This paper is concerned with consensus algorithms for multi-agent systems. Motivated by a recently proposed distributed algorithm that guarantees average consensus for undirected and time-invariant communication graphs using the so-called equal neighbour model, which assumes agents to weight the incoming information equally, we propose a generalisation of this weighting strategy and extend the average consensus algorithm to this generalised case. We propose four special weighting strategies with guaranteed convergence to average consensus and compare them with the equal neighbour model. Simulation studies show that proposed weighting strategies outperform the equal-weight strategy. For the special case of the star topology this is analytically shown.