Consensus and voting reliability

Consensus and voting reliability applies the cascade-resistance score to a voting ensemble: how much a majority across several agents lowers the chance a fault reaches the output. The lift is the Condorcet jury theorem at work: when each ballot is cast independently and is right more often than not, the majority beats any single voter and improves as the panel widens, because one voter’s error lands in the minority and is outvoted.

Independence is the load-bearing condition, and an ensemble built from one model, one prompt, and one retrieved context breaks it by construction. Those agents resample a single judgment instead of casting independent ballots, so a shared error rides into the majority and the Condorcet guarantee lapses.

The trap specific to voting is unanimity. A panel whose members inherited one poisoned context returns an agreeing, confident, wrong answer with every surface signal of a reliable one, and the more correlated the voters, the more unanimous the failure looks. So test independence rather than assume it: vary the seed, model, prompt, and retrieved context across voters, then check that their errors stay uncorrelated before crediting the majority. Ballots that miss together are one voter wearing several hats. A vote at least fixes each ballot before any voter can sway another, the read-and-revise coupling a debate relies on, but that structural separation cannot manufacture the statistical independence a shared context has already broken.

To grade an ensemble, inject a fault into one voter and read its cascade resistance. A wiring that keeps the fault in the minority contains it; one where error propagation correlates the ballots lets a single injected fault set the blast radius for the whole panel, the correlated wiring the multi-agent failure-mode pillar catalogs. Independence is the variable that decides which ensemble you built, and it is measurable before you ship.