Talent, luck and success: simulating meritocracy and inequality with stochasticity

The paper

People

Fig. 1. The 2D simulation of random events from the paper

Events and simulation

Key results

Fig. 2. Top: the talent distribution of individuals (normally distributed) from the paper. Bottom: the distribution of final capital values after a single run of simulation (80 steps) from the paper.
Fig. 3. The talent-capital scatter plot after a run of simulation from the paper

Criticism

Can we do better?

Implementing the model

  • At every time step, flip a coin: there is a probability, P_event, that an event happens. It can be either a lucky or an unlucky event.
  • If an event occurs, there’s 50–50 chance of it being lucky or unlucky.
Fig. 4. The distribution of talent and capital after a single run of simulation from the new model.
Fig. 5. An individual’s capital change over time. A blue dot means a lucky event and the red, an unlucky event.

Why it looks like average people are more successful

Fig. 6. Talent-capital (normally distributed talent) scatter plot from a single-run simulation. Every dot represents the final amount of capital of an individual.
Fig. 7. Talent-capital (uniformly distributed talent) scatter plot from a single-run simulation.

Now the fun part!

Fig. 8. The talent-capital relationship and its meaning in terms of meritocracy, economic inequality and stochasticity.
  • If talent and capital show positive correlation, we can say that the world is meritocratic; the more talented you are, the more successful you are likely to be.
  • Due to luck, inevitably there is a degree of stochasticity, which creates a cloud of dots, not a straight line. If there is a wide spread of dots at a given talent value, you may say the world is more stochastic (more luck-driven), which in turn, makes it less meritocratic because then the talented are no more successful than the average.
  • The width of capital distribution is a measure of economic inequality. The wider it becomes, the more inequality exists.

The effect of stochasticity

  • A small P_event value means the world is deterministic and predictable.
  • A large P_event value means a highly stochastic and unpredictable world.
Fig. 9. Talent-capital relationship with various P_event values. Note that 1) when an event happens, there’s 50–50 chance of it being lucky or unlucky, and 2) the y axis is in log scale.
  • When P_event is small, nothing really happens and everyone’s capital is more or less the same as the start amount (C=10).
  • However, the more stochastic the world becomes (wider cloud of dots) , the more often our lives are bombarded by unpredictable lucky and unlucky events, which creates large economic inequality.
  • With high stochasticity (P_event>0.1), talent becomes more useful because people have to be smart enough to profit from the lucky events. Therefore, we start seeing positive correlation in the high stochasticity settings, which means talent does matter in this setting.
  • Also, with high stochasticity, more people fall into poverty because of the imbalance between the return of the lucky and unlucky events; unlucky events always punish individuals
  • but the lucky events only take effect if you are smart enough to get profit out of them:

Scenario 1: Balanced unlucky events

Fig. 10. Comparing the talent-capital relationship between imbalanced and balanced unlucky events.

Scenario 2: Talent directly affects the return of luck

Fig. 11. Comparing the talent-capital relationship between Scenario 1 (default) and Scenario 2 (talent affects the return of luck).

Scenario 3: Paycheck (“Hard work pays off”)

If you have work, you can bounce back from bad luck!

Fig. 12. An individual’s capital change over time with paycheck. Blue dots mean lucky events and the red mean unlucky events. Note that y axis is in linear scale.

Paycheck and inequality

Fig. 13. Talent-capital relationship with various paycheck weight (w) parameter values.

With vs. without paycheck

Fig. 14. Comparing talent-capital relationship for with and without paycheck. Note that w is the same (w=1) in all plots.

Scenario 4: Interest rate

Interest rate without paycheck

Fig. 15. Talent-capital relationship with various interest rates (r) when there is no paycheck.

Interest rate with paycheck

Fig. 16. Talent-capital relationship with various interest rates (r) when there is paycheck (w=1).
Fig. 17. Comparing talent-capital relationship for 0% and 10% interest rates (r). Note that paycheck (w=1) exists in all plots.

Scenario 5: “The rich get luckier, the poor get unluckier”

  • At every time step, we compute a z-score for every individual based on the capital distribution of the population of that time step.
  • Then we compute cumulative probability for each z-score, which becomes the probability of an event being lucky for the next time step.
  • For instance, at a given time step, if your capital is within the top 1% of the population, at the next time step, if an event happens, there’s 99% chance that it is a lucky event and 1% chance that it’s an unlucky event.
  • On the other hand, if your capital is within the bottom 1% of the population, at the next time step, if an event happens, there’s 1% chance of it being lucky and 99% chance of it being unlucky.
Fig. 18. Comparing talent-capital relationship for Scenario 5. Note that now the maximum of the y-axis is nearly 10²⁴, which used to be 10¹¹ in previous figures. Paycheck (w=1) and interest rate (10%) exist.

