 Here, I introduce a mechanism to stabilize the value of a coin named “X”. To this end, this
mechanism controls the supply of X such that its value is always (moving towards) the median of 2n+1 items including X. The 2n items can be gold, crude oil, water, bitcoin, ether, USD, EUR, corn, or anything of homogenous value.

I would suggest n > 10 for more stability. But here I provide an example with n=3 for simplicity.
Let’s assume at time t=0, we have:
1 USD = \$1
1 EUR = \$1.11
1 gram gold = \$47
1 gram silver = \$.54
1 barrel crude oil = \$59.2
1 Ether = \$151
Therefore, at this time:
1X = 1 USD = .9 EUR = 0.0212 gram gold = 1.852 gram silver = 0.0169 barrel crude oil = 0.0066 Ether.
Which means they have the same value and markets are indifferent between them. However, as time passes their relative values change. Here, we define this vector as the benchmarks for all times:

V = (1 USD, .9 EUR, 0.0212 gram gold, 1.852 gram silver, 0.0169 barrel crude oil, 0.0066 Ether)

All the components have the same value at time t=0 but later on, they can have different values and can be sorted based on market preferences. We don’t need to sort them though. The only thing that we need is that 1 X should be more valuable than three of them and less valuable than three of them so 1 X is always the median. To this end, we design an optimal control mechanism that determines the supply of X based on the rank of X. If four items are preferred to 1 X (i.e. two are less valuable), the mechanism cuts the supply until X becomes more valuable than three and becomes the median. If four items are less valuable than X, the mechanism increases the supply so to lower the value of X becoming the median again. There can also be a reserve pool so that when the value of X goes too low (e.g. ranked sixth), the system buys back and burns X to increase its value. It is all about optimal controller design.

Such currency has numerous advantages and desirable properties:

1. It is not sensitive to any one item, because it is median, not average. So for example, if Ether becomes useless due to quantum supremacy, the last item will become less valuable than 1X and it does not matter how much less valuable. Or if crude oil becomes very expensive, it is always more valuable than 1X and it does not matter how much more valuable. Essentially they each have one unweighted “Vote” in calculating the median.
2. We do not need the exact values of the items. We only need to know how many items are more or less valued than 1 X. A simple oracle can detect it in a Blockchain. There are also some on-chain mechanisms that can detect it without oracles. The important thing to detect is when the rank of 1X changes, like when an item that was less valuable than 1X becomes more valuable than 1X. That is the only information the controller needs.
3. The traders and arbitrators know that this mechanism makes 1X the median eventually, so they buy and sell X when it moves in either direction and essentially they absorb most of the shocks before the supply controller is triggered. In fact, the prospect of 1 X becoming the median, is a strong force in the markets that pushes the value of 1 X towards the median at all times.

An interesting extension to this controller would be a time-variant multiplier for X. This
multiplier can be (1+b) t so that the controller pushes (1+b) t .X instead of 1 X toward the median.
If b > 0, it imposes inflation and b < 0 will imposes deflation. For example if b = +.1, the
controller makes the value of 1X, 1.1X and 1.21X the value median at times t = 0, 1 and 2 respectively. This inflation can allow for a higher supply of currency which can be used as a reward. On the other hand, if b = -.01 , the controller makes the value of 1X, .99X and .98X the median value at times t = 0, 1 and 2 respectively. This is a risk-free interest rate for the coin holders.
Because the value of their coins increases according to a precise formula.
One can easily implement such coin as a token on a Blockchain like Ethereum.

Hamed Khaledi, PhD
Visiting Scholar of Finance