A galaxy-wide isolationist movement holding that the Syndicate was a mistake and every species is better off alone.
Carl first heard of the Great Consensus from Loita, the kua-tin he assassinated on the fifth floor. Rishi describes it as a philosophy gaining momentum across many systems: that the Syndicate was a mistake and that all peoples would be better off on their own. Its many strands range from mild separatism to open xenophobia — ironic, he notes, given the name. The Bloom Party kua-tin preach racial purity and reject the cultural influence of so-called 'dry' races; the The Mantids disdain species they consider weaker and inferior; and among the naga, some merely want alien communities to have no say in how naga live.
Princess Vinata was, according to Rishi, a firm believer, hardened by having seen war on alien soil. Her version of the Great Consensus was to steal an entire fleet, load a whole generation aboard, and flee in a direction none of the tunnel threads point — to leave the galaxy's politics behind entirely. Rishi claims he is only a proponent-explainer of the philosophy and not a believer, and his own treaty offer to Earth runs directly counter to it.
The ideological backdrop for the naga's plan to abandon the Syndicate and flee the galaxy.
Also appears in books you've already read — spoiler-safe to their endings: