“This genie will make all your money order wishes come true” by Eric Steuer is licensed under CC BY 2.0

Letting the Gini Out of the Bottle


This article, outlining a principle which might at first seem counter-intuitive, is for current and would-be crypto investors, i.e. investors in any form of Distributed Ledger Technology (DLT).

It is written by someone who has no redeemable investments in crypto-currencies, other than substantial time spent studying them in detail, including the historical setup of an ICO.

The article follows an inspirational first mention of the Gini Coefficient by Chris Crawford.

Metcalf’s Law

There exists solid formal research evidence, that the market value of a DLT token follows Metcalf’s law, averaging out market fluctuations.

We see this in the studies of several tokens, in several separate studies, including Bitcoin, carried out over periods up to ten years; the entire well known history of tokenised distributed ledger (i.e. Bitcoin etc).

Metcalf’s law shows that the token value is equal to the square of the number of users in the network, multiplied by a utility co-efficient.

Metcalf’s law further shows that the number of users over time grows by an amount which approximates to an exponential netoid (a form of s-curve), which is heavily dependent on the value of a “Virality” factor, which again is related to utility.

Utility is a measure of desirability; how useful the facility of the token is to the user.

Both parts of Metcalfs law apply throughout the entire time that the utility remains unchanged.

The utility is a measure of how useful (and thus attractive), the service of the token is to users. For example, the utility of Dash is pretty much the same as the utility of Bitcoin, they both simply provide an alternative means of transferring funds to someone else.

The utility of social media including Facebook has been shown by similar academic research to be orders of magnitude higher than that of a simple crypto-currency.

In fact, the utility of a social media appears to be the highest known of any network type.

So the ideal token is one integrated with a social media.

With no other changes, the token with the highest value will always be the one that started first, as it will always maintain a generous head start over any others starting later with the same utility.

The difference in price over time increases heavily exponentially, with the leader pulling away from a follower, by a difference in value equal to the square of the difference between the numbers of users, where the numbers of users are given by the values at the corresponding points in time on the metcalf growth netoid, which applies equally but time shifted to both, and which itself is exponential.

If a token encounters scaleability problems affecting usability, as did both Ethereum and Bitcoin around the end of 2017, then the utility factor goes down. Thus the price goes down, as we saw, with subsequent impact on all of the followers, even though their utilities might have been unaffected, the market momentum brought all of the prices down.

The thing to remember is market deviations from Metcalfs law are temporary.

The underlying value of all tokens genuinely unaffected by any scale limit will eventually rebound to where they would have been with no market effects, driven simply by the number of users in the network, which will continue to increase, driven simply by the utility, because there was never any change in the utility of a truly scaleable solution.

IOTA is an example with no known scaleability limit.

Enter the Gini

So, what does the increased number of addresses actually mean, in the case of a token network?

It means that new users are being drawn into the network, receiving payment from existing users, in return for products or services rendered, or perhaps even for free.

Think about that for a second or two. When a new user is added to the network, the number of network members has increased by one. Anyone added to a network increases the value of the token by a value equal to the square of the number of existing users, + 1.

So, each successive user added, increases the value of the token by a greater amount than the previously added user.

By this, the token stock is effectively dispersed by some amount, assuming no new tokens were generated to cover the transactions.

The result is a reduction in inequality.

The Gini coefficient is a measure of inequality. It is applied to an economy. Lower values of Gini result in higher valued economies. By that, we mean the ones with the highest desirability to most people.

Inequality is desired by most people. Inequality is something attractive to most people.

The market is comprised of many people. Desirability is reflected directly in the market value of the token.

Increasing the number of addresses has the effect of improving the Gini coefficient.

In other words, reducing inequality has the effect of increasing the desirability of, and thus the value of the token.

Since the token value is related to the square of the number of users, and the number of users is linearly related to the number of tokens needed to create those new users (for example, by donation), we see linear outlays are outweighed by square law returns.

In other words, if you really want to be rich, start by giving out some of those tokens you are desperately “Hodling”, to those who need them.

Now we see the maths backing up a distinctly religious message:

It doesn’t pay to be greedy.

Let that Gini out of the bottle!



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