Can it be worse?

Fig. 19. Talent-capital relationship for Scenario 5. No paycheck (w=0), 10% interest rate. Note that the minimum of the y-axis is much smaller than Fig. 18.

Scenario 6: Income tax

  • First, compute z-score for every individual based on their capital among the population.
  • Compute a rate as we did to compute the probability of an event being lucky but we now scale this number so that they fall in a specific range defined by minimum and maximum rates.
  • For instance, let’s assume we have [0.1 (10%), 0.4 (40%)] range of tax rate. If your capital is within the top 1% of the population, your tax rate is 99% × (0.4–0.1) + 0.1 = 39.7%. If you’re at the bottom 1%, your tax rate is 1% × (0.4–0.1) + 0.1 = 10.03%.
  • Tax is calculated after a paycheck is earned, and deducted from the total capital.
Fig. 20. Talent-capital relationship for various tax rates. P_event = 0.1, paycheck (w=1) and 10% interest rate. Minimum tax rate is set to 0.01.

Scenario 7: Social safety net

Fig. 21. Comparing talent-capital relationship with or without social safety net. Paycheck (w=1) exists and interest rate is 10%. The start amount of capital is 10.

Other scenarios

  • Uneven starting amount of capital: the paper and the scenarios above assume everyone starts with the same amount of capital. What will happen if the amount of capital is a random number drawn from a distribution? Uniform, normal or log-normal?
  • Redistributing wealth (the total amount of capital): we never tracked the total amount of capital but if the rich make a lot more money than the poor, what is going to happen if we distribute the rich’s high income to the poor? What kind of redistribution strategy can we choose?
  • Capitalism (a fraction of the poor’s labor goes to the rich): in a capitalistic society, employees work for employers and some fraction of the value of the employees’ labor goes to employers. This is definitely going to worsen the inequality, but how much?
  • The rich pay to get away with unlucky events: we also see this happening in our society. If the rich pay a certain price to change their fate, how would the talent-capital relationship look?
  • A group of people are inflicted by bad events all at the same time: this is similar to what natural disasters do. In this scenario, 2D simulation can be actually useful although we will have to redefine lucky and unlucky events.
  • The rich live longer, the poor live shorter: so far, we have assumed that everyone has the same number of time steps. Unfortunately, in real world, the rich are likely to have more access to better medical service and they might live longer because of that.
  • Inheritance: speaking of lifespan, what happens if individuals can reproduce and pass down the wealth to their children?
  • Basic income: we saw how helpful a paycheck is to prevent people from falling into poverty. However, in our model, a paycheck depends on talent. What if we have a term that is constant and independent of talent? What will its effect be compared to a paycheck?
  • Stochastic pay: the paycheck in our model is deterministic and proportional to one’s talent. We all know that this is not the case in the real world. Talented people can have a hard time getting a decent job and they might end up having menial jobs with low pay. This means luck can affect our paycheck as well.
  • Time-variable pay: people’s paycheck may vary over time as well. They can get promotions over time and make more money, or the opposite can occur.
  • The poor pay more to buy things than the rich: last year, while listening to WNYC’s On the Media podcast, I learned interesting facts about poverty such as that being poor is very expensive. For instance, you can’t buy things in bulk and so you end up paying more. You can’t buy healthy food, you become sick, and then you pay money for medical expenses. When this ironic fact is implemented in our model, how would the talent-capital relationship look?
  • Debt: in our models, the capital can go as low as possible but is never negative. In reality, people may borrow money and accumulate debt. What’s going to happen if we allow debt in a society? What if the interest rate is applied to debt as well as capital?

Future ideas

Fitting parameters

  • How large is the effect of luck in a society compared to others?
  • How often do random events happen in a country, and how this affects people’s lives?

Timing of events

  • How should people prepare for their future?
  • What kind of economic measures can we take to protect senior citizens?

Conclusions

Stochasticity disrupts meritocracy

The steepness of the talent-success slope is related to fairness and inequality

Paychecks protect people from poverty even in the worst case

Data visualization can provide insights on socioeconomic problem

Acknowledgment

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ML Ops / MLE / Data Science / AI Ethics

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Hongsup Shin

Hongsup Shin

ML Ops / MLE / Data Science / AI Ethics

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