Consensus with Stochastic Broadcast

Abstract: We study binary consensus in the \emph{stochastic broadcast model}, which assumes $n\geq 2$ processes communicating synchronously by message broadcasts. At each round, every process broadcasts a message to all the other processes. Each broadcast succeeds independently with some probability $p\in[0,1]$. If a broadcast succeeds, all processes receive the message, and if it fails, no process receives the message. The sender does not know whether its broadcast was successful or not. In this model, consensus is not solvable; the objective is to design, for a given number of rounds $r$, consensus algorithms that terminate in $r$ rounds, minimizing the probability of error disagreement. This problem has been studied in depth for 2 processes [DISC 2025]. We extend the study to $n> 2$.