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Simulation Outcomes
The chief goal of this simulation is to evaluate the relationship between the amount of defectors and the probability of group collapse. So what is group collapse? The tandapay protocol can be thought of through the lens of a decentralized insurance protocol. Imagine an insurance protocol with N users, who all pay in k dollars each month. If no claim happens, they get their refunds back. However, if a claim does happen, they can decide whether to pay their premium like normal, or not pay (a.k.a, "Defect").
If N=100 and k=100, then we have a pool of $10,000 each month. When a claim happens, we pay out $10,000 even if people defect. However, as the number of people remaining decreases, the more they have to pay to cover the $10,000 premium. There is only so much they will tolerate before they also defect. Someone may be fine paying a premium of $100, but if 50 people defect and there are only 50 remaining, and now they have to pay $200 to cover their portion of the claim, they may not be willing to do that.
In essence, this creates an effect known as, "death spiraling," which amplifies the voices of the minority group of defectors, by creating cascading waves of defectors. As the size of this minority group (defectors) increases, so does the cost of covering the premium for the remaining members, which makes them more likely to defect themselves.
When viewing the simulation's settings menu, users will see an option titled, "percent honest defectors." This option is NOT the percentage of users who will actually defect. The amount of users who actually defect relies on several other variables such as "percent independent".
For more information, see: Defectors in Detail
With the previous explanation of the distinction between "percent honest defectors" and actual "defectors", let's perform a search through the domain of "percent honest defectors". The outcome of this search can be seen below:
| Value | Wins Percent | Draws Percent | Losses Percent |
| 0.1 | 0.0 | 2.0 | 98.0 |
| 0.1175 | 1.0 | 0.0 | 99.0 |
| 0.135 | 1.0 | 4.0 | 95.0 |
| 0.1525 | 2.0 | 2.0 | 96.0 |
| 0.17 | 7.0 | 19.0 | 74.0 |
| 0.1875 | 10.0 | 26.0 | 64.0 |
| 0.205 | 25.0 | 28.0 | 47.0 |
| 0.2225 | 28.0 | 44.0 | 28.0 |
| 0.24 | 60.0 | 24.0 | 16.0 |
| 0.2575 | 74.0 | 20.0 | 6.0 |
| 0.275 | 80.0 | 16.0 | 4.0 |
| 0.2925 | 79.0 | 19.0 | 2.0 |
| 0.31 | 84.0 | 15.0 | 1.0 |
| 0.3275 | 92.0 | 7.0 | 1.0 |
| 0.345 | 95.0 | 5.0 | 0.0 |
| 0.3625 | 95.0 | 5.0 | 0.0 |
| 0.38 | 99.0 | 1.0 | 0.0 |
| 0.3975 | 100.0 | 0.0 | 0.0 |
| 0.415 | 100.0 | 0.0 | 0.0 |
| 0.4325 | 100.0 | 0.0 | 0.0 |
| 0.45 | 99.0 | 1.0 | 0.0 |
All Roots:
0.5020643879416782
0.24282861995857888
-0.01581793911995869
Real Roots:
0.5020643879416782
0.24282861995857888
-0.01581793911995869
Possible Solutions:
0.24282861995857888
Linreg Model:
y = -8230.088274920787x^3
+ 6000.352175105803x^2
+ -906.4037375577141x^1
+ 34.12865682396028x^0
Modeling the data with a regression model, we can see that there is a sharp S curve in the data, and the point where the probability of group collapse is closest to 50% is about 0.242828. This is right in the middle of our S-curve. So, how many actual defectors are there to create a 50% probability of group collapse?