Monday, January 09, 2012

Rank these possibilities by probability

Susan is 28 years old, single, outspoken, and very bright. She majored in philosophy. As a student she was deeply concerned with issues of discrimination and social justice and also participated in anti-nuke demonstrations.

Please rank the following possibilities by their probability. List them LOW to HIGH. (Just post your answers. Other comments I may block so that others can enjoy the question.)

1. a kindergarden teacher
2. works in a bookstore and takes yoga classes
3. an active feminist
4. a psychiatric social worker
5. a member of the Sierra club
6. a bank teller
7. an insurance salesperson
8. a bank teller and an active feminist

1. There is no question in the post...

2. LOW

an insurance salesperson
a bank teller
a bank teller and an active feminist
works in a bookstore and takes yoga classes
a kindergarden teacher
a member of the Sierra club
an active feminist
a psychiatric social worker

HIGH

3. Near-zero probability (ascending)
1,4,7,8,6

Nonzero probability (ascending)
2,5,3

4. an insurance salesperson
a kindergarden teacher
a bank teller
a member of the Sierra club
works in a bookstore and takes yoga classes
an active feminist
a psychiatric social worker
a bank teller and an active feminist

5. 1,2,8,3,4,7,5,6

6. 3, 5; (then the rest are much less likely) 1, 2, 4, 6, 7, 8.

7. Can you please make the post clear. What are these possibilities for?
Is it about "She will marry a person who is"
1)
2)

8. ``There is no question in this post.''

was a question, though it may depend on how you define `question' .

9. `Can you please make the post clear...'

I mean the probabilities that SHE is
a kindergarden teacher, etc.

10. LOW
A bank teller and an active feminist
A bank teller
Works in a bookstore and takes yoga classes
A kindergarden teacher
A member of the Sierra club
A psychiatric social worker
An active feminist
An insurance salesperson
HIGH

11. It's clear that Anonymous at 9:18am is trolling, saying that women will marry and not work.

My ranking:

low

an insurance salesperson
a member of the Sierra club
a kindergarden teacher
works in a bookstore and takes yoga classes
an active feminist
a bank teller
a psychiatric social worker
a bank teller and an active feminist

high

Perhaps this is a trick question and Susan is actually a PhD in computer science. (Yes, I know at least one philosophy major who is now an assistant professor of computer science.)

12. a bank teller and an active feminist
an active feminist
a member of the Sierra club
works in a bookstore and takes yoga classes
a psychiatric social worker
a bank teller
an insurance salesperson
a kindergarden teacher

(Drago)

13. Susan does not have a PhD or a Masters or a Bachelors in Comp Sci or math. Don't try to outthink the question.

14. Low
- an insurance salesperson
- a bank teller
- a kindergarden teacher
- a psychiatric social worker
- a bank teller and an active feminist
- works in a bookstore and takes yoga classes
- a member of the Sierra club
- an active feminist
High

There is a mixture between vocation and beliefs embedded that make it a little hard to balance nicely. I assumed the lack of information was relevant, and that the order of the description was important.

Just a guess :-)

Paul.

15. my list, now with estimates:

2-3 orders of magniture smaller than the top choice below:

a bank teller and an active feminist

1-2 orders of magnitude smaller than the top choice below:

an active feminist
a member of the Sierra club

1 order of magnitude smaller than the top choice below:

works in a bookstore and takes yoga classes

slightly less likely than the top choice below:

a psychiatric social worker
a bank teller
an insurance salesperson

top choice (on the order of 1-2%)

a kindergarden teacher

16. This comment has been removed by a blog administrator.

17. a kindergarden teacher
works in a bookstore and takes yoga classes
an active feminist
a bank teller
an insurance salesperson
a bank teller and an active feminist
a member of the Sierra club
a psychiatric social worker

18. Sorry people, my prognosis is more pessimistic:

a member of the Sierra club
an active feminist
works in a bookstore and takes yoga classes
a kindergarden teacher
a bank teller
a bank teller and an active feminist
an insurance salesperson
a psychiatric social worker

19. HIGH
a kindergarden teacher
a psychiatric social worker
a bank teller
works in a bookstore and takes yoga classes
a member of the Sierra club
an insurance salesperson
an active feminist
a bank teller and an active feminist
LOW

I think there is almost no correlation between Susan's believes while studying and a job she lands. So tried to sort it assuming her competence and likelihood of jobs and convictions.

