arnold8020's comments

Back in 2017, I was wondering about this in the context of the 80-20 rule, and believe I have a simple answer (posted to hacker news way back, https://news.ycombinator.com/item?id=16618385). Basically you need two things: 1) Some slight advantage 2) The network effect, that is, the probability of competing depends on the current winnings.

If you have these two things, you get 80-20 like distributions, you get the explanation for why winners keep winning. If you are interested, you can find my simulation and analysis at

http://www.cs.toronto.edu/~arnold/research/80-20/

Kind of shocking how well this works. The intuition is, why has coke won, well they had some initial advantage, and so they won a bit. Now that they have won a bit, they can finance themselves into more competition. For example, they can place themselves into more stores, into more restaurants etc. Now they get a chance to compete more.

Running the simulation yields interesting results, for example, in the two columns below, the left is Household income in 1970 broken into quintiles. The right column is simulation results.

    4.1%                         6.7%

   10.8%                        11.5%

   17.4%                        16.0%

   24.5%                        23.3%

   43.3%                        45.6%

Interesting how well the top 3 or 4 quintiles match between the simulation and the real world data.

If you run the simulation with different rules, the real world quintiles do not match the simulation quintiles nearly as well. You can tweak the simulation to see this as well.

The simulation can be tweaked to handle cases such as inheritance, so an actor with different ability inherits the wealth of a past actor.

I modified the simulation as follows:

I allowed it to evolve for a single generation, enough time for the top 20% of the population to have 80% of the wealth. I now choose a random sample from the top 20% of the population to follow, lets call them T20.

I now repeatedly

1) pass the wealth of all actors to actors with new, random abilities

2) let the new actors compete for a generation (the same number of competitions we used above)

Result: After 3 generations of steps 1 and 2 above, 80% of T20 has lost almost all their wealth, 10% has lost 75% of their wealth, 10% has done really well, growing it by a factor of 8, due to capable ancestors for three generations.

Amazing, it matches the statistics in https://www.theglobeandmail.com/globe-investor/globe-wealth/...

Below is a repost, but fits very appropriately here, the results are very similar! The pdf pre-dates my small work on this, but you may find the simulation interesting,

http://www.cs.toronto.edu/~arnold/research/80-20/

Basically you need two things:

1) Some slight advantage

2) The network effect, that is, for example, the probability of competing depends on the current winnings.

(compare with the linked pdf, pg: 548 'Why do we call this a “rich-get-richer” rule? Because the probability that page L experiences an increase in popularity is directly proportional to L’s current popularity.')

If you have these two things, you get 80-20 like distributions, you get the explanation for why winners keep winning. If you are interested, you can find my simulation and analysis at

http://www.cs.toronto.edu/~arnold/research/80-20/

Kind of shocking how well this works. The intuition is, why has Coke won, well they had some initial advantage, and so they won a bit. Now that they have won a bit, they can finance themselves into more competition. For example, they can place themselves into more stores, into more restaurants etc. Now they get a chance to compete more. When I run with rules:

r1) Actors have normally distributed abilities,

r2) Actors are chosen randomly based on current winnings, the more you have won, the more you compete,

r3) Winner of competition wins one point from the loser,

You get interesting results, for example, in the two columns below, the left is Household income in 1970 broken into quintiles. The right column is simulation results.

    4.1%                         6.7%

   10.8%                        11.5%

   17.4%                        16.0%

   24.5%                        23.3%

   43.3%                        45.6%

Interesting how well the top 3 or 4 quintiles match between the simulation and the real world data.

More such comparisons can be found at http://www.cs.toronto.edu/~arnold/research/80-20/

If you run the simulation with different rules, the real world quintiles do not match the simulation quintiles nearly as well. You can tweak the simulation to see this as well.

The simulation can be tweaked to handle cases such as inheritance, so an actor with different ability inherits the wealth of a past actor. When I run this simulation, around 80-90% of top 20% actors lose all wealth in 3 generations.

I believe that the situation is simpler and more powerful than what the article claims.

Basically you need two things:

1) Some slight advantage

2) The network effect, that is, for example, the probability of competing depends on the current winnings.

