Every prompting guide tells you to put your constraints in priority order. None of them says what precedence is for. It is for deciding which of your instructions gets broken — which only matters once no output can satisfy them all, and that is a question you can answer exactly.
Make the answer a small object (length, tone, format, language, code, greeting) and there are 576 of them. Make the request a small object too and there are 36. Every instruction is now a predicate: a set of situations it fires in, and a set of the 576 answers it permits.
function satSet(active, out){
out.set(ALL_ONES);
for (const a of active) bsAnd(out, a.m, out); // commutative, associative
return out;
}
Feasibility is a set intersection, so it cannot depend on the order of your rules — asserted, not argued, bit-identical under reversal on 2,160 checks. Every number below: https://dev48.infy.uk/prompt/day69-instruction-precedence.html
The dumbest strategy ties the best one, exactly
Twelve rules, 400 prompts, all 36 situations each: 14,400 cases, exhaustive.
| strategy | tok/call | broke a critical rule | whole-set obedience | collateral |
|---|---|---|---|---|
| as written | 222.5 | 7.25% | 94.3% | 0.0% |
| sort the critical rules last | 222.5 | 2.78% | 94.3% | 0.0% |
| print "(priority n)" on all twelve | 270.5 | 3.83% | 94.3% | 0.0% |
| delete the conflicting rule | 184.2 | 1.27% | 88.5% | 20.2% |
| attach an exception clause instead | 229.7 | 1.27% | 92.4% | 5.3% |
| keep only the critical rules | 74.5 | 1.27% | 67.6% | 68.8% |
Three strategies land on the identical 183 of 14,400 cases, to the last one. That is not luck: once the critical rules are intact and satisfiable, a critical rule can only break where the critical rules contradict each other, which is a property of what you marked critical and not of what you did about it. 1.27% is a floor, and the cheapest way to reach it is a two-minute deletion.
Which is why the careful fix has to justify itself on the next column along. A single-column scoreboard would have made "delete nine rules" the best idea on the page.
The free re-order also beat the paid annotation outright — 2.78% against 3.83% at +48 tokens on every call, forever. Stacking them recovers 0.069 points.
What the measurement contradicted
Three things, and I built the page around the first one being wrong.
I wrote the numbering strategy expecting it to win, with re-ordering as the cheap control. It lost twice: worse than the free fix alone, and worth 0.069 points on top of it. The mechanism is legible once measured — a numbered prompt is still in whatever order it grew in, so its printed priorities fight its own recency, while sorting makes the two agree for nothing.
I assumed over-constraint was the failure mode. Twelve rules leave 70.3 of 576 answers standing and pin 0.00% of cases to exactly one answer. The story about long prompts squeezing the space to a point is not what happens. Contradiction is what happens: only 4.47% of rule pairs clash, but twelve rules is 66 pairs and 1 − (1 − 0.0447)⁶⁶ is 95.1%, measured 90.8%.
And an assertion failed once in 5,400. Chasing it turned up something the page had no idea about: the maximum score is shared by more than one answer in 100% of cases, because the instructions that fire never constrain every attribute. So the answer you get is decided by something not in your prompt at all. The assertion asked for index equality; it now asserts score-optimality and counts the ties.
5,920 in-page assertions, 38,773 in the verifier.
Part of a from-scratch series — one prompting technique a day, measured rather than described: https://dev48.infy.uk/promptfromzero.php
