In this paper, we introduce the anonymous proposer vector consensus problem in which a set of processes decide on a vector of values, where each value is a proposal made anonymously by a single process. In a distributed survey, for example, a solution to anonymous proposer vector consensus allows non-faulty processes to put forward a potentially controversial opinion that is not tied to their identity. More specifically, a non-faulty process' proposal is indistinguishable from that of all non-faulty processes, even in the presence of timing attacks. We also define the anonymous all-to-all reliable broadcast problem which ensures the properties of reliable broadcast hold with the same anonymity guarantee. For each problem, we present a protocol that solves it in presence of Byzantine faults. Solving anonymous all-to-all reliable broadcast, Anonymous All-to-all Reliable Broadcast Protocol (AARBP) executes in two regular and one anonymous message delays with the same message complexity as n invocations of Bracha's reliable broadcast protocol. Solving anonymous proposer vector consensus, Anonymous Proposer Vector Consensus Protocol (AVCP) is a reduction to binary consensus which can terminate in three regular and one anonymous message delay.
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