called the Kemeny rule. We show that, under appropriate regularity conditions, the median rule is the unique judgement aggregation rule which satisfies three axioms: Ensemble Supermajority Efficiency, Reinforcement, and Continuity. Our analysis covers aggregation problems in which the consistency restrictions on input and output judgements may differ. We also allow for issues to be weighted, and provide numerous examples in which issue weights arise naturally.

scholarly journals Data integration with high dimensionality

Biometrika ◽  
2017 ◽  
Vol 104 (2) ◽  
pp. 251-272 ◽  
Author(s):  
Xin Gao ◽  
Raymond J. Carroll
Keyword(s):  
Data Integration ◽  
Information Criterion ◽  
Regularity Conditions ◽  
Continuous Variables ◽  
Penalty Term ◽  
Marginal Likelihoods ◽  
Physical Measurements ◽  
Data Source ◽  
Model Size ◽  
Special Case

Summary We consider situations where the data consist of a number of responses for each individual, which may include a mix of discrete and continuous variables. The data also include a class of predictors, where the same predictor may have different physical measurements across different experiments depending on how the predictor is measured. The goal is to select which predictors affect any of the responses, where the number of such informative predictors tends to infinity as the sample size increases. There are marginal likelihoods for each experiment; we specify a pseudolikelihood combining the marginal likelihoods, and propose a pseudolikelihood information criterion. Under regularity conditions, we establish selection consistency for this criterion with unbounded true model size. The proposed method includes a Bayesian information criterion with appropriate penalty term as a special case. Simulations indicate that data integration can dramatically improve upon using only one data source.

scholarly journals Neutrality and relative acceptability in judgment aggregation

2019 ◽  
Vol 55 (1) ◽  
pp. 25-49
Author(s):  
Zoi Terzopoulou ◽  
Ulle Endriss
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Practical Interest ◽  
Judgment Aggregation ◽  
Aggregation Rule ◽  
Impossibility Theorem ◽  
Collective Acceptance ◽  
Special Case

AbstractOne of the fundamental normative principles in social choice theory is that of neutrality. In the context of judgment aggregation, neutrality is encoded in the form of an axiom expressing that, when two possible judgments enjoy the same support amongst the individuals, then either both or neither of them should be accepted. This is a reasonable requirement in many scenarios. However, we argue that for scenarios in which individuals are asked to pass judgment on very diverse kinds of propositions, a notion of relative acceptability is better suited. We capture this notion by a new axiom that hinges on a binary “acceptability” relation A between propositions: if a given coalition accepting a proposition p entails the collective acceptance of p, then the same should be true for every other proposition q related to p via A. Intuitively, pAq means that p is at least as acceptable as q. Classical neutrality is then a special case where all propositions are equally acceptable. We show that our new axiom allows us to circumvent a classical impossibility theorem in judgment aggregation for certain scenarios of practical interest. Also, we offer a precise characterisation of all scenarios that are safe, in the sense that any aggregation rule respecting the relative acceptability between propositions will always return logically consistent outcomes.

Spreadsheets based on interval constraint satisfaction

1994 ◽  
Vol 8 (1) ◽  
pp. 27-34 ◽  
Author(s):  
Eero Hyvönen
Keyword(s):  
Problem Solving ◽  
Constraint Satisfaction ◽  
Trial And Error ◽  
Top Down ◽  
Typical Situation ◽  
Input And Output ◽  
Inexact Data ◽  
Computational Paradigm ◽  
Special Case ◽  
Interval Constraint

AbstractSpreadsheets are difficult to use in applications, where only incomplete or inexact data (e.g., intervals) are available-a typical situation in various design and planning tasks. It can be argued that this is due to two fundamental shortcomings of the computational paradigm underlying spreadsheets. First, the distinction between input and output cells has to be fixed before computations. Second, cells may have only exact values. As a result, spread-sheets support the user only with primitive iterative problem solving schemes based on trial-and-error methods. A constraint-based computational paradigm for next generation interval spreadsheets is presented. The scheme makes it possible to exploit incomplete/inexact data (intervals), and it can support problem solving in a top-down fashion. Current spreadsheets constitute a special case of the more general interval constraint spreadsheets proposed.

Displacement Analysis of the Generalized Clemens Coupling, The R-R-S-R-R Spatial Linkage

1975 ◽  
Vol 97 (2) ◽  
pp. 575-580 ◽  
Author(s):  
D. M. Wallace ◽  
F. Freudenstein
Keyword(s):  
Fourth Order ◽  
Constant Velocity ◽  
Degrees Of Freedom ◽  
Input Output ◽  
Closed Form Solutions ◽  
Input And Output ◽  
Order Polynomial ◽  
Special Case ◽  
Output Equation ◽  
Fourth Order Polynomial

The Clemens Coupling is a constant-velocity, universal-type joint for nonparallel intersecting shafts. This mechanism is a spatial linkage with five links connected by four revolute pairs, R, and one spherical pair (ball-and-socket joint), S, which is located symmetrically with respect to the input and output shafts. The Clemens Coupling is a special case of the R-R-S-R-R spatial linkage with general proportions, which will, therefore, be called the Generalized Clemens Coupling. This paper gives the algebraic derivation of the input-output equation for the general R-R-S-R-R linkage and demonstrates that it is a fourth-order polynomial in the half tangents of the crank angles. The effect of housing-error tolerances on the displacements of the Clemens Coupling has also been considered. The results demonstrate feasibility of closed-form solutions for five-link mechanisms with kinematic pairs having more than two degrees of freedom.

