A few simple facts that some people find surprising the first time they hear them.

Imagine $100 is behind door A or B and I give you independent hints about which. The hint says either A or B but is right only 55% of the time.

First hint is worth $5, second hint is worth... $0!
Why? Because the second hint never makes you *want* to change your decision. (Think about the four possible hint combinations.)

This is a key idea behind a beautiful paper by Meg Meyer, here:

If you want the second hint to be useful, you need to make it biased, "favoring" the leading option, so that if it comes back a surprising negative against the leader, you might actually change your decision.

Meyer uses this to derive implications about organizations.

Anyway, coming back to our clues. If I give you a million clues, that's worth.... about $50, since you'll guess right basically for sure.

How does the value of information behave in between? How much are 8 clues worth? I found the answer to this unexpected too.

I thought 8 clues would be worth considerably more than 1 clue. Maybe not 8 times more but, like, 4 times more?

In fact, you were willing to pay $5 for the first clue, and are willing to pay only $6 more for the next seven clues!

Your probability of guessing right with 8 clues is only about 61%.

So the value of clues goes up rather shallowly.

40 clues are worth only $23. One hundred clues doesn't even get you to being right 90% of the time.

Beware of people selling you binary clues! Especially in even numbers.


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More from @ben_golub

24 Apr
David Blackwell would be turning 102 today.

He's best known for the Blackwell information ordering, the way to formalize when some signals give you more information than other signals.

A thread on Blackwell's lovely theorem and a simple proof you might not have seen.

Blackwell was interested in how a rational decision-maker uses information to make decisions, in a very general sense. Here's a standard formalization of a single-agent decision and an information structure.

One way to formalize that one info structure, φ, dominates another, φ', is that ANY decision-maker, no matter what their actions A and payoffs u, prefers to have the better information structure.

While φ seems clearly better, is it definitely MORE information?

Read 18 tweets
8 Apr
Our perceptions of some of the things we experience are deeply inaccurate. 🧵

Case 1: The vast majority of restaurants get few visits and go out of business quickly. This seems surprising because the typical restaurant you experience is busy and long-lived.

The gap between reality and perception happens because few people experience any given unpopular, short-lived restaurant. Precisely because it is unpopular and short-lived!

The brilliant @CFCamerer, who gave this example, notes that it's not just curious but consequential.

We, including aspiring restauranteurs, undersample unsuccessful restaurants so badly that it can make the restaurant business intuitively feel easy.

So too many people start restaurants who should have done other things instead.

Read 15 tweets
4 Mar
Excited to watch this talk by @renee_bowen_lyn : a model of echo chambers in social networks and how they take way less "behavioral error" than you might have thought to get started. Image
Paper here if you want to follow along


2/ Image
Behind the scenes there's a sort of puzzle based on a "naive martingale intuition": if there's abundant data and you understand the information process you're seeing, then a Bayesian should converge to accurate beliefs.

Well, information is abundant so.... what gives?

3/ Image
Read 29 tweets
23 Jan
Ok, my own answer to @JSEllenberg's question.

Here are some important statements that come up in economics:

"Nice estimators are consistent even in complicated models."
"Nice financial markets are informationally efficient."

"Nice markets have price equilibria."
"Nice games have Nash equilibria."

The way these ideas are taught to Ph.D. economists in any field, even in core courses, involve very explicitly and extensively ideas extending ones in basic analysis.

In particular, those ideas are: convergence (in fairly big spaces), integration and probability/martingales, continuity and fixed points.

Though you could get across aspects of these ideas at a high school level, econ grad school doesn't do them that way.

Read 7 tweets
23 Jan
One amusing feature of math classes at the master's level or above is that they almost take pride in not motivating the subject in external terms. For example, here's a page from a canonical textbook in algebraic geometry.

This does a good job of reminding me of how Lecture 1 in such classes often felt, which is roughly, "The motivation for this class is fuck you. Let k be an arbitrary algebraically closed field. Now..."

Which was not a problem when I had my own motivations!

At some point it stopped being enough. Incidentally, I don't think my economics courses were much better in the way of giving some great external motivation: I just found a cycle of self-reinforcing curiosity that kept me happily studying that subject.

Read 9 tweets
4 Jan
If you think Bean Dad is a symptom of a broken media ecosystem (and it certainly is), may I remind you of the SUMMER OF 2001.

Also known as the SUMMER OF THE SHARK. Networks and print media were *obsessed* with shark attacks.

1/3 Image
An irony is that there were actually relatively few shark attacks, but all I remember playing in the gym on CNN was shark stuff.

I also remember thinking that if this is what they need to amplify, then surely we were due for something bad. (In fact, we were.)

The old guard media with their vast editorial discretion amplify all sorts of dumb garbage: random kidnapping, shark attack.

Bean Dad type stuff is at least weirder and somewhat more democratic.

So I think critics of new media should recalibrate a little bit on old media.

Read 5 tweets

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