Interval consensus: from quantized gossip to voting

We design distributed and quantized average consensus algorithms on arbitrary connected networks. By construction, quantized algorithms cannot produce a real, analog average. Instead, our algorithm reaches consensus on the quantized interval that contains the average. We prove that this consensus in reached in finite time almost surely. As a byproduct of this convergence result, we show that the majority voting problem is solvable with only 2 bits of memory per agent.