Average orientation is the worst environment

2017-11-27

Results of 100,000 experiments

Under the condition that the top 70% receive the reward, those who followed the strategy of making their behavior closer to the average of the observed behavior of others (average-oriented strategy) had an 85% chance of receiving the reward, whereas those who followed the strategy of changing their behavior away from the average (anti-average-oriented strategy) had a 60% chance of receiving the reward.

Conversely, under the condition that the top 30% receive compensation, the average-oriented strategy was 15%, while the anti-average-oriented strategy was 40%.

in other words

If a majority of people receive compensation, it is more advantageous to take an average orientation

Otherwise, it is more advantageous to move away from the average

Innovation changes costs, culture and attitudes. Flexible trial and error is necessary, but as a result of current education, many people lack the principles and motivation to base their decisions on.

We thought it would be interesting if a mathematical model could express the difference between an environment where the average is optimal and an environment where the average is the worst.

modelling (e.g. a system, etc.)

There are n agents.

Each agent has a D-dimensional "action vector". This shall represent their behavior.

Initially, the action vector follows a normal distribution

Each agent can observe the behavior of others

There are many design options for how to make it observable, but we'll make it observable with probability p

It would be interesting to design a system where only people close to the action can be observed.

Each agent can modify his or her own behavior based on observations of others' behavior

There are also design options on how to fix it.

In this case, "Find the average value of the observed information and update your behavior in the direction of moving closer/further away from that average".

It would be interesting to see the median instead of the mean and the shape of the distribution.

If the action is a, the mean is m, and the learning rate η is 0.5 or -1:.

$ a_{new} = a + \eta (m - a)

A random vector is chosen as the evaluation axis, and rewards are given to q * N participants in descending order of value along the axis.

Image of "Reward the top 10%"

Setting q = 90% also creates a situation where "disadvantages are given to the bottom 10% of grades".

I think this nonlinearity is the key, but it would be interesting to experiment with changing it.

Run this experiment 100,000 times and observe how the probability of receiving a reward changes with behavior modification strategies

code:p=0.5, eta=0, 0.5, -1.0:

# q = 0.7

0.70119 0.84714 0.60523

# q = 0.3

0.29822 0.15266 0.39567

source

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