TOOL | Propagation & containment
Which agent topology holds up when a step can fail
Enter a per-agent success rate and a team size. See end-to-end success, caught and escaped failures for five computed topologies and a single-agent baseline, ranked with intervals from sample counts.
Enter a per-agent success rate and a team size. The comparator ranks five multi-agent topologies against a single-agent baseline: pipeline, supervisor, majority vote, debate with a shared blind spot, and blackboard, drawing the pattern names from our multi-agent orchestration-patterns research and the gate model from our cascading-failures research. The cascade reliability calculator owns a chain's step-by-step arithmetic; this page compares shapes.
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Top topology
78.7%
Debate | +8.7 pp vs single agent | 5 agents, 3 voters
These figures are a five-agent, three-voter illustration at 95% per-agent success, 70% whole-task success, beta 0.3 and no gate. Replace every input with your own numbers.
End-to-end rates for five computed topologies, the swarm (not computed), and the single-agent baseline at a 70.0% whole-task rate and a 95.0% per-agent rate across 5 agents (3 voters).
| Topology | Success | Caught | Escaped | vs baseline |
|---|---|---|---|---|
| Single agent | 70.0% | 0.0% | 30.0% | 0.0 pp |
| Pipeline | 77.4% | 0.0% | 22.6% | +7.4 pp |
| Supervisor | 73.5% | 0.0% | 26.5% | +3.5 pp |
| Majority vote | 78.4% | 0.0% | 21.6% | +8.4 pp |
| Debate | 78.7% | 0.0% | 21.3% | +8.7 pp |
| Blackboard | 77.4% | 0.0% | 22.6% | +7.4 pp |
| Swarm | Not computed | Not computed | Not computed | Not computed |
Debate’s unanimous-wrong share: 9.0% of runs carry a shared-cause failure that makes every panelist wrong the same way.
Success rate by topology as the per-agent rate varies, holding 5 agents and 3 voters.
| Topology | 50% | 60% | 70% | 80% | 90% | 95% | 99% |
|---|---|---|---|---|---|---|---|
| Single agent | 70.0% | 70.0% | 70.0% | 70.0% | 70.0% | 70.0% | 70.0% |
| Pipeline | 3.1% | 7.8% | 16.8% | 32.8% | 59.0% | 77.4% | 95.1% |
| Supervisor | 3.0% | 7.4% | 16.0% | 31.1% | 56.1% | 73.5% | 90.3% |
| Majority vote | 78.4% | 78.4% | 78.4% | 78.4% | 78.4% | 78.4% | 78.4% |
| Debate | 78.7% | 78.7% | 78.7% | 78.7% | 78.7% | 78.7% | 78.7% |
| Blackboard | 3.1% | 7.8% | 16.8% | 32.8% | 59.0% | 77.4% | 95.1% |
| Swarm | Not computed | Not computed | Not computed | Not computed | Not computed | Not computed | Not computed |
series = p^n; supervisor = pHub * p^n; vote = P(Bin(k, pWhole) >= floor(k/2) + 1)How?
How this is calculated
Three outcomes. Every shape returns three fractions that sum to exactly one. Success: the run delivers a correct result end to end. Caught: the run fails, and a gate, a tie or a validator makes the failure visible before anyone acts on it. Escaped: a wrong result reaches the consumer unflagged. The three columns together are the full picture; a shape that converts escaped failures into caught ones has improved the system even when its success rate stays the same.
The baseline. One agent does the whole task. Its success rate is the whole-task rate, the rate the reader measured on the full task. Nothing is downstream, so nothing contains the failure: the entire failure column is escaped. This row is the bar every multi-agent shape is measured against, and the whole-task rate is a separate observation from the per-agent rate. A subtask is smaller than the whole task, so the per-agent rate is normally higher.
Series topologies: pipeline, supervisor, blackboard. In a pipeline of n steps, every step must succeed, so end-to-end success is the per-agent rate raised to the nth power. A supervisor multiplies that product by its own plan-and-merge rate, the hub rate, and nothing checks the hub. A blackboard of n agents writing one shared store follows the same product. All three share the same exponential-decay shape on success: the choice between a pipeline, a supervisor and a blackboard does not change the reliability curve, and only the split between caught and escaped shifts with the gate. The chain's own step-by-step arithmetic, the per-step budget, and what one retry buys per step belong to the cascade reliability calculator; common-cause failure along a chain belongs to the correlated cascade simulator. This page compares shapes rather than restating the chain.
The vote. The vote and debate rows use the whole-task rate, since each voter attempts the whole task. For an odd panel of three or more independent voters, a majority beats a single voter whenever each voter is right strictly between 50% and 100% of the time, and the lift grows with panel size. Success is the probability that at least a strict majority (floor of k/2 plus 1) of the panel is correct, computed from the binomial tail. An even panel can tie. A tie delivers no answer and is counted as caught, never folded into success. The retry strategy optimizer already ships a majority-vote policy over k attempts of one path on one task and prices each attempt; this page votes k agents in a topology and prices nothing. Use both together when you need the number and the bill.