20. LOW

a bank teller
a bank teller and an active feminist
an insurance salesperson
a kindergarten teacher
a psychiatric social worker
works in a bookstore and takes yoga classes
a member of the Sierra club
an active feminist

HIGH

21. I'll take a stab at a subset, the job she has. While its possible to get a teaching certificate or a psych degree, you don't mention anything beyond the philosophy degree (though it seems that anyone majoring in philosophy is going to have a vocation NOT in philosophy WHP); so low to high:

psychiatric social worker
kindergarten teacher
an insurance salesperson
bank teller
works in a bookstore and takes yoga classes

The top three don't require any degrees so I ranked them more likely. Unfortunately, you placed two seemingly independent events (vocation and personal interests) into one choice, but I'll ignore it for now.

Independently considering the rest, low to high:

bank teller and active feminist
an active feminist
a Sierra Club member

The conventional wisdom might say that banking and feminism may be incompatible, but we're only talking about a teller position, not a CEO or someone in a position to cause real harm. Sierra Club membership is "easy": donate a few bucks and you're a member; you did not say "active" member so I assume that since its "easy" it has a higher probability.

22. LOW
a kindergarten teacher
an insurance salesperson
a bank teller and an active feminist
works in a bookstore and takes yoga classes
a member of the Sierra club
a bank teller
a psychiatric social worker
an active feminist
HIGH

23. LOW

dentist
presidential candidate
pediatrician
journalist
mechanical engineer
senator
tennis player

HIGH

24. LOW

7. an insurance salesperson
1. a kindergarden teacher
4. a psychiatric social worker
6. a bank teller
8. a bank teller and an active feminist
2. works in a bookstore and takes yoga classes
3,5. an active feminist, a member of the Sierra club

HIGH

25. high to low
8 1 2 4 3 6 5 7

26. LOW

works in a bookstore and takes yoga classes
a bank teller and an active feminist

a psychiatric social worker
a kindergarden teacher
a bank teller
an insurance salesperson

a member of the Sierra club

an active feminist

HIGH

27. Lo<7<6<8<1<2<4<5<3<Hi

28. I don't understand the question ?
rank answer choices by probability ? but wat is the question ?

29. Low

an active feminist
a member of the Sierra club
a psychiatric social worker
a bank teller and an active feminist
an insurance salesperson
a bank teller
works in a bookstore and takes yoga classes
a kindergarden teacher

High

30. With the ranking period now almost done, let's see if we can guess why GASARCH regards this question as being interesting.

My own guess is that GASARCH is interested in how humans rank probabilities in comparison to how WATSON ranks probabilities.

In particular, we have the following mathematically rigorous ordering constraint:

LOWER PROBABILITY
(8) bank teller and feminist
(having strictly lower probability than each of)
(3) bank teller
(6) feminist
HIGHER PROBABILITY

But that is not how humans think -- humans instinctively aggregate probabilities into narratives. That is why some of the guesses on this post have illogically ranked (8) as having higher probability than (6) and/or (3).

My guess as to the point of GASARCH's post is simply this: IBM's Watson ranks probabilities illogically too, and thus (in effect) incorporates some kind of human-type narrative synthesis algorithm. And moreover (my guess is that) this illogical-ranking algorithm has turned out to be essential to Watson's overall answer-guessing capacity.

The common-sense point being, that future generations of Watson will need a narrative-construction skill if it is ever to function effectively in providing medical diagnostic services. Perhaps for IBM, the surprising lesson of the Jeopardy challenge has been that probability-ranking algorithms are wholly inadequate to the task of constructing explanatory narratives.

31. For some reason, this reminds me of a question that Bill G. once posed me:

Bill: There are 30 faculty in our dept. What is the probability that some two of them share a birthday?

Me: Umm...65%?

Bill: No, it's probability 1 since there are two faculty in our dept. who share a birthday.

32. My preliminary guess was that close to half of the respondents would mark "bank teller and active feminist" as more probable than either of "bank teller" or "active feminist" alone. This would be consistent with previous research in cognitive biases.

33. LOW
works in a bookstore and takes yoga classes
a bank teller and an active feminist
a kindergarten teacher
a psychiatric social worker
an insurance salesperson
a bank teller
a member of the Sierra club
an active feminist
HIGH