Every compositional reliability argument for agent systems does the same thing: bound each agent, multiply, report the product. Multiplying is only licensed if the agents fail for unrelated reasons — and a reviewer checking a writer is usually the same model with a different prompt. Over 18,000 preregistered missions scored by deterministic code, two instances of one model failed together on 36.3% of missions where multiplying predicts 14.6%. Of the missions where either agent failed, both failed on 90.0%.
Two agents, one number. If they run in a chain — the second works on what the first produced, and both have to be right — the multiplication is conservative: correlated failures bunch up on the same missions, so the pipeline is a little better than the product says. If they run as a double-check — one writes, one reviews, and you only lose when both miss — the same correlation runs the other way, and the product is the number you were relying on. Set the per-agent failure rate and flip between the two.
The direction is a two-line result in the paper, not a judgement call. For a chain the gap between reality and the product is exactly the covariance of the two verdicts, so positive dependence adds to measured reliability. For redundancy the same covariance adds to the probability that every path fails at once — which is the quantity redundancy was bought to shrink. A dashboard that multiplies returns a reassuring number either way, and nothing in the pipeline says which of the two cases you are in.
The experiment holds the first agent fixed and swaps the second. Every mission is scored by deterministic code — order arithmetic, refund policy, transaction limits, watchlist screening — never by another model, so a "failure" is a definite contract violation rather than a low score. Step through the three arms and watch the four cells of the co-failure table move.
The odds ratio is the honest summary here, and in the same-model arm it is about 784: given that one agent failed, the other is hundreds of times more likely to have failed too than its own rate would suggest. That is not the handoff leaking. The same effect shows up in the two topologies where the model nodes never see each other's output — parallel branches into a deterministic merge, and three workers into a 2-of-3 vote — and in an unmanipulated control pair with no channel between the workers at all, which sits at a log odds ratio of about 5.1.
Three levels were registered in advance: keep the model, keep the vendor but shrink the model, or leave the vendor entirely. The prediction was a clean ordering across all three. What survived is the first step and not the second — and the paper reports the failed half as a null rather than quietly dropping it. Step through the three topologies; each bar is the drop in log odds of co-failure against the same-model arm, with the bootstrap interval on the difference.
So the useful lever is model identity, and only the first rung of it. Six of six comparisons — three topologies, two statistics — show that sharing a model produces significantly more co-failure than either alternative. Zero of three show a reliable gap between a smaller model from the same vendor and a model from a different one. The practical reading is narrow and worth stating exactly: put a different model on the second seat, and do not pay extra for a different logo on the same reasoning.
Every arm sits well to the right of its own prediction. Substituting a model narrows the gap without closing it: the weakest association measured anywhere in the campaign is still an odds ratio of about 18.5, in parallel branches with a different-vendor model on the second seat. There is no arm in which the two agents behave like independent evidence.
This is the part to steal for your own dashboards. Jaccard overlap, Kendall's tau and the phi coefficient are all bounded by how often each agent fails, so an arm whose two agents fail at different rates is penalised for a reason that has nothing to do with whether their failures line up. Hold the coupling absolutely fixed below and drag the second agent's failure rate. Three numbers slide; two do not.
In the measured data this is not hypothetical. The same-vendor arm swaps in a weaker model, whose failure rate climbs to 50.8% against the first agent's 39.3%, and its Jaccard overlap lands below the different-vendor arm's — reading naively, that says leaving the vendor increased correlated failure, which inverts the mechanism the experiment was built to test. The two marginal-free statistics put the arms back in the right order. If your reliability dashboard reports overlap between two components that fail at different rates, it can rank your options backwards.
The common shape in production: a model does the work, a second call reviews it, and the review is usually the same model behind a different prompt. Set your volume and your per-agent miss rate, then switch the second seat between the same model and a different one. The escape rate is computed from the association measured in the corresponding arm — your volume and your miss rate are yours to supply, and the multiplier is the paper's.
The paper works the same arithmetic on a 2-of-3 vote and gets a smaller but still one-directional answer: three workers each satisfying their contract 61% of the time fail the vote 33.8% of the time if they are independent, and about 37% under a joint consistent with the measured pairwise association — a 9.6% relative increase in exactly the quantity the quorum was bought to reduce. Marginals and a pairwise correlation do not pin down a three-way failure, so that one is an illustration of magnitude rather than a bound.