The Philos Marketplace blockchain system is a proposed hierarchical blockchain architecture which allows a large number of individual blockchains to operate in parallel. These parallel chains achieve consensus among one another on a limited set of core operations, while allowing each on-chain application to manage its own data independently of others. This architecture addresses the scalability issues of traditional linear blockchains, but requires novel consensus mechanisms. A central feature of the Philos consensus mechanism is its trust algorithm, which assigns each network node a numerical trust value (or score) indicating the quality of recent past performance. This trust value is then used to determine a node's voting weight at the higher levels of consensus. In this paper, we formally define the Philos trust algorithm, and provide several illustrations of its operation, both theoretically and empirically. We also ask whether a misbehaving node can strategically exploit the algorithm for its personal gain, and show that this type of exploitation can be universally prevented simply by enforcing a mild limit on the number of participants in each of the parallel chains.