The debate. A debate panel adds a shared blind spot. A fraction beta of each panelist's failures traces to a cause every panelist shares: a flawed rubric, a subtlety outside the training distribution, a prompt flaw that steers every panelist the same way. The residual per-panelist failure rate is set so the marginal failure rate stays at exactly one minus the whole-task rate, following the beta-factor common-cause model from reliability engineering. At beta zero the debate reproduces the independent vote exactly. At beta one the panel is worth a single voter. Between those endpoints the relationship is not monotone: success can be higher than the independent vote while the share of runs where a shared cause makes every panelist wrong (the unanimous-wrong share, beta times the whole-task failure rate) rises. Both numbers are reported side by side because the reliability story is in the pair. The correlated cascade simulator applies the same beta-factor model along a serial chain; this page applies it across parallel voters.
Intervals. A confidence band on success appears only when the reader supplies counts behind the whole-task rate or the per-agent rate. The comparator computes a Wilson score interval on the entered rate and pushes both bounds through the same formula that produced the point estimate. Each row's success never falls as its own rate rises: the series rows follow the per-agent rate; the single-agent, vote and debate rows follow the whole-task rate. Pushing the bounds of either rate through is valid, and each row's band comes from the counts behind that row's own rate. No band appears on beta, gate, the hub rate, the team size or the panel size: those are structural assumptions, and the page says so. The band is an interval on the reliability estimate under the stated shape assumptions, not an exact joint confidence region.
Limits and assumptions. These figures are closed-form arithmetic on rates and team sizes you enter. Nothing is measured on a running system, and the per-agent rate is an observation you bring from your own evaluations. The glossary defines cascade resistance as a composite score between zero and one; this page returns per-shape success rates with intervals and no such composite, because the rates carry their own meaning and a single number would hide which topology won and why. Propagation radius, the distance a fault travels, is a quantity this page deliberately does not chart. The depth picture and the failure families each shape amplifies are in the multi-agent failure-modes research; the breadth picture is documented there but drawn nowhere.
Formula: series = p^n; supervisor = pHub * p^n; vote = P(Bin(k, pWhole) >= floor(k/2) + 1)
Questions
Why do the pipeline and the blackboard return the same success rate?
Both are series compositions: every agent's subtask must succeed for the run to succeed, so end-to-end success is the per-agent rate to the nth power in both cases. The blackboard splits caught and escaped differently because its validate-on-write gate catches faults per step rather than once at the end, but the success column is the same. A supervisor follows the same curve, multiplied by the hub rate. All three series topologies decay exponentially in the team size. Only the vote and debate rows use the binomial tail, which is a qualitatively different curve.
How does the debate differ from a simple vote?
A vote assumes each voter fails independently. A debate adds a shared blind spot, controlled by beta: a fraction of each panelist's failures traces to a cause every panelist shares. When beta is above zero, the panel can be unanimously wrong on a run, and the share of unanimously wrong runs rises with beta even when the all-clean rate stays high. The vote row is a special case of the debate row at beta zero.
Why can adding voters lower the success rate?
When each voter is correct less than half the time, a majority of an odd panel is more likely to agree on the wrong answer than on the right one. A larger odd panel helps at rates strictly between 50% and 100% and hurts at rates strictly between 0% and 50%. Adding one voter to an odd panel makes it even, and an even panel can score below one voter even above 50%: three voters at a 70% whole-task rate give 78.4% success, and four give 65.2%.
When should I use the cascade reliability calculator for a chain?
This page gives you the chain's end-to-end success in one row, but the cascade reliability calculator shows you which step spends the budget, derives the per-step target from your end-to-end goal, and tells you what one retry buys at each step. Use this page to decide whether a chain is the right shape; use the cascade calculator to tune the chain you chose.
Does this page price any topology in tokens or dollars?
It does not. The retry strategy optimizer prices a majority vote over k attempts in your own cost unit, and cost per successful task prices a single path with retries. This page compares shapes by reliability alone so the ranking is independent of what you pay per call.
Why is the swarm row empty?
A swarm's handoff path changes every run. There is no fixed composition to raise to a power or sum over a majority, so there is no closed-form reliability to compute. The row is listed because the multi-agent orchestration-patterns research names five patterns and a silent omission would read as an oversight. The pattern and the trade-off it makes (adaptivity bought with attribution) are documented there.
Sources
- Probabilistic Risk Assessment Procedures Guide for NASA Managers and Practitioners, chapter 7: modeling and quantification of common cause failures (the beta-factor model behind the debate row's residual failure rate)
- Probable Inference, the Law of Succession, and Statistical Inference (Wilson score interval)