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 (i.e., fault tolerant). To achieve this, we show that the post-execution verification (PEV)-based mechanism presented by Porter et al. (2008) is applicable if and only if agents' valuations are risk-neutral (i.e., the solution is almost universal). We then consider a more advanced 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 applicable if and only if the trust aggregation is multilinear. Given this characterisation, we further demonstrate how this mechanism can be successfully applied in a real-world setting. Finally, we draw the parallels between our results and the literature of efficient mechanism design with general interdependent valuations
