Weighted voting systems: reliability versus rapidity
The weighted voting system (WVS) consists of n units that each provide a binary decision (0 or 1) or abstain from voting. Each unit has its own individual weight. System output is 1 if the cumulative weight of all 1-opting units is at least a pre-specified fraction τ of the cumulative weight of all...
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| Published in | Reliability engineering & system safety Vol. 89; no. 2; pp. 177 - 184 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Elsevier Ltd
01.08.2005
Elsevier |
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| Online Access | Get full text |
| ISSN | 0951-8320 1879-0836 |
| DOI | 10.1016/j.ress.2004.08.017 |
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| Abstract | The weighted voting system (WVS) consists of
n units that each provide a binary decision (0 or 1) or abstain from voting. Each unit has its own individual weight. System output is 1 if the cumulative weight of all 1-opting units is at least a pre-specified fraction
τ of the cumulative weight of all non-abstaining units. Otherwise, system output is 0. The system input is either 0 or 1. Every unit is characterized by probability of making decisions 0 and 1 and by probability of abstaining for each input. The system fails if its output is not equal to its input.
This paper shows that if the WVS consists of units that need different time to produce their outputs, the decision time of the entire system depends on the distribution of unit weights and on the value of
τ. It shows also that a tradeoff exists between the system reliability and its rapidity.
An algorithm that finds the system parameters maximizing its reliability under constraint imposed on the expected system decision time is suggested. Illustrative examples are presented. |
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| AbstractList | The weighted voting system (WVS) consists of n units that each provide a binary decision (0 or 1) or abstain from voting. Each unit has its own individual weight. System output is 1 if the cumulative weight of all 1-opting units is at least a pre-specified fraction tau of the cumulative weight of all non-abstaining units. Otherwise, system output is 0. The system input is either 0 or 1. Every unit is characterized by probability of making decisions 0 and 1 and by probability of abstaining for each input. The system fails if its output is not equal to its input. This paper shows that if the WVS consists of units that need different time to produce their outputs, the decision time of the entire system depends on the distribution of unit weights and on the value of tau. It shows also that a tradeoff exists between the system reliability and its rapidity. An algorithm that finds the system parameters maximizing its reliability under constraint imposed on the expected system decision time is suggested. Illustrative examples are presented. tau threshold factor, (0 < =tau < =1) n number of units belonging to WVS K number of different voting results in WVS I WVS input (proposition to be accepted or rejected), I{0,1} Pr{v} probability of event v pi Pr{I=i} dj(I) decision (output) of individual unit j D(I) decision of the entire WVS Pr{dj(I)=s|I=i},i{0,1},s{0,1,x} Qis Pr{D(I)=s|I=i}, i{0,1},s{0,1,x} R Pr{D(I)=I}, WVS reliability U-function representing all the possible different states of a subsystem containing m fastest voting units when system input is I 'negative' weight of unit j (weight of unit j when dj(I)=0) 'positive' weight of unit j (weight of unit j when dj(I)=1) tj time when the decision dj(I) of voting unit j becomes available T expected WVS decision time T* maximum allowed expected decision time total weight of units that have decision time not greater than tm and vote for the proposition acceptance total weight of units that have decision time not greater than tm and vote for the proposition rejection probability that the proposition I is rejected at time tm probability that the proposition I is accepted at time tm 1(x) unity function: 1(TRUE)=1, 1(FALSE)=0 WVS weighted voting system UF U(z)-function The weighted voting system (WVS) consists of n units that each provide a binary decision (0 or 1) or abstain from voting. Each unit has its own individual weight. System output is 1 if the cumulative weight of all 1-opting units is at least a pre-specified fraction τ of the cumulative weight of all non-abstaining units. Otherwise, system output is 0. The system input is either 0 or 1. Every unit is characterized by probability of making decisions 0 and 1 and by probability of abstaining for each input. The system fails if its output is not equal to its input. This paper shows that if the WVS consists of units that need different time to produce their outputs, the decision time of the entire system depends on the distribution of unit weights and on the value of τ. It shows also that a tradeoff exists between the system reliability and its rapidity. An algorithm that finds the system parameters maximizing its reliability under constraint imposed on the expected system decision time is suggested. Illustrative examples are presented. |
| Author | Levitin, Gregory |
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| Cites_doi | 10.1016/j.ress.2003.08.006 10.1109/24.106777 10.1016/S0951-8320(03)00074-7 10.1016/0895-7177(91)90026-4 10.1109/24.765926 10.1109/T-C.1971.223133 10.1016/S0951-8320(02)00012-1 10.1016/S0951-8320(00)00089-2 10.1109/24.257833 10.1109/24.295001 10.1109/24.295008 10.1057/jors.1980.137 |
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| Keywords | Probabilistic approach Decision support system Voting Decision making System reliability Failures Distribution system |
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| Snippet | The weighted voting system (WVS) consists of
n units that each provide a binary decision (0 or 1) or abstain from voting. Each unit has its own individual... The weighted voting system (WVS) consists of n units that each provide a binary decision (0 or 1) or abstain from voting. Each unit has its own individual... |
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| SubjectTerms | Applied sciences Decision theory. Utility theory Exact sciences and technology Operational research and scientific management Operational research. Management science Reliability theory. Replacement problems |
| Title | Weighted voting systems: reliability versus rapidity |
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