The open vote network ( [10]) is a secure two-round multi-party protocol facilitating the computation of a sum of integer votes without revealing their individual values. This is done without a central authority trusted for privacy, and thus allows decentralised and anonymous decision-making efficiently. As such, it has also been implemented in other settings such as financial applications, see e.g. [15, 17]. An inherent limitation of is its lack of robustness against denial-of-service attacks, which occur when at least one of the voters participates in the first round of the protocol but (maliciously or accidentally) not in the second. Unfortunately, such a situation is likely to occur in any real-world implementation of the protocol with many participants. This could incur serious time delays from either waiting for the failing parties and perhaps having to perform extra protocol rounds with the remaining participants. This paper provides a solution to this problem by extending with mechanisms tolerating a number of unresponsive participants, the basic idea being to run several sub-elections in parallel. The price to pay is a carefully controlled privacy loss, an increase in computation, and a statistical loss in accuracy, which we demonstrate how to measure precisely.