A more detailed scenario is always less likely and usually more convincing

The arithmetic that cannot be argued with

The probability that two things both happen can never exceed the probability of either one on its own. Adding a detail to a description narrows the set of futures it covers, so every extra condition takes the probability down or leaves it unchanged. This is not a finding about psychology; it is a property of how probability works, and there is no interpretation under which it fails.

What people do with detailed descriptions runs the other way. A scenario with several specific elements — a cause, a mechanism, a consequence, a named context — feels more likely than a bare statement of the outcome alone, because the details make it easier to picture and easier to believe. Plausibility increases while probability decreases, and the two feelings are not distinguished.

The classic demonstration, and the objections to it

The best-known experiment gives a character sketch and asks people to rank statements about the person, some of which are conjunctions of the outcome with a detail that fits the sketch. A large majority rank the conjunction as more probable than one of its own components, which is impossible.

That result has been picked over for decades and the objections deserve a hearing. Critics argue that participants read the single-component statement as implying the absence of the other component, which is a normal conversational inference rather than a probability error, and that changing the wording or asking in terms of frequencies out of a hundred people reduces the effect considerably. Defenders reply that it persists under wordings designed to block those readings. The honest summary is that the effect is real, that it is sensitive to how the question is asked, and that the size of it in any given format is not fixed.

Where the detail buys its credibility

The interesting part is not the puzzle but where the same structure appears in serious work. A risk assessment describing a specific chain of events, a business forecast built on a named sequence, a strategy that assumes a particular competitor responds in a particular way — each is a conjunction, and each is being judged partly on how coherent the story is.

The person presenting such a scenario is not being dishonest by adding detail, and often they add it because the audience asks for it. Detail is what makes a possibility discussable. But the more complete the story becomes, the smaller the share of futures it describes, and nothing in the presentation makes that shrinkage visible.

The mirror image is the more dangerous one

If a conjunction is overrated, a disjunction is underrated. The probability that at least one of several things goes wrong is higher than the probability of any single one, and often much higher than people assume when they consider the list item by item.

This is why plans fail in ways nobody predicted while every individual prediction was reasonable. The question “could this particular thing derail us?” gets a comforting answer six times, and the question that actually matters — could any of them, or something not on the list — never gets asked in that form. A worked illustration, purely hypothetical: six independent steps each with a nine-in-ten chance of going smoothly leave rather less than a six-in-ten chance that all six do. The arithmetic is unremarkable and almost nobody performs it.

Reading a scenario for its hidden conjunctions

The practical technique is to count the conditions. Take the story apart into the claims that must each be true for it to happen, and ask whether you would bet on each one separately. If there are five and you would give each a fair chance, the compound claim is weak however good the narrative sounds.

Then check whether the conditions are genuinely separate, since they often share a cause, in which case the naive multiplication understates the joint probability. Both mistakes are common and they push in opposite directions, which is a reason to be explicit about the structure rather than to apply a rule of thumb about detail.

When detail is legitimate

None of this means specific forecasts are worse than vague ones. A specific claim is more useful precisely because it is riskier: it can be scored, it can be prepared for, and it commits the person making it. The error is not in adding detail but in letting the detail raise your confidence.

There is also a case where detail genuinely should raise your probability, and it is worth naming so the rule is not applied blindly. If the added element is evidence rather than a further prediction — something already known to be true — then it is not a conjunction at all, and it can properly make the remaining claim more likely. The test is whether the detail is something that has happened or something that still has to.