# aidsim: a monetary aid distribution simulator

if i have some amount of cash, which people should i aid financially? the poor or the smart ones? i've built a little simulator to help me think about this question.

# the human model

i model an individual person with two variables:

• potential: it's a person's "smartness". the average is 1. with a small probability it can be even negative too, e.g. for criminals. note that you cannot alter someone's potential. it's a fixed number.
• wealth: the amount of money the person has. the average value is e (euler's number, 2.72), the minimum is 1. wealth is something you can increase later on by sending aid to the person.

both variables are normally distributed just how i imagine reality is.

i measure the person's value like this:

• value = potential * log(wealth)

the average person of potential 1 and wealth 2.71 will have a 1 * log(2.72) = 1 value.

# log(wealth)

using log(wealth) to model reality seems relatively accurate to me. think of a very poor, hungry student and give them $10. then he might not starve the night so those $10 have a very large utility for him. now take a rich student and give them $10. it changes nothing. however if you give him $100,000 then he might go to an elite school and improve his own value significantly. but that needed exponentially more wealth to afford. the richer someone is, the less utility each individual dollar has. i think the natural logarithm function nicely fits this phenomenon.

# potential is unmeasurable

in my simulation i won't allow selecting beneficiaries based on potential. consider a genius who was never given proper food, care, never learned to read and write. no matter how large potential he has, he will not have a chance to demonstrate it. you actually need to invest a lot of effort (wealth) into creating a supportive environment for the person to thrive. and then you can measure the value of the person but that value already contains the environmental factor, log(wealth).

# visualization

below you will see two scatterplots. the y axis on both graphs is the value of each person. the x axis of the first one is the potential, on the second one it's the wealth. each person will be represented by a single dot on each scatterplot.

i added visualization because it's nice visually seeing which slice of population are you selecting and aiding.

# goal

suppose you have to distribute 10k wealth and your goal is to increase the total amount of value gained. you can choose to give the money to a combination of x% worthiest and y% poorest population.

• which slice of population would you give the aid?
• which slice do you pick if you can aid only 100 people?

in @/aiddist i'll share my own observations.

# the simulator

published on 2022-10-09

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