Abstract
Non-centralized recommendation-based decision making is a central feature of several social and technological processes, such as market dynamics, peer-to-peer file-sharing and the web of trust of digital certification. We investigate the properties of trust propagation on networks, based on a simple metric of trust transitivity. We investigate analytically the percolation properties of trust transitivity in random networks with arbitrary in/out-degree distributions, and compare with numerical realizations. We find that the existence of a non-zero fraction of absolute trust (i.e. entirely confident trust) is a requirement for the viability of global trust propagation in large systems: The average pair-wise trust is marked by a discontinuous transition at a specific fraction of absolute trust, below which it vanishes. Furthermore, we perform an extensive analysis of the Pretty Good Privacy (PGP) web of trust, in view of the concepts introduced. We compare different scenarios of trust distribution: community- and authority-centered. We find that these scenarios lead to sharply different patterns of trust propagation, due to the segregation of authority hubs and densely-connected communities. While the authority-centered scenario is more efficient, and leads to higher average trust values, it favours weakly-connected “fringe” nodes, which are directly trusted by authorities. The community-centered scheme, on the other hand, favours nodes with intermediate in/out-degrees, in detriment of the authorities and its “fringe” peers.
Highlights
Several social and technological systems rely on the notion of trust, or recommendation, where agents must make their decision based on the trustworthiness of other agents, with which they interact
An even more direct example is the web of trust of digital certification, such as the Pretty Good Privacy (PGP) system [4,5], where regular individuals must certify the authenticity of other individuals with digital signatures
We present an analysis of trust propagation based on the notion of transitivity: If agent a trusts agent b, and agent b trusts agent c, to some extent, agent a will trust agent c
Summary
Several social and technological systems rely on the notion of trust, or recommendation, where agents must make their decision based on the trustworthiness of other agents, with which they interact. This leads to a trust metric defined as tu,v. It can be seen that this definition does not suffer from the same problems of Eq 2, again by considering the same complete graph example, with uniform direct trust c Since in this situation every target vertex has N{2 in-neighbours different from the source, and the shortest path to each of these in-neighbours is of length one, the value of pervasive trust can be calculated as (N {2)c3 zc tu,v~ (N{2)cz , ð9Þ for u=v, which converges to tu,v&c2 for N&1. We only emphasize that our approach is derived directly from the simple notion of trust transitivity, is easy to interpret, propagates absolute values of trust, and makes no assumption whatsoever about the network topology, and direct trust distribution
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