The Fundamental Theorem of Voting Schemes

Loeb, Daniel E.

doi:10.1006/jcta.1996.0006

Cited by 7 publications

(6 citation statements)

References 12 publications

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“…In fact, [14,18] show that any NDC can be decomposed into a tree of 2-of-3 majorities. The Tree and HQC systems have decompositions that are read-once; i.e., each variable is input to a single 2-of-3 majority, so Theorem 4.7 can be used.…”

Section: Composite Systemsmentioning

confidence: 99%

How to Be an Efficient Snoop, or the Probe Complexity of Quorum Systems

Peleg¹,

Wool²

2002

SIAM J. Discrete Math.

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Abstract.A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication, and dissemination of information.When the elements may fail, a user of a distributed protocol needs to quickly find a quorum all of whose elements are alive or evidence that no such quorum exists. This is done by probing the system elements, one at a time, to determine if they are alive or dead.This paper studies the probe complexity PC(S) of a quorum system S, defined as the worst case number of probes required to find a live quorum or to show its nonexistence in S, using the best probing strategy.We show that for large classes of quorum systems, all n elements must be probed in the worst case. Such systems are called evasive. However, not all quorum systems are evasive; we demonstrate a system where O(log n) probes always suffice. Then we prove two lower bounds on the probe complexity in terms of the minimal quorum cardinality c(S) and the number of minimal quorums m(S). Finally, we show a universal probe strategy which never makes more than c (S) 2 − c(S) + 1 probes; thus any system with c(S) ≤ √ n is nonevasive.

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Section: Composite Systemsmentioning

confidence: 99%

How to Be an Efficient Snoop, or the Probe Complexity of Quorum Systems

Peleg¹,

Wool²

2002

SIAM J. Discrete Math.

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“…involving a single``committee'' or a large number of one-person``committees.'' A MIF is said to be prime if it cannot be expressed as a composition F [G 1 , ..., G n ] in any other way [17].…”

Section: 42mentioning

confidence: 99%

Voting Fairly: Transitive Maximal Intersecting Families of Sets

Loeb

Conway

2000

Journal of Combinatorial Theory, Series A

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“…In the preceding article, [3] we studied the composition of several games. In such a composition, the voters of one game are replaced by committees each voting according to the rules of the other games.…”

Section: Introductionmentioning

confidence: 99%

“…That is to say, all games can be thought of as compositions of triples of simpler games, where the simplest games of all are dictatorial. See [3] for additional motivation and notation.…”

Section: Introductionmentioning

confidence: 99%