Choices and Considerations

Check your thinking

Is your mind leaning without telling you?

Try it

  1. Step 1, the number rule
  2. Step 2, the movie
  3. Step 3, the arch
  4. Step 4, the plans
  5. Step 5, the ranges

1 The number rule

I have a rule for three numbers. 2, 4, 6 fits it. Test sets of your own to find the rule, as many as you like.

    When you think you know it, pick the rule.

    What just happened

    Each step was a classic experiment, cut down to a few seconds. Your lean on the wall came from your own answers. A few answers from one person cannot prove a bias. The studies below come from many people, and they do not all hold up equally well.

    Why your wall is not a verdict

    Each step took one answer, from one person, on one day. Ask again next week and you might answer the other way. So a lean on your wall is a hint about where to look, not a finding about you.

    Studies get around this by comparing many people. In the arch step, visitors here get a high or a low number at random. One guess cannot show anchoring. Across many people, those shown a high number guess higher than those shown a low one (Klein and others, 2014).

    StepWhat it testsHow well it holds upYour wall
    The number ruleConfirmation: testing only what you expect to passIn Wason’s 1960 study, 6 of 29 people named the rule on their first try. Nearly all the wrong rules were narrower ones, such as “increasing intervals of two”.Not tried yet
    The movieSunk cost: money already spent steering what you do nextReal but small. When 36 labs reran a sunk cost study in 2014 with 6,344 people, it showed up again, about as small as first reported, and was clear in only half of the 36 samples (Klein and others, 2014).Not tried yet
    The archAnchoring: a first number pulling your guess toward itHolds up strongly. In the same 2014 rerun, all four anchoring questions came back large, larger than the original report. Experienced legal professionals were pulled by a sentence demand they rolled with dice themselves (Englich, Mussweiler and Strack, 2006).Not tried yet
    The plansFraming: the same facts, worded as gains or as lossesReal, but smaller than first reported. In 1981, 72% of 152 people chose the sure plan when it said “saved”, and 78% of 155 chose the gamble when it said “die” (Tversky and Kahneman). The 2014 rerun found the effect again at about half its original size.Not tried yet
    The rangesOverconfidence: ranges drawn too narrowOne of the steadiest findings. In studies like this one, ranges people call 90% sure catch the right answer less than half the time (Moore and Healy, 2008).Not tried yet

    Why testing what fits feels like proof

    Testing sets you expect to pass is not foolish. Klayman and Ha (1987) showed it is often a good strategy. It fails when your guess sits inside the real rule, the way “up by 2” sits inside “any numbers that go up”. Then every test you expect to pass does pass, and none of them can tell you that you are wrong.

    Each dot is a set of three numbers. Sets inside the smallest box fit “up by 2”, and they all fit the real rule too.

    What helps

    Three habits push back. The first is to consider the opposite: before you settle, ask what would show you are wrong, then go and look for it. In the number rule, that means testing a set you expect to fail. In two experiments, telling people to consider the opposite cut bias more than telling them to be fair and unbiased (Lord, Lepper and Preston, 1984).

    A second example: a coworker who seems cold

    You think a coworker does not like you. Every short reply looks like proof, and the friendly ones slip past unnoticed. That is the number rule again: you are only testing sets you expect to pass.

    Consider the opposite. If they did like you, what would you expect to see on a busy day? Probably the same short replies. Now look for what would tell the two apart: count the friendly moments too, or ask them how things are.

    The second is a pre-mortem, the same move aimed at a plan. Imagine it is a year from now and the plan has failed, and write down why. Psychologist Gary Klein built the method to bring doubts out before a plan starts, not after (Harvard Business Review, 2007).

    The third is to start from the reference class: before your own story, ask how long or how much it took others in the same spot. Students guessed their honors thesis would take about 34 days on average. It took 55.5 days (Buehler, Griffin and Ross, 1994).

    Practice with feedback helps, a little, for a while. In two experiments, one game with personal feedback cut bias by 31.94% or more right away and 23.57% or more two months later; a video helped less (Morewedge and others, 2015). A 2025 review of 41 studies that taught students about biases found a small average gain (Swaryandini and others). What lasts is the habit: before you settle, ask what would prove you wrong.

    What we left out, and why

    Some famous ideas about the mind are not settled, so this room does not teach them as fact.

