Measuring Inequality
Although most of us hold as an ideal some form of "equality" among people, it is a fact that human beings are not all equal in every measurable sense. Many systems of government are built upon ideals of treating eachother as equals before the law, equal voting rights or even higher concepts of equality such as aligning the wealth and/or income levels of individuals and/or demographic and ethnic groups across society.
The foundational principle of equality in Hive is by shares. Every user has the right to control and ownership of their accounts, every share among those accounts is considered equal, and every users votes are proportional to those shares.
The Gini Coefficient
Just like countries though, we can examine equality beyond the founding principles. In Economics there is a tool for measuring inequality known as the Gini Coefficient. Without diving into the details, the closer a Gini Coefficient is to 0, the more equality. The closer to 1, the more inequality.
Typically it is applied to measures of income and wealth, but don't be mislead - although wealth inequality is often discussed and sometimes measured, the underlying data is extremely inconsistent and lacking across the world. As a consequence, relying on the data available can end up with highly misleading results (such as a recently perpetuated myth that The Netherlands is the most unequal countries in the world).
Be warned, this map of wealth inequality is highly misleading
On the other hand, while income inequality might in principle be less important than overall wealth inequality, the data surrounding income is broadly far more comprehensive and reliable than that of wealth, so measures of the Gini Coefficient as applied to income ends up with more meaningful results.
Inequality on Hive
There are many ways beyond just wealth and income we could choose to look at inequality on Hive, but just as before there may be different degrees of accuracy. While we have precise numbers of balances of Hive across all accounts, some accounts represent many users (exchanges), and sometimes one user has many accounts. This is more of a problem for Hive and HBD overall than it is if we look at Vesting Shares (otherwise known as Hive Power), because while large amounts of Hive and HBD are held by exchanges on behalf of users, at least up till now this is not the case for Hive Power. Beyond balances, we can also look at forms of income inequality on Hive - author rewards, curation rewards or rewards overall. We could even look at more esoteric forms of equality among metrics like followers per account, votes per account, comments per post per account etc., but I will not explore them all in this post.
Below are some of the measurements of inequality based on current statistics. For account balances I removed 
| Metric | Gini Coefficient |
|---|---|
| Vesting Shares (Hive Power) | 0.996221 |
| Hive | 0.999332 |
| HBD | 0.998853 |
| Follower Count | 0.910177 |
These figures paint a picture of Hive as likely more unequal than any country in the world. Hive however is not a country, it's a new cryptocurrency project that has been around for less than 8 years. It should be compared to other cryptocurrency projects, but those will have their own challenges as the assumption that one address = one user would be even less valid for most other crypto projects.
Further, Hive has over 1 million (1,055,564 at time of writing) accounts that never made a transaction. If we exclude such accounts, this is how our results change:
| Metric | Gini Coefficient |
|---|---|
| Vesting Shares (Hive Power) | 0.995050 |
| Hive | 0.998159 |
| HBD | 0.997996 |
| Follower Count | 0.859226 |
This shows an improvement, but Hive remains a highly unequal place. What if we only include users active in the last 30 days?
| Metric | Gini Coefficient |
|---|---|
| Vesting Shares (Hive Power) | 0.963378 |
| Hive | 0.983600 |
| HBD | 0.986151 |
| Follower Count | 0.821649 |
Better, still highly unequal.
Rewards Inequality
Let's now instead look at something more comparable to Income Inequality - rewards and engagement metrics. Here I suspect we have much lower levels of inequality, and instead of giving a single figure per stat, we can take a look at how inequality has changed over the lifetime of the project. As a consequence of that, we can also apply Granger Analysis to determine if levels of rewards inequality factor into user retention as well as contribute to the price of Hive.
Below is the chart of how author rewards inequality has changed since the fork from Steem. Remember - bigger number = less equal.
As we can see, there has been a slow decline in rewards inequality since the fork from Steem. In the first year after the split, the rewards Gini coefficient ranged between 0.85 and 0.75. More recently it is in a much narrower range around 0.75.
The story becomes more interesting when we look back at the full lifetime of the project - including the days of Steem, before the split. Here, there is much more of a story of changing levels of rewards inequality in the project.
There have been substantial shifts in the level of inequality in author rewards over the years, particularly during the Steem era. If we overlay the hard forks that had major changes to the tokenomics of author and curation rewards, we see that there aren't really immediate changes in rewards equality after any of them except perhaps Hard Fork 16 all the way back in 2016. This is especially the case with hard fork 21, where it appears that the decline in rewards inequality afterwards is just the continuation of a trend alread in place through 2018.
Indeed after the split from Steem, the rate of decline in rewards inequality has slowed, perhaps due to just an overall smaller userbase.
Conclusions - Hive is getting more equal, albeit slowly.
Based on balances alone, Hive is an extremely unequal place compared to almost any nation state, however it is probably not fair in the first place to make that comparison. Comparisons with other cryptos requires further analysis and normalizing to something close to 1 account = 1 user.
Author rewards on Hive reflect a much more equal, but still quite unequal space. The trend is towards greater equality over time. That trend began in earnest with hard fork 19 and slowed after the split from Steem.
Hard forks which changed the tokenomics of Hive had little immediate impact on the level of rewards inequality, but may have had effects that more and more impact over time (particularly hard fork 19). My personal view is that it is likely cultural shifts in the way the Hive community thinks about the reward pool likely had bigger impact than changes to tokenomics.
In my next post, I plan to analyze the impact that levels rewards inequality have on user retention and the price of Hive - to test the idea that users leave because of perceived unfairness over rewards.
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