Majority Consensus and the Local Majority Rule

Mustafa, Nabil H.; Pekec, Aleksandar

doi:10.1007/3-540-48224-5_44

Cited by 20 publications

(15 citation statements)

References 15 publications

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“…In [7], it has been shown that there is no synchronous deterministic two-state automaton that can solve binary voting problem in a connected network. Several two-state automata have been proposed for the ring topology [8], [9], the most successful of which can get the correct result in nearly 83% of initial configurations of selected votes [10]. In order to circumvent the impossibility result of [7], asynchronous and probabilistic automata have also been presented in CA community [11]- [13].…”

Section: Introductionmentioning

confidence: 99%

Distributed Voting/Ranking With Optimal Number of States per Node

Salehkaleybar

Sharifnassab

Golestani

2015

IEEE Trans. on Signal and Inf. Process. over Networks

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Considering a network with n nodes, where each node initially votes for one (or more) choices out of K possible choices, we present a Distributed Multi-choice Voting/Ranking (DMVR) algorithm to determine either the choice with maximum vote (the voting problem) or to rank all the choices in terms of their acquired votes (the ranking problem). The algorithm consolidates node votes across the network by updating the states of interacting nodes using two key operations; the union and the intersection. The proposed algorithm is simple, independent from network size, and easily scalable in terms of the number of choices K, using only K ×2 K−1 nodal states for voting, and K ×K! nodal states for ranking. We prove the number of states to be optimal in the ranking case; this optimality is conjectured to also apply to the voting case. The time complexity of the algorithm is analyzed in complete graphs. We show that the time complexity for both ranking and voting is O(log(n)) for given vote percentages, and is inversely proportional to the minimum of the vote percentage differences among various choices.

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Section: Introductionmentioning

confidence: 99%

Distributed Voting/Ranking With Optimal Number of States per Node

Salehkaleybar

Sharifnassab

Golestani

2015

IEEE Trans. on Signal and Inf. Process. over Networks

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“…Specifically, each node in the network has a binary opinion that is consistent with the majority opinion of its neighbors. Local majority rule is commonly used in studying opinion dynamics in social networks (see, for example, [1,2]). Under the local majority model, we show that for a general network, the IDSC problem is co-NPcomplete and the MIDS problem is NP-hard.…”

Section: Information Dominating Setmentioning

confidence: 99%

The Minimum Information Dominating Set for Opinion Sampling in Social Networks

Gao

Zhao

Swami

2016

IEEE Trans. Netw. Sci. Eng.

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We consider the problem of inferring the opinions of a social network through strategically sampling a minimum subset of nodes by exploiting correlations in node opinions. We first introduce the concept of information dominating set (IDS). A subset of nodes in a given network is an IDS if knowing the opinions of nodes in this subset is sufficient to infer the opinion of the entire network. We focus on two fundamental algorithmic problems: (i) given a subset of the network, how to determine whether it is an IDS; (ii) how to construct a minimum IDS. Assuming binary opinions and the local majority rule for opinion correlation, we show that the first problem is co-NP-complete and the second problem is NP-hard in general networks. We then focus on networks with special structures, in particular, acyclic networks. We show that in acyclic networks, both problems admit linear-complexity solutions by establishing a connection between the IDS problems and the vertex cover problem. Our technique for establishing the hardness of the IDS problems is based on a novel graph transformation that transforms the IDS problems in a general network to that in an odd-degree network. This graph transformation technique not only gives an approximation algorithm to the IDS problems, but also provides a useful tool for general studies related to the local majority rule. Besides opinion sampling for applications such as political polling and market survey, the concept of IDS and the results obtained in this paper also find applications in data compression and identifying critical nodes in information networks.

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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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Majority Consensus and the Local Majority Rule

Cited by 20 publications

References 15 publications

Distributed Voting/Ranking With Optimal Number of States per Node

Distributed Voting/Ranking With Optimal Number of States per Node

The Minimum Information Dominating Set for Opinion Sampling in Social Networks

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

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