    The Dunning-Kruger effect
    The famous graph may be mostly a quirk of the statistics. With sounder tests on 929 people, Gignac and Zajenkowski (2020) found no sign of it, though a smaller effect may still exist for some skills.
    Social priming
    The idea that a passing cue, like a flag or a picture of money, quietly changes what people believe. In the 2014 rerun, flag priming and money priming did not replicate (Klein and others).
    Ego depletion
    Willpower as a tank that runs low. A test across 23 labs and 2,141 people found almost no effect (Hagger and others, 2016); a 2025 test across 14 samples with a much harder task found one (Dang and others). Unresolved.
    The backfire effect
    The fear that correcting a false belief makes people hold it harder. Across 52 issues and more than 10,100 people, no correction backfired (Wood and Porter).
    Growth mindset hype
    Short lessons promising big gains at school. Across 63 studies the average effect on grades was tiny and faded after correcting for bias (Macnamara and Burgoyne, 2023); another review found modest gains for the students expected to benefit most (Burnette and others, 2023).

    Where you’ll meet this

    WhereWhat pulls on youTry this
    A bad movie you paid forSunk cost. The ticket money is gone either way.Ask: would I pay right now to see the rest?
    The first price you see on a car lotAnchoring. The sticker sets the range you bargain inside.Look up what the car sells for before you go, and say your number first.
    News you likeConfirmation. A story that agrees with you feels checked.Read the best case from the other side first, then look again.
    A vivid story on the newsAvailability. What is easy to picture feels common.Ask how often it happens, out of how many, before you judge the risk.
    “95% fat free” or “5% fat”Framing. The same fact, dressed as a gain or a loss.Say it the other way round, then decide.
    “The kitchen will take two weekends”Overconfidence. Our ranges are too narrow.Ask how long jobs like this took other people, then widen your range.

    What Scripture says

    Six blind men in grey and brown cloaks walk in a line that slopes from upper left to lower right through a village, each holding a staff or the shoulder of the man ahead. The leader at the right has fallen backwards into a ditch and the next man is toppling after him; a church stands in the background.
    The Blind Leading the Blind (The Parable of the Blind), Pieter Bruegel the Elder, 1568. Museo e Real Bosco di Capodimonte, Naples. Public domainBruegel painted the parable in Matthew 15:14. Each man holds on to the one ahead, and the line slopes down into the ditch.

    There is a way which seems right to a man, but in the end it leads to death.

    Proverbs 14:12In context. There is a way that seems right to a person, but it ends in death.

    Thus he showed me and behold, the Lord stood beside a wall made by a plumb line, with a plumb line in his hand. The LORD said to me, “Amos, what do you see?” I said, “A plumb line.” Then the Lord said, “Behold, I will set a plumb line in the middle of my people Israel. I will not again pass by them any more.

    Amos 7:7-8In context. In a vision the Lord holds a plumb line against Israel to show how far it has gone crooked, and announces judgment. The true line is God’s standard, not our own; this site borrows the picture of checking against it.

    Why do you see the speck that is in your brother’s eye, but don’t consider the beam that is in your own eye?

    Matthew 7:3In context. Jesus warning against judging others: see the beam in your own eye before the speck in your brother’s.

    The way of a fool is right in his own eyes, but he who is wise listens to counsel.

    Proverbs 12:15In context. A fool’s way looks right to him; a wise person listens to counsel.

    Leave them alone. They are blind guides of the blind. If the blind guide the blind, both will fall into a pit.”

    Matthew 15:14In context. Jesus about the Pharisees, who put their traditions above God’s command: blind guides leading the blind into a pit.

    Watch

    Veritasium. 5 min. Veritasium runs the classic number-rule puzzle on strangers, showing how we test ideas by looking only for what confirms them. Open on YouTube
    Wireless Philosophy. 5 min. Yale's Laurie Santos explains anchoring: how a first number, even an arbitrary one, pulls our estimates toward it. Open on YouTube
    Marginal Revolution University. 6 min. Thinking on the margin, with everyday examples like walking out of a bad movie, shows why money already spent should not decide what you do next. Open on YouTube

    Use it on your choice

    When you score your options, the first number you write becomes an anchor for the rest. Score each option twice: once as its fan, once as its fiercest critic. Then look again.

    Score your options