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The dining cryptographers network (or DC-net) is a seminal technique devised by Chaum to solve the dining cryptographers problem -- namely, how to send a boolean-OR bit anonymously from a group of participants. In this paper, we investigate the weaknesses of DC-nets, study alternative methods and propose a new way to tackle this problem. Our protocol, Anonymous Veto Network (or AV-net), overcomes all the major limitations of DC-nets, including the complex key setup, message collisions and susceptibility to disruptions. While DC-nets are unconditionally secure, AV-nets are computationally secure under the Decision Diffie-Hellman (DDH) assumption. An AV-net is more efficient than other techniques based on the same public-key primitives. It requires only two rounds of broadcast and the least computational load and bandwidth usage per participant. Furthermore, it provides the strongest protection against collusion -- only full collusion can breach the anonymity of message senders.