↩ ExploRational · A Catalogue of Divergent Rationality
explorational · a divergent move
Show two opposed people the same mixed evidence and both walk away more convinced. “Be fair” does nothing. One procedural question — suppose the reverse were true: what would I expect to see? — measurably breaks the machine. Why does a procedure work where an exhortation fails?
In 1979, Lord, Ross and Lepper handed proponents and opponents of capital punishment the same pair of studies — one finding a deterrent effect, one finding none. Each camp rated the congenial study sound and the uncongenial one methodologically shaky, and both left more convinced than they arrived: mixed evidence drove opposed readers further apart. The paper named the mechanism biased assimilation — the evidence was shared; the scrutiny was not.
Five years on, Lord, Lepper and Preston tested two repairs. Instructing subjects to be unbiased changed nothing. Instructing them to ask, study by study, whether they would have made the same evaluation had the results pointed the other way eliminated the effect. The mechanism involves no dishonesty: each side takes friendly results at face value and works hostile ones over until a flaw turns up — one always does — so identical evidence lands with unequal weight. The instrument below builds that machine from arithmetic and hands you both 1984 switches side by side.
the signature instrument
Two readers, opposite priors on one claim, the same stream of studies. Congenial studies are banked whole; uncongenial ones are scrutinized down to λ of their weight — that single asymmetry is the entire machine. Every number below computes live from that rule.
The same studies, read twice
—
going through the motions ↤ · λ_eff = λ + s·(1−λ)
uncongenial studies keep λ of their weight
readers start at ± half this, in log-odds
50 = dead even · away from 50, the stream truly favors a side
equal quality throughout: each study worth ±0.40
the machine
Run the default: forty studies, dead even, each worth 0.40 log-odds. Reader A banks each pro study whole and shaves each con study to 0.16; reader B does the reverse. That asymmetry nets each reader 0.24 log-odds per pro-and-con pair, in opposite directions: A finishes at 99.7%, B at 0.3% — 11.6 log-odds apart where their priors justified 2.0.
More information therefore often fails to close a disagreement: a mixed stream is fuel to a biased assimilator — every batch supplies congenial material to bank and uncongenial material to discount, so both camps strengthen, and each ledger shows only diligence.
what to try
Polarize two honest readers on identical evidence. Load the polarization machine: A ends at 99.7%, B at 0.3% — the gap grows 2.0 → 11.6 on forty studies whose net weight is zero. Flip consider the opposite: both end where their priors put them, ±1.0, hugging the dashed line — the stream had nothing net to teach, and nobody now claims it did.
Try the exhortation, then the sincerity slider. Click “be unbiased”: the note prints the unchanged numbers. Turn the procedure on and drag sincerity: 50% ends the gap at 6.80; 10% at 10.64. Polarization shrinks by exactly the sincerity you spend — growth = 9.6 × (1 − s).
Let the evidence actually be one-sided. Load the one-sided preset, procedure on: A ends +10.6, B +8.6 — both past 99.9%; symmetric scrutiny flattened nothing real. Procedure off: A overshoots to 12.52 while B drags to 4.76, crossing only at study 24. Drop λ to 0.10: B ends at −2.92 — more certain of the losing side, unreachable by an 80/20 stream.
a procedure, not a virtue
The 1984 question works because it is executable. Would I rate this study the same if its result pointed the other way? takes an input — the study in front of you — runs an operation — your own scrutiny, aimed for once at your own side — and returns one weight, whoever it favors. In the engine that is λeff → 1: flip the toggle and the trajectories snap parallel to the dashed line, ending a prior’s-width apart instead of fanning away.
“Be unbiased” fails because it has no operand. Biased assimilation does not feel like bias from the inside; it feels like reading carefully. The exhortation addresses a mood, and the mood was already fine: subjects told to be fair complied, in their own eyes, while their weights moved as before. The procedure addresses the next study on the desk: a computation in place of a virtue.
model
One update rule, disclosed. Belief is log-odds L. A study favoring direction d = ±1 carries weight w = 0.40 — a likelihood ratio near 1.5, an unremarkable study. If it agrees with the reader’s current lean, L ← L + w·d; if it opposes, L ← L + λeff·w·d, with λeff = λ + s·(1 − λ): λ the scrutiny discount, s the sincerity of the procedure. On an even, crossing-free stream the gap grows by exactly N·w·(1 − λeff) — polarization falls linearly, and only linearly, with sincerity.
Calibration is directional: the engine reproduces the structure of the findings — polarization from mixed evidence (1979); elimination under the procedure, nothing under the exhortation (1984) — not their effect sizes, which lived on attitude scales. Mark what symmetry declines to do: shared evidence never shrinks the prior gap; the procedure only stops it growing. When the stream truly favors a side, accumulated weight swamps both priors and both readers land there — whichever side wins under the procedure won by evidence.
the move ↔ the machine
| In the engine | At your desk |
|---|---|
| the prior ±L₀ | the side you already hold — the lean every new study is measured against. |
| a congenial study | evidence that flatters your side: waved through, banked at face value. |
| the discount λ | the extra scrutiny the other side’s evidence gets — “the methodology looks shaky” — until only λ of its weight survives. |
| polarization | both camps strengthened by the same facts — the gap grown past what the priors justified. |
| the procedure | running your scrutiny against your own side too: one weight per study, whoever it favors. |
| token opposition | the ritual version — question asked, discount kept; sincerity near zero, machine untouched. |
how this opening fails
risk · token opposition
The move’s named risk. Considering the opposite in name only leaves λ where it was: at sincerity 0.10 the gap still ends at 10.64 of its unbidden 11.60 — the ritual bought back less than one log-odd. Polarization shrinks by (1 − s), exactly; a consider-the-opposite performed for the record changes nothing and adds a certificate of fairness to the same machine.
boundary · symmetry is not both-sidesism
On the 80/20 preset the procedure delivers both readers past 99.9% on the same side — lopsided evidence stays lopsided, and must. The procedure symmetrizes scrutiny; it never tops up the weaker side. Handing the underdog extra weight would be a new bias installed in the name of removing one.
model · λ is stylized
A single λ stands in for discounting that varies, in life, by person, topic, and stakes; studies arrive as independent, equal-weight, honestly reported units; log-odds add as if the readers were otherwise ideal Bayesians. The direction of every demonstration survives those simplifications; the exact numbers do not pretend to — shaped to the 1979 and 1984 findings, not fitted to them.
Point the same skepticism at your own side — fairness is a procedure, not a mood.
can you use it?
RECOGNITION — Which is consider-the-opposite? A: assigning a colleague to argue against you. B: asking yourself, before concluding, 'suppose the reverse were true — what would I then expect to see?' C: listing pros and cons.
B. It is a solo procedure that redirects your own search machinery at the evidence it skipped. A is the devil's advocate (a role); C is a tally, not a reversal.
THE NEAREST NEIGHBOR — The devil's advocate also introduces opposition. What distinguishes consider-the-opposite from it?
Who performs it. Consider-the-opposite is a procedure you run in your own head; the devil's advocate is a social role assigned to someone. The first debiases the thinker; the second stress-tests a group.
PRODUCTION — You are convinced a candidate is the strongest applicant. Run the procedure: name two things you would expect to observe if the opposite were true, then check whether you actually have that evidence.
A version: if they were weak, I'd expect vague answers on specifics and reference checks that hedge. Do I have their specifics, or did I fill gaps with their confidence? Yours works if the reversal names observable evidence, not a feeling.