Modelling dependence in simple and indirect majority systems

1989 ◽  
Vol 26 (1) ◽  
pp. 81-88 ◽  
Author(s):  
Philip J. Boland ◽  
Frank Proschan ◽  
Y. L. Tong
Keyword(s):  
Decision Theory ◽  
Majority Rule ◽  
Reliability Theory ◽  
Correct Decision ◽  
Coherent Systems ◽  
Monotonicity Results ◽  
Do So

Majority systems are encountered in both decision theory and reliability theory. In decision theory for example a jury or committee employing a majority rule will make the ‘correct' decision if a majority of the individuals do so. In reliability theory some coherent systems function if and only if a majority of the components work properly. In this paper results concerning the reliability of majority systems are developed which are applicable in both areas. Two models incorporating dependence between individuals or components in majority systems are introduced, and various monotonicity results for their reliability functions are established. Comparisons are also made between direct (or simple) and indirect majority systems.

Modelling dependence in simple and indirect majority systems

1989 ◽  
Vol 26 (01) ◽  
pp. 81-88 ◽  
Author(s):  
Philip J. Boland ◽  
Frank Proschan ◽  
Y. L. Tong
Keyword(s):  
Decision Theory ◽  
Majority Rule ◽  
Reliability Theory ◽  
Correct Decision ◽  
Coherent Systems ◽  
Monotonicity Results ◽  
Do So

Majority systems are encountered in both decision theory and reliability theory. In decision theory for example a jury or committee employing a majority rule will make the ‘correct' decision if a majority of the individuals do so. In reliability theory some coherent systems function if and only if a majority of the components work properly. In this paper results concerning the reliability of majority systems are developed which are applicable in both areas. Two models incorporating dependence between individuals or components in majority systems are introduced, and various monotonicity results for their reliability functions are established. Comparisons are also made between direct (or simple) and indirect majority systems.

Formal Decision Theory and Majority Rule

Ethics ◽  
1982 ◽  
Vol 92 (2) ◽  
pp. 199-206 ◽  
Author(s):  
Glen O. Allen
Keyword(s):  
Decision Theory ◽  
Majority Rule

When Do Conflicting Parties Share Political Power?

2015 ◽  
Vol 2 (2) ◽  
pp. 139-151 ◽  
Author(s):  
Marco Battaglini ◽  
Lydia Mechtenberg
Keyword(s):  
Majority Rule ◽  
Political Power ◽  
Small Extent ◽  
Simple Majority ◽  
Proportional Rule ◽  
Simple Majority Rule ◽  
Electoral Outcome ◽  
Costly Punishment ◽  
Voting Rule ◽  
Do So

AbstractWe conduct a laboratory experiment to study the incentives of a privileged group (the “yellows”) to share political power with another group (the “blues”). The yellows collectively choose the voting rule for a general election: a simple-majority rule that favors them, or a proportional rule. In two treatments, the blues can use a costly punishment option. We find that the yellows share power voluntarily only to a small extent, but they are more inclined to do so under the threat of punishment, despite the fact that punishments are not sub-game perfect. The blue group conditions punishments both on the voting rule and the electoral outcome.

Theories of Majority Rule

1932 ◽  
Vol 26 (3) ◽  
pp. 452-469 ◽  
Author(s):  
John Gilbert Heinberg
Keyword(s):  
Canon Law ◽  
Majority Rule ◽  
Greek City ◽  
External Resources ◽  
The People ◽  
Long Run ◽  
The Rich ◽  
City States ◽  
The Right ◽  
Do So

The term “majority rule” is as impossible to escape as it is apparently difficult to define with precision. Aristotle generally employed it to designate the conduct of government by the poor citizens, who were more numerous than the rich, in the Greek city states. In canon law, it meant the verdict of the maior and sanior pars of a small group. Frederic Harrison wrote about the “rule” of the “effective majority”—that section of any community or social aggregate, which, for the matter in hand, practically outweighs the remainder. He explains that it may do so “by virtue of its preponderance in numbers, or in influence, or in force of conviction, or in external resources, or in many other ways.” Sir George Cornewall Lewis thought that where the ultimate decision is vested in a body there is no alternative other than to count numbers, and to abide by the opinion of a majority. But in alleging that “no historian, in discussing the justice or propriety of any decision of a legislative body, or of a court of justice, thinks of defending the decision of the majority by saying that it was the decision of the majority,” he did not anticipate the view of the English historian Hearnshaw. According to the latter, “The faith of a democrat requires him to believe that in the long run the majority of the people finds its way to the truth, and that in the long run it tries to do the right.”

