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Psychologists Don't Know Math

Posted by Zonk on from the one-plus-one-equals-your-mother dept.

stupefaction writes "The New York Times reports that an economist has exposed a mathematical fallacy at the heart of the experimental backing for the psychological theory of cognitive dissonance. The mistake is the same one that mathematicians both amateur and professional have made over the Monty Hall problem. From the article: "Like Monty Hall's choice of which door to open to reveal a goat, the monkey's choice of red over blue discloses information that changes the odds." The reporter John Tierney invites readers to comment on the goats-and-car paradox as well as on three other probabilistic brain-teasers."

1 of 566 comments (clear)

  1. Re:The problem is a fallacy by daveime · · Score: 0, Troll

    No, No and No ... your chances to choose the car are NOT 1/3, because monty will ALWAYS eliminate one goat ...

    I get so tired of this one, so here's the truth table I always trot out.

    We have 3 doors numbered 1,2,3 ... the car (C) is behind one, and the goats (G) are behind the other two. Whichever one I choose, Monty is constrained to open one of the remaining doors that has a goat behind it. Then I may choose to change or not to change.

    I apologise for the font, only way to preserve the formatting.

    1 2 3 You Monty Change WIN/LOSE

    C G G 1   2     NO     WIN
    C G G 1   2     YES    LOSE
    C G G 1   3     NO     WIN
    C G G 1   3     YES    LOSE
    C G G 2   3     NO     LOSE
    C G G 2   3     YES    WIN
    C G G 3   2     NO     LOSE
    C G G 3   2     YES    WIN

    G C G 1   3     NO     LOSE
    G C G 1   3     YES    WIN
    G C G 2   1     NO     WIN
    G C G 2   1     YES    LOSE
    G C G 2   3     NO     WIN
    G C G 2   3     YES    LOSE
    G C G 3   1     NO     LOSE
    G C G 3   1     YES    WIN

    G G C 1   2     NO     LOSE
    G G C 1   2     YES    WIN
    G G C 2   1     NO     LOSE
    G G C 2   1     YES    WIN
    G G C 3   1     NO     WIN
    G G C 3   1     YES    LOSE
    G G C 3   2     NO     WIN
    G G C 3   2     YES    LOSE

    So, a 24 state truth table ... now examine the last two columns.

    In 6 cases, you stay with your original choice, and you WIN
    In 6 cases, you stay with your original choice, and you LOSE
    In 6 cases, you switch your choice, and you WIN
    In 6 cases, you switch your choice, and you LOSE

    So ...

    In the 12 cases where you stay with your original choice, 6 are WINS, 6 are LOSE
    In the 12 cases where you switch your choice, 6 are WINS, 6 are LOSE

    50:50 ... always was, always will be.