Learned helplessness: a belief that stops you trying never meets the evidence¶

Level: 101 · for anyone who has failed at something often enough to stop trying

One line: A learner who judges "does trying work?" from their own record, with nothing but honest counting, becomes helpless after enough failures, and stays helpless even after the world changes, because only a try adds to the record. The cure is not to believe harder but to make trying cheap enough to restart the record: a small step, or someone like you succeeding.

The experiment¶

Chapter 2 of Todd Zakrajsek's The New Science of Learning (third edition, 2022), "Discovering Yourself as a Learner", tells the story. In 1975 Donald Hiroto and Martin Seligman gave college students a loud noise. One group had a button that stopped it; the other had a button that did nothing. Later, in a room where a lever on the wall stopped the noise, the first group quickly found the lever. The second group mostly did not look. They had learned to be helpless: when trying has not worked before, there is no reason to think it will work now. The book's everyday versions are the student who has failed statistics twice and stops enrolling, and the reader of astronomy books who rules out a science major after bad science grades at school.

The book's point is that this is not a character flaw. A strong, intelligent person can be trapped in a situation an outsider thinks is easy to escape. The program shows why: helplessness is what honest counting produces, once the counting has stopped.

Judging from a record¶

Section 1 gives the learner the simplest fair rule for "how likely is it that trying works?", Laplace's rule of succession: after s successes in n tries, estimate

(s + 1) / (n + 2)

With no evidence that is ½. One failure brings it to ⅓, not to 0; ten failures in a row bring it to 1/12. The learner then tries a task only when the estimate is worth the effort, here when it reaches 3/10. That is the whole model: a count and a threshold.

Verified output of learned_helplessness.py — regenerated by tools/run_examples.py, never hand-typed.

1. Judging from a record: the rule of succession

   After s successes in n tries, estimate the chance of success as
   (s + 1) / (n + 2). No evidence gives 1/2; each try moves it.

   record            estimate
    0 of 0  worked      1/2 = 0.50
    1 of 1  worked      2/3 = 0.67
    0 of 1  worked      1/3 = 0.33
   10 of 10 worked    11/12 = 0.92
    0 of 10 worked     1/12 = 0.08
    5 of 10 worked      1/2 = 0.50

   One failure gives 1/3, not 0. Ten failures in a row give 1/12.

2. The experiment: ten button presses, then twenty rounds at a lever

   Both learners try the lever only if their estimate is at least 3/10.
   The lever always works. What differs is what the button taught them.

   A, whose button worked
     estimate after the button:   11/12 = 0.92
     rounds in which it tried:   20 of 20
     estimate after 20 rounds:    31/32 = 0.97

   B, whose button did nothing
     estimate after the button:    1/12 = 0.08
     rounds in which it tried:   0 of 20
     estimate after 20 rounds:     1/12 = 0.08

   B's estimate never moves, because only a try produces evidence.
   The lever works every round, and B never finds out. Nothing in B's
   reasoning is wrong: 1/12 is the right conclusion from B's record.
   What is wrong is that the record stopped growing.

3. Remedy one: start small

   A small step is worth trying at a chance of 1/20, and 1/12 is above
   that, so B tries small steps. Each succeeds and joins the record.

   small successes   estimate      worth a real task?
          0            1/12 = 0.08   no
          1            2/13 = 0.15   no
          2            3/14 = 0.21   no
          3            4/15 = 0.27   no
          4            5/16 = 0.31   yes

   4 small successes undo ten failures enough to try the real thing.

4. Remedy two: watch someone similar succeed

   Another person's success counts as evidence in proportion to how much
   like you they are: weight 1 for a classmate in your situation, less
   for someone you do not identify with.

   weight   successes watched before a real try is worth it
        1   4
      1/2   8
      1/4   15
     1/10   38

   Study Tip 2.2 in numbers: ask someone like you to show you.

5. Two forms of pessimism as two ways of counting

   Pervasiveness: filing the button's ten failures under 'trying never
   works', so they count against the lever too. Kept apart, the lever
   starts with no record, estimate 1/2, and B tries it at once.

   Permanence: treating old evidence as if the world never changes. Let
   each round shrink the old record by a factor of 9/10 instead:

   round   old failures still counted   estimate
       0          10.00                0.08
       5           5.90                0.13
      10           3.49                0.18
      15           2.06                0.25
      20           1.22                0.31

   Believing 'this is how it will always be', B waits forever; letting
   the past fade, B tries the lever after 20 rounds, without any new
   success at all.

6. The ABC example: one flunked biology exam

   Belief: 'I am stupid, and I might as well drop out of college.'
   That is a claim about every subject, for ever, with chance 0.
   The record is one biology exam, 0 of 1:  biology estimate 1/3.
   After help and one passed retake, 1 of 2: biology estimate 1/2.
   Reframed: 'I am not doing well on biology exams right now, and could
   use some help.' That is the belief the evidence supports.

Why B never finds the lever¶

Section 2 runs the experiment. Learner A's button worked ten times, so A's estimate is 11/12, A pulls the lever in every round, and every pull succeeds. Learner B's button failed ten times, so B's estimate is 1/12, below 3/10, and B never pulls. The lever works in every round of the twenty, and B's estimate after twenty rounds is still exactly 1/12.