Comment on Formal Decision Theory and Majority Rule

Ethics ◽  
1982 ◽  
Vol 92 (2) ◽  
pp. 207-210
Author(s):  
Russell Hardin
Keyword(s):  
Decision Theory ◽  
Majority Rule

Warnings and Expert Opinions An Evaluation Methodology based on Fuzzy Probabilities

1992 ◽  
Vol 36 (13) ◽  
pp. 940-944
Author(s):  
John G. Kreifeldt
Keyword(s):  
Decision Theory ◽  
High Probability ◽  
Good Practice ◽  
Reliability Theory ◽  
Evaluation Methodology ◽  
Voluntary Standards ◽  
Expert Opinions ◽  
Standards And Guidelines ◽  
Low Probability ◽  
Fuzzy Probabilities

A number of mandated and voluntary standards and guidelines expressed as good practice have been set out for the design of warnings. However, the question always arises as to whether or not a given warning will accomplish (or would have accomplished) its purpose of preventing injury whether or not it follows such guidelines. The answer to this question must be phrased in probabilities and sometimes only in qualitative form such as “low probability”, “high probability”, “more probable than not”, etc. In order to obtain such answers, experts are often consulted for their opinions. A methodology is presented which can be used as a basis for checking the consistency of the final conclusions or opinions using the concept of “fuzzy probabilities” and conceptually simple computations. The methodology is also of use to the expert in formulating his opinion rationally and deducing its implications clearly. This methodology is presented here in the context of the opined probability of effectiveness of warnings and instructions although it may be used in any context in which the total proposition can be phrased as a set of interrelated sub propositions as is common in reliability theory, decision theory, etc.

Cargo Mechanics (Application of Seakeeping--Revisited)

1986 ◽  
Vol 23 (03) ◽  
pp. 230-241
Author(s):  
Bruce L. Hutchison
Keyword(s):  
Risk Analysis ◽  
Decision Theory ◽  
Reliability Theory ◽  
Ship Motions ◽  
Basic Concepts

The basic concepts of modern risk and reliability theory are reviewed. Application of these concepts to topics arising in the analysis of ship motions, cargo sea-fastening design and voyage risk studies is explored. The role of risk analysis in decision theory is briefly discussed and the paper concludes with a suggested program of analysis for marine activities and enterprises subject to sea-action induced risk.

More on optimal allocation of components in coherent systems

1996 ◽  
Vol 33 (02) ◽  
pp. 548-556 ◽  
Author(s):  
Fan C. Meng
Keyword(s):  
System Reliability ◽  
Binary Systems ◽  
Optimal Allocation ◽  
Reliability Theory ◽  
Parallel System ◽  
System Level ◽  
Coherent Systems ◽  
Component Level ◽  
Multistate Systems ◽  
Permutation Equivalent

More applications of the principle for interchanging components due to Boland et al. (1989) in reliability theory are presented. In the context of active redundancy improvement we show that if two nodes are permutation equivalent then allocating a redundancy component to the weaker position always results in a larger increase in system reliability, which generalizes a previous result due to Boland et al. (1992). In the case of standby redundancy enhancement, we prove that a series (parallel) system is the only system for which standby redundancy at the component level is always more (less) effective than at the system level. Finally, the principle for interchanging components is extended from binary systems to the more complicated multistate systems.

scholarly journals Hazard rate ordering of order statistics and systems

2006 ◽  
Vol 43 (02) ◽  
pp. 391-408 ◽  
Author(s):  
Jorge Navarro ◽  
Moshe Shaked
Keyword(s):  
Order Statistics ◽  
Random Vector ◽  
Hazard Rate ◽  
Rate Function ◽  
Reliability Theory ◽  
Hazard Rate Function ◽  
Coherent Systems ◽  
Hazard Rate Order ◽  
Limiting Behaviour ◽  
Hazard Rate Ordering

LetX= (X1,X2, …,Xn) be an exchangeable random vector, and writeX(1:i)= min{X1,X2, …,Xi}, 1 ≤i≤n. In this paper we obtain conditions under whichX(1:i)decreases iniin the hazard rate order. A result involving more general (that is, not necessarily exchangeable) random vectors is also derived. These results are applied to obtain the limiting behaviour of the hazard rate function of the lifetimes of various coherent systems in reliability theory. The notions of the Samaniego signatures and the minimal signatures of such systems are extensively used in the paper. An interesting relationship between these two signatures is obtained. The results are illustrated in a series of examples.

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