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16 Nov, 4 tweets, 1 min read
Some networks words
a few more
a few more

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More from @ben_golub

Ben Golub Profile picture
8 Nov
"Reductionist" (i.e., most economic) theories of collective action explain acts like voting by individual incentives, perhaps including "social" phenomena via payoff terms like social pressure or warm glow.

A short thread about an (old) complaint about such theories.

1/
A reductionist theory might say: when you vote, you're almost certainly not pivotal, but you value praise for helping, or you just like the identity of standing for X.

BUT: "praise," "blame," and "identity" are not individualistic ideas.

2/
Praise, blame, identity, etc. make sense only in a community and a culture that gives them meaning.

"Individualistic" accounts with these special payoff adjustments are incomplete without some engagement with the sources of those "non-individualistic" reasons and motives.

3/
Read 12 tweets
Ben Golub Profile picture
6 Nov
I have a game:

discuss historical events in the year corresponding to Biden's lead in the Georgia count. Your first number is 1709.
Ok, the year corresponding to TRUMP's lead, and per @DecisionDeskHQ via @kiragoldner, your next number is 1479.
Your next number is 1267.

Read 4 tweets
Ben Golub Profile picture
6 Nov
the sage @JSEllenberg gave me one weeks ago
It was a lot about fish, some about Russia
🎏🇷🇺
Read 4 tweets
Ben Golub Profile picture
22 Oct
A thread on what we can learn about polarization of opinions from a simple behavioral network model.

Remember the DeGroot model? It says you decide what to think tomorrow by taking an average of what you and your friends think today.

Examples:

1/
Here is a condensed way of writing it using vector notation, which turns out to be very useful!

Here W has no negative entries, and each row sums to 1 (that's called "row-stochastic"). That makes sense, since each person is averaging others' views.

2/
We often want to think of the weights as coming from a social network, maybe something like this. The network tells you who are the friends that you listen to.

So we'd better establish a way of thinking of the updating weights as coming from a network.

3/
Read 26 tweets
Ben Golub Profile picture
20 Oct
Suppose two people each have some private information about, say, a stock. The first says her posterior expectation of its price, then the second learns from her statement and says his, etc.

Will they reach a consensus? Under common priors, yes. (See below.)

1/
People often learn this from GP (below), but they assume finite probability spaces & really use that.

Tweet proof shows that convergence to consensus doesn't rely on finiteness, and holds much more generally. (When was the martingale proof first written down?)

2/ Image
If we do assume each of us has a finite partition of the states, the tweet proof immediately implies convergence in finitely many steps:

our partitions can only change finitely many times, given that convergence happens, it must happen in finite time.

3/3
Read 4 tweets
Ben Golub Profile picture
19 Oct
An application of Aumann's agreeing-to-disagree result: certain kinds of war between rational countries are puzzling.

Since war involves destruction, better for one to surrender and bargain. But maybe each believes it'll get more by fighting? Suppose a country fights iff

1/3
it thinks it will win with prob > 0.5. In the notation below, let X = indicator that I win. Then war means it's common knowledge that Y>.5>Z.

That's impossible, but the proof below doesn't quite show it. Exercise: show there's no CK event E on which Y>Z.

War here is like speculative trade (cf. no-trade theorem): it can't happen due to different information ALONE, because by Aumann both of us can't rationally expect to win.

Thus, if war is zero-sum or worse, it entails irrationality or different priors.

3/3
Read 5 tweets

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