B's reasoning has no mistake in it. Given B's record, 1/12 is the right estimate. The trouble is structural: evidence about trying comes only from trying. A belief low enough to stop you trying cuts off the only evidence that could raise it, so it stays where it is however much the world changes. The book puts it the same way: someone who has not escaped before "has no reason to believe the situation has changed unless advised otherwise".

This is the same loop the metacognition lesson found, turned round. There, a feeling of knowing kept a student from testing themselves. Here, a feeling of not being able to keeps a learner from testing the world.

The two remedies, in numbers¶

The book offers two ways to rebuild self-efficacy, and the program shows why both work: each lets evidence back in without asking the learner to believe anything they have no reason to believe.

Start small (section 3). A small step costs little, so it is worth trying even at a chance of 1/12. Each small success joins the record, and after four of them the estimate is 5/16, enough to try the real task. This is Study Tip 2.1 from the chapter page: start as small as necessary, but finish what you set.

Watch someone similar succeed (section 4). Someone else's success is evidence too, counted in proportion to how much their situation is like yours. Four successes by a classmate in your position are worth as much as four of your own; someone you do not identify with, counted at a tenth, takes 38. That is why the book says to share a similar person's success, and why Study Tip 2.2 says to ask someone to show you.

Pessimism as bad bookkeeping¶

The book lists three distortions behind negative thoughts, after Seligman's Learned Optimism: personalization (this is all my fault), pervasiveness (this will spoil everything else too) and permanence (it will always be like this). Two of them are ways of counting evidence, and section 5 changes each one:

Pervasiveness files the button's ten failures under "trying never works", so they count against the lever too. Kept apart, as evidence about buttons, they leave the lever with no record, estimate ½, and B tries it at once.
Permanence keeps old evidence at full weight for ever, as if the world could not change. Let the old record fade by a tenth each round and B tries the lever after twenty rounds, without a single new success.
Personalization files the failure under "me", and "me" goes everywhere you go. That is what makes it pervasive and permanent at once.

The ABC technique¶

To unlearn this, the book adapts Albert Ellis's ABC technique: an Antecedent (an event) prompts a Belief about yourself, which leads to a Consequence (what you do). Change the belief and the consequence changes. The example: you flunk a biology exam (A), think "I am stupid, and I might as well drop out" (B), and withdraw (C). Section 6 checks the belief against the record. It claims something about every subject, for ever, with a chance of 0; the evidence is one biology exam, and the rule of succession gives biology ⅓. The reframed belief, "I am not doing well on biology exams right now, and could use some help", is not a kinder story. It is the belief the evidence supports, and it leads to a different C: get help with biology.

What the program does not show¶

The learner is a model. People do not compute (s + 1)/(n + 2), the threshold of 3/10 and the fading factor of 9/10 are chosen for the example, and no number here is a measurement of anyone. What the model shows is the structure: a rule that never tries below a threshold can never learn it was wrong, whatever the numbers. The research the book cites, from Seligman's early studies to his Learned Optimism (1990) and the positive psychology that followed, is about people, and the resources page lists the books.

Try it¶

Find your button. Name one thing you stopped trying because it failed before. How many tries is your record, and when was the last?
Separate the files. Write the failure as narrowly as the evidence allows: which course, which kind of exam, which month.
Pick the small step. Something cheap enough to try at a low chance, that produces a success or a failure you can count.
Change the numbers. Set BIG_COST to 1/2 and rerun: how many small successes does B need now?

Flashcards¶

The page as a deck of Anki cards: learned_helplessness.txt. Import with File → Import. Tags: definition, experiment, remedy, pessimism, trap.

Po polsku, w skrócie¶

Wyuczona bezradność (Seligman) to stan, w którym ktoś przestaje próbować, bo wcześniej próby nie działały. W doświadczeniu Hiroto i Seligmana z 1975 roku studenci, których przycisk nie wyłączał hałasu, później nawet nie szukali dźwigni, która go wyłączała.

Program pokazuje, że do bezradności nie potrzeba żadnego błędu w rozumowaniu. Wystarczy uczciwe liczenie: po s sukcesach na n prób szansa wynosi (s + 1)/(n + 2), a próbujemy tylko wtedy, gdy szansa jest dość duża. Po dziesięciu porażkach szacunek spada do 1/12 i uczeń przestaje próbować. A ponieważ dowody o próbach daje tylko próba, szacunek już nigdy się nie zmienia, nawet gdy dźwignia działa za każdym razem.

Wyjścia są dwa i oba wpuszczają nowe dowody. Małe kroki: tanią próbę opłaca się podjąć nawet przy małej szansie, a cztery drobne sukcesy wystarczą, żeby znów spróbować czegoś dużego. Cudzy sukces: gdy ktoś podobny do nas dał radę, to też jest dowód. Trzy formy pesymizmu (to moja wina, to zepsuje wszystko, tak będzie zawsze) to błędy księgowe: porażka z jednej sprawy trafia do akt „ja", które obowiązują wszędzie i na zawsze. Technika ABC każe sprawdzić przekonanie z dowodami: jeden oblany egzamin z biologii mówi coś o biologii, teraz, a nie o wszystkim, na zawsze.