#### The “Rich Get Richer” Concept in Proof-of-Stake Systems

The “rich get richer” (RGR) concept is applied to many scenarios and is used to describe the concentration of resources by entities who have an “unfair” advantage over those who lack the same resources. In every monetary system, an accumulation of resources can be observed, even in systems as simple as games of Monopoly. However, many frivolously describe the staking process of Peercoin as being a similar mechanic due to the roughly 1% annual returns that exist through the minting process. This is incorrect and must be represented honestly.

Start by defining the distinction between a “nominal” and “real” value. A “nominal” value as its name (Latin root “nom” means “name”) implies, exists due to a communicative label placed upon such object. For example, prior to the 1970’s a single dollar bill represented “one dollar’s worth” of gold. More importantly, the summation of the physical nature of the one dollar bill was not equivalent to the ounce of gold; solely the ascribed value. There was no physical difference between a one dollar bill and five dollar bill for all intents and purposes. Sparing the discussion of devaluation and inflation, the idea that a visible change in the ink on a piece of paper from a one to a five would inherently change the value must be understood and accepted for a correct understanding. “Real” value of an object comes from a value comparison between two or more objects. Let’s say you are a young child and your parents pay you a dollar a week for doing your chores (making your bed, cleaning your room, etc), and at the end of the week, you get to go to the local dollar store and buy a toy (valued at \$1). Your week of work is equivalent to one toy a week and can be represented as \$1 for a week’s worth of chores, or one week of chores for one toy, or \$1 for a toy, and so on. This system of comparison ties the worth of each piece of the system together, communicating value about each participating piece and its “real” value.

Now, let’s say the local dollar store changes ownership and is rebranded to the two-dollar store. Now instead of one week of chores, you need two. Your parents graciously double your chore money so the system can be maintained. Now you make \$2 a week for one week of chores and are still able to buy one toy. Your income has increased by double, while your purchasing power has remained the same. Put simply, although you are now making \$2 instead of \$1, which is a nominal increase, the amount of time you are working and what you can buy with that money in its triangular relationship has remained the same, maintaining the real value.

In most cases, people use this colloquialism to describe a disparity between rich and poor. The difference in the amount of money held by either side is staggering on many occasions, however, this is not a function of an unfair system. During a game of Monopoly, over a number of terms, money is exchanged between parties and eventually, one individual holds the majority of the money while other players each declare bankruptcy. In the real world, this same system appears as few individuals tend to hold a disproportionate amount of wealth, relative to the majority of individuals and is described through the Pareto distribution. However, this Pareto distribution does not solely exist in finance, but also in creative works, including writing, film, visual media, and music. The majority of great works produced in each domain were produced by an extreme minority of individuals. Individuals such as Elvis Presley and Garth Brooks have sold some hundreds of millions of albums while (assuming) the majority of individuals in our daily lives have sold none (Decluttr). This is not an unfair system, but rather the result of specialization and the exchange of Elvis’s time for a skill which was honed to an expert level. Every moment Elvis spent playing guitar was a moment not spent cooking or learning medicine. This opportunity cost presents itself in every situation and dedication to one domain generally leads to specialization and an increase in ability over time.

As such, those who spend a great deal of time learning a business and developing products in the market have an increased chance of having success. Repeatedly investing such money will lead to an increase in their overall net worth (not accounting for inflation). A 10% increase in net worth for a college student may only be \$1000, but for a millionaire, this would be around \$100,000. Note this, because it will be important in a moment. The millionaire may be able to open a restaurant which makes his returns \$120,000 in the following year, while the college student unable to dedicate time to a job outside of school, will not be presented with the same opportunities. There is no moral corruption, or unfairness to this situation, rather just a difference of opportunities and choice of time being spent with the available resources.

For Peercoin’s proof-of-stake method, these concepts become important as many claim PoS leads to an increase in the resources of the wealthy when compared to those who hold less. Minting 1% of a wallet in an annual period means if Individual A holds 100 Peercoin, that at the end of the year, they will have roughly 101 Peercoin. If Individual B holds 10,000 Peercoin, at the end of the same year, they will have roughly 10,100 Peercoin. As of today, Peercoin is trading at roughly \$1, which is convenient for this comparison. Individual A only gained the equivalent of \$1, while B gained \$100. However, these increases are only nominal. This cannot be stressed enough. The relative increase in both A and B’s resource capacity is exactly the same. If both got 5% annual returns, they would still be exactly the same as the other at the end of a 365 day period. Even though there is a difference in the annual returns, there is no increase in the percentage of the owned supply. Both A and B’s resource pile remains equivalent to each other in “real” terms, even if “nominally” they have changed. The minting system is closed and does not offer advantages for in staking to increase production.

However, both individuals must participate in the staking process to avoid the roughly 1% annual inflation. If there were a third participant, Individual C, who chose not to stake, would be losing out to the other participants. In theory, if Individual C held 20,000 Peercoins, and never minted, would, in theory, eventually be caught by either individuals A or B. Therefore, to maintain the percent of supply owned relative to all other participants, staking and minting is strongly advised as protects the security of the network, but also provides an economic incentive. You cannot generate more time to age your transactions faster. It simply cannot be done, making RGR irrelevant and a nonsensical application of theory. Those who attempt to apply such logic are doing so through fallacious methods, relying on the crowd to observe only the “nominal” changes and not the “real” changes.

If you are interested in how the Pareto distribution governs distribution, you can read more here: https://en.wikipedia.org/wiki/Pareto_distribution