Listen to Your Neighbors: How (Not) to Reach a Consensus

Mustafa, Nabil H.; Pekec, Aleksandar

doi:10.1137/s0895480102408213

Cited by 19 publications

(9 citation statements)

References 34 publications

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“…For a slightly different dynamic, 12 several theorems from Mustafa and Pekev (2004) entail that many other graphs have the same convergence function. All of these networks are very highly connected and are thus very close to the complete graph.…”

Section: Complete Networkmentioning

confidence: 99%

“…This model has been used in mathematics(Durrett and Steif 1993;Goles and Olivos 1980;Granville 1991;Holley and Liggett 1975;Moran 1994a Moran ,b, 1995Mustafa and Pekev 2004;Steif 1994), computer science(Flocchini et al 1998;Hassin and Peleg 2001;Královic 2001;Nakata et al 1999Nakata et al , 2000Peleg 1998Peleg , 2002, biology(Agur 1987;Agur et al 1988;Clifford and Sudbury 1973), and social psychology(Latané and Nowak 1997;Poljak and Sura 1983).…”

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confidence: 99%

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Social structure and the effects of conformity

Zollman

2008

Synthese

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Conformity is an often criticized feature of human belief formation. Although generally regarded as a negative influence on reliability, it has not been widely studied. This paper attempts to determine the epistemic effects of conformity by analyzing a mathematical model of this behavior. In addition to investigating the effect of conformity on the reliability of individuals and groups, this paper attempts to determine the optimal structure for conformity. That is, supposing that conformity is inevitable, what is the best way for conformity effects to occur? The paper finds that in some contexts conformity effects are reliability inducing and, more surprisingly even when it is counterproductive, not all methods for reducing its effect are helpful. These conclusions contribute to a larger discussion in social epistemology regarding the effect of social behavior on individual reliability.

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Section: Complete Networkmentioning

confidence: 99%

mentioning

confidence: 99%

Social structure and the effects of conformity

Zollman

2008

Synthese

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“…Yet another related line of works contains the opinion formation in social networks: instead of spatially related nodes, we have persons with friends, and a person might change his opinion to conform to the majority opinion of his group. This has been studied both as social dynamics and as abstract process on graphs, see, e.g., [1,17,22,11,18,26]. Majority vote among neighbors has also been studied as model for some spin systems in physics, see e.g., [21,15,25,6].…”

Section: Previous Workmentioning

confidence: 99%

Local event boundary detection with unreliable sensors: Analysis of the majority vote scheme

Braß

Shin

2015

Theoretical Computer Science

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In this paper we study the identification of an event region X within a larger region Y , in which the sensors are distributed by a Poisson process of density λ to detect this event region, i.e., its boundary. The model of sensor is a 0-1 sensor that decides whether it lies in X or not, and which might be incorrect with probability p. It also collects information on the 0-1 values of the neighbors within some distance r and revises its decision by the majority vote of these neighbors. In the most general setting, we analyze this simple majority vote scheme and derive some upper and lower bounds on the expected number of misclassified sensors. These bounds depend on several sensing parameters of p, r, and some geometric parameters of the event region X. By making some assumptions on the shape of X, we prove a significantly improved upper bound on the expected number of misclassified sensors; especially for convex regions with sufficiently round boundary, and we find that the majority vote scheme performs well in the simulation rather than its theoretical upper bound.

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“…Through the concepts of graph convexity we can model, and eventually solve, problems in contexts that requires some disseminating process, such as contamination [2,4,29], marketing strategies [20,41,42], spread of opinion [5,29], spread of influence [41,43] and distributed computing [35,38,44,46]. Some natural convexities in graphs are defined by a set P of paths in G, in a way that a set S of vertices of G is convex if and only if for every path P = v 0 v 1 .…”

Section: Introductionmentioning

confidence: 99%

On the Geodetic Hull Number of Complementary Prisms

Coelho,

Nascimento

et al. 2018

Preprint

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Let G be a finite, simple, and undirected graph and let S be a set of vertices of G. In the geodetic convexity, a set of vertices S of a graph G is convex if all vertices belonging to any shortest path between two vertices of S lie in S. The convex hull H(S) of S is the smallest convex set containing S. If H(S) = V (G), then S is a hull set. The cardinality h(G) of a minimum hull set of G is the hull number of G. The complementary prism GG of a graph G arises from the disjoint union of the graph G and G by adding the edges of a perfect matching between the corresponding vertices of G and G. Motivated by the work of Duarte et al. [31], we determine and present lower and upper bounds on the hull number of complementary prisms of trees, disconnected graphs and cographs. We also show that the hull number on complementary prisms cannot be limited in the geodetic convexity, unlike the P3-convexity.

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Listen to Your Neighbors: How (Not) to Reach a Consensus

Cited by 19 publications

References 34 publications

Social structure and the effects of conformity

Social structure and the effects of conformity

Local event boundary detection with unreliable sensors: Analysis of the majority vote scheme

On the Geodetic Hull Number of Complementary Prisms

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