Please tell me which you think is more probable:I went with A on the grounds that in many cases economic development takes place despite rather than because of "wise and capable leadership". Such leadership may be useful but seems to be neither necessary nor sufficient for development.

(A) a country succeeds at economic development, or

(B) a country succeeds at economic development with a wise and capable leadership.

Anyway, go vote!

Update: Given the bet discussed in the comments section the following comes from Bill Easterly's blog:

On one level, A is the right answer, because B is a subset of A. A contains all successes, both (1) those achieved with wise leadership, and (2) those achieved with any other means. B only contains (1), and so is less likely than A. Well known psychology experiments find the same thing -- that many people have what is called the “conjunction fallacy” (again from my continuing Mlodinow and Kahneman obsession) that would cause them to choose (B). A set of outcomes that fits a plausible story is thought to be larger than one unrestricted by ANY story, even though ANY restriction on the set of possible outcomes always makes that set less likely than an unrestricted set. An explanation usually trumps no explanation, even if it gets the probabilities wrong!But he then writes

But on another level, the reaction of many readers made me aware of how I had phrased the alternatives too sloppily, which taught me something about how the language we commonly use is often fuzzy on exactly what probabilities we are talking about. I think many of those who voted B were interpreting the question differently: when is development success more likely? With good leadership (B)? Or when the quality of the leadership is unspecified, and so could be either good or bad (A)? Obviously (B). Neither our brain wiring nor our education is good enough to give us linguistic precision about probability and randomness. So my sloppy language created a coalition in favor of (B) between an incorrect answer and a correct answer!

## 12 comments:

Paul, it's a math problem. Think about it. Say X is economic development and R is wise leadership. Then

p(X)> p(X)*p(R)

What if, what Easterly is trying to get at is p(X)+p(R). It depends on the relationship between X and R.

Nah, it's a math problem. He didn't say "conditional on", he said "with". $50 bet if you're up for it.

X|R>X|~R but p(X) >> p(X)*p(R)

How do we determine a winner?

Contract on iPredict.

"This contract pays $1 if Paul is right"

Closing price is the last traded price at a set date.

I wonder if it'd work.

Isn't the correct formulation:

1) P(succeed | randomly picked leader wisdom/capability from distribution); vs

2) P(succeed | wise leader)

Perhaps the forumulation debate is Easterly's point.

Contract on iPredict.

"This contract pays $1 if Paul is right"

Then pay the dollar now! I'm always right!!! :-)

I'm sure Easterly will reveal the answer. If he doesn't, no resolution to bet. If Easterly says it's just a math problem, I win.

Matt: The first I read as unconditional probability; the second, conditional.

Crampton: but since every country has a leader, the first is also implicitly conditional.

And shouldn't your formulation be:

p(X) >> p(X|R)*p(R)

instead of

p(X) >> p(X)*p(R)

If so, then >> is not true.

Matt: your version's better than mine, yup.

p(X) >> p(X|R)*p(R)

especially since p(R)=lim x-->0

http://en.wikipedia.org/wiki/Conjunction_fallacy

http://www.overcomingbias.com/2007/09/conjunction-fal.html

So either I win the bet or the wording was too ambiguous for it to be called.

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