TY - JOUR
T1 - Consistency dynamics in accusation-endorsement networks with an external judge
AU - Nishimura, Joel
AU - Goodloe, Oscar
N1 - Funding Information:
A scholarship from the Barrett, The Honors College at Arizona State University and by a New College Undergraduate Inquiry and Research Experiences (NCUIRE) Fellowship from the New College of Interdisciplinary Arts and Sciences at Arizona State University.
Publisher Copyright:
© 2020 The authors. Published by Oxford University Press. All rights reserved.
PY - 2020/2/20
Y1 - 2020/2/20
N2 - Previous network models have imagined that connections change to promote structural balance, or to reflect hierarchies. We propose a model where agents adjust their connections to appear credible to an external judge or observer. In particular, we envision a signed, directed network where positive edges represent endorsements or trust and negative edges represent accusations or doubt, and consider both the strategies an external judge might use to identify credible nodes and the strategies nodes might use to then appear credible by changing their outgoing edges. First, we establish that an external judge may be able to exactly identify a set of 'honest' nodes from an adversarial set of 'cheater' nodes regardless of the cheater nodes' connections. However, while these results show that an external judge's task is not hopeless, some of these theorems involve network structures that are NP-hard to find. Instead, we suggest a simple heuristic that an external judge might use to identify which nodes are not credible based upon their involvement with particular implicating edge motifs. Building on these notions, and analogously to some models of structural balance, we develop a discrete-Time dynamical system where nodes engage in consistency dynamics, where inconsistent arrangements of edges that cause a node to look 'suspicious' exert pressure for that node to change edges. We demonstrate that these dynamics provide a new way to understand group fracture when nodes are worried about appearing consistent to an external judge or observer.
AB - Previous network models have imagined that connections change to promote structural balance, or to reflect hierarchies. We propose a model where agents adjust their connections to appear credible to an external judge or observer. In particular, we envision a signed, directed network where positive edges represent endorsements or trust and negative edges represent accusations or doubt, and consider both the strategies an external judge might use to identify credible nodes and the strategies nodes might use to then appear credible by changing their outgoing edges. First, we establish that an external judge may be able to exactly identify a set of 'honest' nodes from an adversarial set of 'cheater' nodes regardless of the cheater nodes' connections. However, while these results show that an external judge's task is not hopeless, some of these theorems involve network structures that are NP-hard to find. Instead, we suggest a simple heuristic that an external judge might use to identify which nodes are not credible based upon their involvement with particular implicating edge motifs. Building on these notions, and analogously to some models of structural balance, we develop a discrete-Time dynamical system where nodes engage in consistency dynamics, where inconsistent arrangements of edges that cause a node to look 'suspicious' exert pressure for that node to change edges. We demonstrate that these dynamics provide a new way to understand group fracture when nodes are worried about appearing consistent to an external judge or observer.
KW - directed networks
KW - dynamical models of networks
KW - game theory
KW - signed networks
KW - structural balance
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U2 - 10.1093/comnet/cnz047
DO - 10.1093/comnet/cnz047
M3 - Article
AN - SCOPUS:85081947442
SN - 2051-1310
VL - 8
JO - Journal of Complex Networks
JF - Journal of Complex Networks
IS - 1
M1 - cnz047
ER -