Leslie Lamport describes a algorithm to come to consensus for the case for
m is the number of traitors in
I perfectly understand why for
n=4, m=1 there is consensus trough a majority vote. Lets suppose (like in Leslies proposal) there are three type of messages for different attack time
(A1, A2, A3). If no majority is reached the default action is retreat (
So even if the commander is a traitor and send different messages
A1,A2,A3 to the three loyal lieutenants they will get (trough the recursive algorithm) to state (
A1,A2,A3). In this case no majority is reached and the default action is taken (
r). Thereby consensus is reached.
Leslie stated, that no consensus cannot be reached with
n=3, m=1. Nonetheless if we apply the upper algorithm to the scenario with
n=3, m=1 for the example that the commander is a traitor, isn't there the same consensus reached? The commander sends
A1, A2 to the two loyal lieutenants, they both will reach the state
(A1, A2) and thereby take the default option
r. There is my mistake?