  We study a general task allocation problem, involving multiple agents that
collaboratively accomplish tasks and where agents may fail to successfully
complete the tasks assigned to them (known as execution uncertainty). The goal
is to choose an allocation that maximises social welfare while taking their
execution uncertainty into account. We show that this can be achieved by using
the post-execution verification (PEV)-based mechanism if and only if agents'
valuations satisfy a multilinearity condition. We then consider a more complex
setting where an agent's execution uncertainty is not completely predictable by
the agent alone but aggregated from all agents' private opinions (known as
trust). We show that PEV-based mechanism with trust is still truthfully
implementable if and only if the trust aggregation is multilinear.