If you have these two things, you get 80-20 like distributions, you get the explanation for why winners keep winning. If you are interested, you can find my simulation and analysis at

http://www.cs.toronto.edu/~arnold/research/80-20/

Kind of shocking how well this works. The intuition is, why has Coke won, well they had some initial advantage, and so they won a bit. Now that they have won a bit, they can finance themselves into more competition. For example, they can place themselves into more stores, into more restaurants etc. Now they get a chance to compete more. When I run with rules:

r1) Actors have normally distributed abilities,

r2) Actors are chosen randomly based on current winnings, the more you have won, the more you compete,

r3) Winner of competition wins one point from the loser,

You get interesting results, for example, in the two columns below, the left is Household income in 1970 broken into quintiles. The right column is simulation results.

    4.1%                         6.7%

   10.8%                        11.5%

   17.4%                        16.0%

   24.5%                        23.3%

   43.3%                        45.6%

Interesting how well the top 3 or 4 quintiles match between the simulation and the real world data.

If you run the simulation with different rules, the real world quintiles do not match the simulation quintiles nearly as well. You can tweak the simulation to see this as well.

The simulation can be tweaked to handle cases such as inheritance, so an actor with different ability inherits the wealth of a past actor. When I run this simulation, around 80-90% of top 20% actors lose all wealth in 3 generations. See for example:

https://www.theglobeandmail.com/globe-investor/globe-wealth/....

I modified the simulation as follows:

I allowed it to evolve for a single generation, enough time for the top 20% of the population to have 80% of the wealth. I now choose a random sample from the top 20% of the population to follow, lets call them T20.

I now repeatedly

1) pass the wealth of all actors to actors with new, random abilities

2) let the new actors compete for a generation (the same number of competitions we used above)

Result: After 3 generations of steps 1 and 2 above, 80% of T20 has lost almost all their wealth, 10% has lost 75% of their wealth, 10% has done really well, growing it by a factor of 8, due to capable ancestors for three generations.

Amazing, it matches the statistics in https://www.theglobeandmail.com/globe-investor/globe-wealth/...

Interesting that you see it as 'winner takes all'. Wondering why you say that. The simulation can be run in various ways. When I run with rules:

r1) Actors have normally distributed abilities,

r2) Actors are chosen randomly based on current winnings, the more you have won, the more you compete,

r3) Winner of competition wins one point from the loser,

You get interesting results, for example, in the two columns below, the left is Household income in 1970 broken into quintiles. The right column is simulation results.

    4.1%                         6.7%

   10.8%                        11.5%

   17.4%                        16.0%

   24.5%                        23.3%

   43.3%                        45.6%

Interesting how well the top 3 or 4 quintiles match between the simulation and the real world data.

If you run the simulation with different rules, the real world quintiles do not match the simulation quintiles nearly as well. You can tweak the simulation to see this as well.

The simulation can be tweaked to handle cases such as inheritance, so an actor with different ability inherits the wealth of a past actor. It would be interesting to see how many generations it takes to loose the wealth to test the adage that wealthy families loose their wealth in 3 generations.

https://www.theglobeandmail.com/globe-investor/globe-wealth/...

Ill try it and get back to you.

I was wondering about this in the context of the 80-20 rule, and believe I have a simple answer. Basically you need two things: 1) Some slight advantage 2) The network effect, that is, the probability of competing depends on the current winnings.

If you have these two things, you get 80-20 like distributions, you get the explanation for why winners keep winning. If you are interested, you can find my simulation and analysis at

http://www.cs.toronto.edu/~arnold/research/80-20/

Kind of shocking how well this works. The intuition is, why has coke won, well they had some initial advantage, and so they won a bit. Now that they have won a bit, they can finance themselves into more competition. For example, they can place themselves into more stores, into more restaurants etc. Now they get a chance to compete more.

About a year ago, I asked similar questions about the 80-20 rule and income distributions. It seems that the simple explanation works surprisingly well. Simulate the following system and it matches real world distributions surprisingly well.

r1) Actors have normally distributed abilities r2) Actors are chosen randomly based on current winnings, the more you have won, the more you compete. r3) Winner of competition wins one point from the loser

You can find what I wrote about this at

http://www.cs.toronto.edu/~arnold/research/80-20/

including the code. It's interesting!