From Paired Comparisons and Cycles to Arrow’s Theorem

2019 ◽  
pp. 62-84
Author(s):  
Donald G. Saari
Keyword(s):  
Democratic Theory ◽  
Impossibility Result ◽  
Preference Aggregation ◽  
Pairwise Comparisons ◽  
Paired Comparisons ◽  
Arrow’S Theorem ◽  
Generic Type ◽  
Arrow's Theorem ◽  
Special Case

What makes paired comparisons so easy to accept is that they arise everywhere, and an appealing aspect of this approach is that it directly compares the merits of two opponents. However, paired comparisons can generate a wide array of difficulties that can lead to what appear to be paradoxes. Preference aggregation based solely on pairwise comparisons is at the heart of Arrow’s theorem. This chapter indicates that the Arrow impossibility result is a special case of a more generic type of problem involving parts and whole, and it offers an interpretation of it that shows that it does not have the implications for democratic theory that it is commonly assumed to have.

The Displacement Analysis of the Generalized Tracta Coupling

1970 ◽  
Vol 37 (3) ◽  
pp. 713-719 ◽  
Author(s):  
D. M. Wallace ◽  
F. Freudenstein
Keyword(s):  
Constant Velocity ◽  
General Mechanism ◽  
Universal Joint ◽  
Displacement Analysis ◽  
Spatial Mechanism ◽  
Input And Output ◽  
Previous Solution ◽  
The Subject ◽  
Algebraic Solutions ◽  
Special Case

The displacement analysis of spatial linkages has been the subject of a number of recent investigations, using a variety of mathematical approaches. Algebraic solutions have been developed principally, in cases in which the number of links, n, is less than or equal to 4. When n > 4, the complexity of the displacement analysis appears to increase by one or more orders of magnitude. In this paper we describe a method, which we call the geometric-configuration method, which we have used when n > 4. The method is illustrated with respect to the algebraic displacement analysis of a five-link spatial mechanism, which includes the Tracta joint as a special case. The Tracta joint is a spatial linkage of symmetrical proportions functioning as a constant-velocity universal joint for nonparallel, intersecting shafts (Myard, 1933). It has four turning or revolute pairs (R) and one plane pair (E), which is located symmetrically with respect to the input and output shafts. The generalization of this linkage, which we call the generalized Tracta coupling, is the R-R-E-R-R spatial linkage with general proportions. The displacement analysis of the general mechanism, for which we know of no previous solution, has been derived. An analysis of the effect of tolerances in the Tracta joint has been included.

scholarly journals On a Theorem due to Alan D. Taylor about Aggregation of Preferences

2018 ◽  
Vol 18 (1) ◽  
pp. 17-31 ◽  
Author(s):  
Somdeb Lahiri
Keyword(s):  
Social Welfare ◽  
Individual Preference ◽  
Utility Functions ◽  
Aggregation Rule ◽  
Impossibility Theorem ◽  
Preference Aggregation ◽  
Individual Utility ◽  
Domain Restriction ◽  
Aggregation Of Preferences ◽  
Pareto Criterion

In this paper, we show that there does not exist any triple acyclic preference aggregation rule that satisfies Majority property, weak Pareto criterion and a version of a property due to Alan Taylor. We also show that there are non-dictatorial preference aggregation rules and in particular non-dictatorial social welfare functions which satisfy the weak Pareto criterion and Taylor’s Independence of Irrelevant Alternatives. Further, we are able to obtain analogous results for preference aggregation functionals by suitably adjusting the desired properties to fit into a framework which uses individual utility functions rather than individual preference orderings. Our final result is a modest generalisation of Sen’s version of Arrow’s impossibility theorem which is shown to hold under our mild domain restriction. JEL: D71

An Analytical Method for Synthesizing the Four-Bar Crank-Rocker Mechanism

1969 ◽  
Vol 91 (1) ◽  
pp. 45-54 ◽  
Author(s):  
F. Y. Chen
Keyword(s):  
Optimal Design ◽  
Analytical Method ◽  
Algebraic Method ◽  
Design Criterion ◽  
Output Link ◽  
Input And Output ◽  
Special Case ◽  
Crank Mechanism

An algebraic method is presented for synthesizing the four-bar crank-rocker mechanisms in general, with the offset slider-crank mechanism as a special case, for coordinating the prescribed input and output link extreme positions. Solutions to the equations of constraint are derived for different cases. Among a large number of the available solutions, an optimal design is governed by a given parameter which is determined based on a design criterion. Numerous examples are provided.

FUZZY VOTERS, CRISP VOTES

2007 ◽  
Vol 09 (01) ◽  
pp. 67-86 ◽  
Author(s):  
PAULO P. CÔRTE-REAL
Keyword(s):  
The Other ◽  
Aggregation Rule ◽  
Preference Aggregation ◽  
Binary Choice ◽  
Preference Structure ◽  
Fuzzy Preferences ◽  
Potential Gain ◽  
Strategy Proofness ◽  
Selection Of ◽  
Fuzzy Preference

In a binary choice voting scenario, voters may have fuzzy preferences but are required to make crisp choices. In order to compare a crisp voting procedure with more general mechanisms of fuzzy preference aggregation, we first focus on the latter. We present a formulation of strategy-proofness in this setting and study its consequences. On one hand, we achieve an axiomatic recommendation of the median as the aggregation rule for fuzzy preferences. On the other hand, we present conditions under which strategic concerns imply the optimality of a crisp voting procedure and argue that there is a potential gain in the integration of the preference and choice aggregation programs — namely that an underlying fuzzy preference structure may also help inform the selection of a choice aggregation rule.

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