Lattices in Social Networks with Influence

Michel Grabisch and Agnieszka Rusinowska

International Game Theory Review (IGTR), 2015, vol. 17, issue 01, 1-18

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 nontrivial states), cyclic terminal classes and unions of Boolean lattices.

Keywords: Influence function; follower function; distributive lattice; aggregation function; convergence; terminal class; C7; D7 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219198915400046
Access to full text is restricted to subscribers

Related works:
Working Paper: Lattices in social networks with influence (2015)
Working Paper: Lattices in social networks with influence (2015)
Working Paper: Lattices in social networks with influence (2015)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:igtrxx:v:17:y:2015:i:01:n:s0219198915400046

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219198915400046

Access Statistics for this article

International Game Theory Review (IGTR) is currently edited by David W K Yeung

More articles in International Game Theory Review (IGTR) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().