1/7 Thread: Ergodicity

Let’s play a game.

Assume you have $100. We’ll flip a coin 100 times. Your wealth will be +50% for each Heads, and -40% for Tails.

Wanna play?

Of course, you should! The expected value for each flip is $5.

But should you really? Let’s figure out.

2/7 Let's say 10,000 people are playing this game.

After flipping the coin 100x, the avg wealth of these 10k people is ~$16,000 although it's kinda volatile.

But $16k from just $100? Wow, you should definitely play this game, right?

Wait...

3/7 So the avg wealth is ~$16,000. What's the median?

51 cents! The median person loses >99% of their wealth!

86% people finish with <$100!

1.7% ends up with >$10,000!

The wealthiest person has $117 million i.e. ~70% of total wealth!

4/7 So if you don't want to play this game, are you exhibiting loss aversion or you're just being rational?

@ole_b_peters wrote a fascinating paper on ergodicity economics last year in "Nature Physics".

Behavioral economics routinely ignores the circumstances around us.

5/7 You should all certainly play the game if 10,000 of "YOU" can simultaneously play the game i.e. there's a 10,000 parallel universe where you are playing the same game.

Since one of "YOU" will certainly win, you can take care of 9,999 of "YOU"s in all the other universes.

6/7 Sigh. That's NOT how our mundane world works.

If a Billionaire and you (assume $100k net worth) play the above game with $50K at stake, you probably should not play this game.

Greater risk aversion can be rational under certain circumstances. And our circumstances differ.

7/7 @ole_b_peters paper: https://www.nature.com/articles/s41567-019-0732-0

Ergodicity primer: https://jasoncollins.blog/2020/01/22/ergodicity-economics-a-primer/

Relevant Animation: https://www.farmersfable.org/