In many edge computing applications, edge devices are required to reach fault-tolerant consensus in order to provide collaborative services in outdoor environments. In this paper, we study a comprehensive $(a,b)$-majority consensus problem based on a novel failure model, which takes $a$ distinct opinions as inputs and outputs a $b$-majority opinion as the final agreement. This problem formulation is drastically different from traditional ones, which usually require a majority consensus from the binary opinions of multiple supporters. It is more practical and flexible as it can accommodate more than 2 input opinions and output one that satisfies the application requirement defined by parameter $b$. We also consider physical layer in our failure model while previous models mainly focus on faults occurred in protocol layer and data layer. Based on this more realistic failure model and a more practical consensus problem definition, we present a distributed protocol for $n$ edge devices to reach an $(a,b)$-majority consensus within $\Theta (n)$ time steps with high probability. Empirical results from our simulation studies validate the fault tolerance property and efficiency of our work in achieving the $(a,b)$-majority consensus.