The illusion of Linda

That people give the wrong answer to the question of Linda may, rather than revealing their lack of understanding of probability theory, be just another example of the power of suggestion & misdirection.

The question has much in common with that old chestnut:

How do you spell the white of an egg? Is it Y-O-K-E or Y-O-L-K?

Has anybody, I wonder, conducted randomised trials, with the subjects randomised to have the alternatives presented to them in slightly different ways.

1 A Linda is a bank clerk & an active feminist
B Linda is a bank clerk

2 A Linda is an active feminist
B Linda is an active feminist & a bank clerk

Or as originally formulated, that is

A Linda is a bank clerk
B Linda is a bank clerk & an active feminist

but with the questioner a schoolchild (or a blonde bimbo, or a little old lady) – that is not someone with the authority of an academic & the power of a teacher.

Perhaps Derren Brown could predict the outcome of such experiments.

Link
Derren Brown

Related posts
Not-so-simply connecting

Telling stories & statistics

Talking about Linda

Talking about Linda

Let’s talk about Linda.

In the beginning we are presented with 6 items of information about her which, we are invited to believe, are severally & collectively, true (P=1).

We are then invited to consider which of two further statements is more likely to be true: that she is a bank clerk or that she is both a bank clerk & a feminist.

The first statement comes as a surprise to those of us with our cultural background, or would have done before the current economic emergency: it is very unlikely (P close to zero) that someone with a philosophy degree would be working as a bank clerk. So what do we do?

Well, perhaps, carelessly forgetting that this second statement also contains the idea that Linda is a bank clerk, we just opt for the more likely second half.

Or perhaps we hurriedly revise our decision to reject the first statement (the information comes after all from someone who is an expert on Linda), but still opt for the second statement to reflect that process which we have undergone, of learning & revision in the light of new information .

But when we understand the fallacy, we might look back to the beginning. And reflect on the odd conclusion that the original introductory statement about Linda is even less likely to be true than the one which makes her both a bank clerk & an active feminist.

Probability all depends on where you stand.

We may also be reflecting what is odd, disturbing, but true: that the probability that I am me is even less than the probability that I exist at all. When the sperm met the egg, the I that I undoubtedly am carried only the tiniest probability of me.

I am what I am because of a lifetime of contingencies.

Link
Stories vs. Statistics

Related posts
Not-so-simply connecting

Telling stories & statistics

Time of birth

The contingency of life

Spermatozoa

Not-so-simply connecting

Last week on In Our Time someone mentioned how logic was transformed when Boole recognised the correspondence between AND and multiplication.

Well yes, but …

Every small child knows that one and one make two.

Three and two make five.

When you progress to the magic of multiplication, then one times one is one and two times three is six.

And still means plus.

When I was introduced to probability theory half a century ago it was through set theory & the union U or intersection ∩ of sets, which certainly helped to get it clear in my mind & so also helped me to avoid the so-called “conjunction fallacy”.

The now classic illustration of this starts with an Anchoring Vignette - a woman named Linda is described. She is single, in her early 30s, outspoken & clever, a philosophy graduate, interested in issues such as nuclear non-proliferation. When asked which of the following is more likely:

A Linda is a bank clerk
B Linda is a bank clerk and is active in the feminist movement

most people choose B. Which is the wrong answer because the probability of two things being true for the same person is found by multiplying the two probabilities together, & since a probability is a fraction, a number between 0 & 1, the product must be less than either of the two probabilities on its own – except of course when one probability is zero, in which case the chance of the two things occurring together is also zero.

While it is perhaps not surprising that those not trained in probability theory may make this mistake, it is startling that even those who do understand feel uneasy about the case of Linda. Could the theory be wrong?

TO BE CONTINUED

Links

In Our Time: Logic
Stories vs. Statistics

Related post

AND AND AND AND OR OR OR

Telling stories & statistics

No, not just another way of expressing the same old, same old canard about damn lies, but an interesting post, Stories vs. Statistics by JOHN ALLEN PAULOS from the New York Times.

One quote I particularly like: "The more details there are in a story, the less likely it is that the conjunction of all of them is true."

Coincidentally I recently heard for the first time of the technique of Anchoring Vignettes - horrible term - used in some social science research.

Interesting attempts to combine the hard ('inhuman') with the more people-friendly approach to sorting out the meaning of life.

Link
Anchoring vignettes in social science research

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Different or the same? (2)

Heteroskedacity