Naturalization science

File:Membership Supply and Demand.PNG
Naturalization science is the study of membership (in terms of activity, growth, recruitment, and practicality).

The term "naturalization science" was coined by Head of Naturalization Satine Ehtya.

## Modeling

### Applying Supply and Demand

It was originally Major Executive Nathan Maine who brought forth the concept that membership could be viewed by simple demand and supply (such as in economics) by representing price (in incentives or otherwise) on the Y-axis and quantity of members on the X-axis. Member supply was postulated by Maine to be virtually uncontrollable (in that the curve could not be shifted by actions of the government or any definable entity) and so Maine theorized that members could be acquired by paying more to incentivize recruitment of them, resulting in a new equilibrium with a higher quantity of members and higher payments for them. He used this concept to derive his original plan for recruitment incentives (as part of the 2013-II Economic Stimulus and Infrastructure Investment Act) and used it to argue for increased use of incentives.

### The Ehtya Curve

 File:Ehtya supply curve.PNG
Though Maine's model was the foundation for the relationship between incentives and membership growth, Head of Naturalization Satine Ehtya pointed out several fundamental problems. The primary issue was the concept of exponential population growth, which was unaccounted for in Maine's model. In late January of 2014, Satine fashioned her own model, utilizing a parabolic function to represent the supply curve, which depicted a steep increase of necessary price at low levels of quantity which would eventually become more and more effective and eventually lead to being able to decrease incentives as exponential growth in members sets in (the point where this cross-over from raising to lowering incentives is called "convergence"). A secondary issue Satine addressed with the Ehtya curve was accounting for inactive recruits, as many of the recruited members tended to slack off and fail to become active and participating members in the Triumvirate, resulting in the incentives actually doing nothing but costing money. Satine did agree with Maine's analysis that the supply of members was largely uncontrollable, stating that the Ehtya curve was static and basically unalterable by actions of the government.

Maine criticized the model as it indicated that government incentives into recruitment would cost an excessive amount of money for little return, whereas his own policy had demonstrated positive results. Satine argued fairly successfully that Maine's incentives had increased membership but not significantly based on the cost, which validated her model. However, Satine was unable to account for short-term fluctuations in membership with her model, leading to the modern model.

### Modern Model

 File:Modern Membership Model.PNG
The modern model combined Maine's original model and Satine Ehtya's supply curve to reflect both long-run and short-run supply and came about in early February of 2014 as a result of work done by both Major Executive Maine and Satine. Maine's linear supply accounted for short-run membership and costs, while Ehtya's accounted for long-run membership and costs. However, the modern model was unclear as to what happened to the short-run member supply after convergence, whether it would start to decline or continue to proceed upward, so the modern model generally is only depicted up to short-run convergence (the point where, were the demand curve to intersect with it, the demand curve would also go through the long-run convergence, i.e. the top of the parabola). The model reflected the exact price of incentives (where short-run member supply intersects with member demand) and the overall price to actually get a member (where long-run member supply intersects with member demand).

The modern model demonstrated several key discoveries though, which have lead to its acceptance:

1. Though demand may increase by a lot, membership generally increases by less.
2. Increasing incentives does increase membership in the short-run, but there are often relapses back to the new long-run equilibrium (a concept of two steps forward, one step back).
3. The government may spend more money on incentives than it makes back in members (not every new recruit is active, many members quickly leave, people game the system, etc.), even though that all happens, the government still spent the money, costing more per individual active member.

## Quantifying

The Department of Naturalization (as well as the office of the Major Executive under Major Executive Maine) was heavily involved in attempting to quantify naturalization data and apply it to the models.

The "base number", the minimum number of citizens at no incentives is assumed to be 20, meaning that there are always at least 20 citizens present regardless of there being incentives or not. This was based on historical data, average membership, and membership prior to the implementation of incentives.

Using historical data from the set of incentives coming from the original passage of the 2013-II ESIIA, the long-term average after implementation of the ∇20-per-member incentive program appears to be 25. This means that the long run membership increased from 20 to 25 active members as a result of ∇20 incentives. However, the short-run increase due to the ∇20 incentives, did temporarily bump citizens to a high of around 28 members, so 28 is accepted as the short-run demand. Using further data, analyzing the retaining of members and overall growth in the long-run (+5 members) compared to the total amount spent (∇360), ∇360/5 = 72, so this becomes the cost per individual member. Utilizing this data, estimates can be made as to the estimated mathematical portrayal of the model, leading to more accurate representations of membership growth.

## Alternative Theories

 File:Modern Membership Model (Inelastic Demand).PNG
### Perfectly Inelastic Demand

It was Major Executive Nathan Maine who originally proposed the idea that the demand curve may be perfectly inelastic (meaning that there is no variation in demand based on price) due to extraordinary necessity and lack of substitutes for members. He originally proposed it to counter an argument made by Satine Ehtya that the Ehtya curve that membership would barely grow despite high incentives. His arguments were that:

1. **Lack of substitutes:** There is no substitute for "members". The government can't, nor the private sector, demand any alternative for a member. There aren't potential alternatives like "robots", there is only one good that works and that is a human member.
2. **High necessity:** Members will always be in demand, regardless of how expensive they may get.

Thus, Maine concluded that demand for members is extremely inelastic (to the point where it can be represented as perfectly inelastic) and should be displayed vertically instead of downward-sloping. Satine Ehtya strongly disagreed with this, stating that while increases in incentives do bring in more members, in the long-run, many of them do not end up becoming active. She also observed that arguing necessity may not be entirely accurate, as the government/private entities are probably less likely to spend money on recruiting incentives as the price rises, despite the necessity.

### Supply-Alteration Theory

Though most modelers and naturalization scientists tend to agree that supply is generally unalterable and impossible/impractical to affect in a significant way, some, such believe that supply can be increased based on ease of access, more public information, and/or steady increases in the membership base via incentives to maintain members.

### Libertarian Concepts

Though incentives were employed to increase membership and the models all indicate them to be effective, many extreme fiscal conservatives argued that the government's program was unnecessary and would only lead to long-term problems in that the government could not afford to spend gratuitous amounts of money on membership growth. They argued that, even without government interference, the free market would encourage membership growth as it is in business' interests to attain more customers and labor. They also postulated that companies could be created to bring in members for a price (eventually, a company called Prime Personnel would offer this).