Lattices in social networks with influence

Michel Grabisch and Agnieszka Rusinowska

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: We present an application of lattice theory to the framework of influence in social networks. The contribution of the paper is not to derive new results, but to synthesize our existing results on lattices and influence. We consider a two-action model of influence in a social network in which agents have to make their yes-no decision on a certain issue. Every agent is preliminarily inclined to say either 'yes' or 'no', but due to influence by others, the agent's decision may be different from his original inclination. We discuss the relation between two central concepts of this model: influence function and follower function. The structure of the set of all influence functions that lead to a given follower function appears to be a distributive lattice. We also consider a dynamic model of influence based on aggregation functions and present a general analysis of convergence in the model. Possible terminal classes to which the process of influence may converge are terminal states (the consensus states and non trivial states), cyclic terminal classes and unions of Boolean lattices.

Keywords: convergence; terminal class; aggregation function; Influence function; follower function; distributive lattice (search for similar items in EconPapers)
Date: 2015-03
New Economics Papers: this item is included in nep-cdm, nep-mic, nep-soc and nep-ure
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00977005v1
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Published in International Game Theory Review, 2015, 17 (1), pp.1-18. ⟨10.1142/S0219198915400046⟩

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Related works:
Working Paper: Lattices in social networks with influence (2015)
Working Paper: Lattices in social networks with influence (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-00977005

DOI: 10.1142/S0219198915400046

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