Quote from: SlipperySlope on March 26, 2014, 09:08:20 PM

Metcalfe's Law Explains 10x Price Growth Vs. 3.2x Transaction Quantity Growth

At least two posters, gbianchi https://bitcointalk.org/index.php?topic=441336.0
and Peter R https://bitcointalk.org/index.php?topic=400235.msg5877592#msg5877592
have presented a theory on the relationship between Bitcoin transactions and bitcoin prices.

The consensus result is that prices are growing in proportion to the square of the transaction quantity and also in proportion to the number of addresses. Peter R uses the Blockchain.info data series that excludes the 100 most popular bitcoin addresses from the recorded transaction quantities.

Here is the outstanding chart provided by Peter R that best illustrates the application of Metcalfe's Law to bitcoin prices . . .

http://i.imgur.com/ktUvPjh.gif

And here is the example device network from the Wikipedia article on Metcalfe's Law. The insight of the law is that the utility of the network, e.g. bitcoin users, is directly related to the number of reachable nodes. The number of connections is the approximately the square of the number of nodes.

http://upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Metcalfe-Network-Effect.svg/220px-Metcalfe-Network-Effect.svg.png

Supposing that Bitcoin completely replaces the current payment infrastructure entails a transaction rate that surpasses the current quantity of bank card transactions. At a growth rate of 3.2x annually, Bitcoin daily transaction quantity will exceed 350 thousand in 8 more years. But applying Metcalfe's law predicts a bitcoin price of 58 billion USD per coin at that point - which is implausible. Therefore it is reasonable to suppose that small-world effects will disconnect the bitcoin price relationship from transaction volume, in that the future whole Bitcoin network will not be uniformly well connected but rather be clusters of well connected nodes. Here is the example graph from the Wikipedia article on small world networks . . .

http://upload.wikimedia.org/wikipedia/commons/thumb/3/37/Small-world-network-example.png/220px-Small-world-network-example.png

I believe Metcalfes Law is already long disconnected.
The curves look good so far but I think it is rather arbitrarily chosen to do so without necessarily reflecting the fundamentals. If Metcalfes linear parameters were instead chosen to closely fit the early phase (first 3-400 days from 17Jul2010), one can see the predicted price values for 2013-2014 would fall well above of what they are currently drawn, hence my introductory statement.

My best guess is that Metcalfes Law was holding true and was suppose to give accurate predictions in a bitcoin-world of independent miners (&users). On contrarily, the vast majority of today miners gather around pools that I suppose can be regarded as super-nodes, where all miners hiding behind them are perceived by the outside bitcoin network as Neffective=k*Nreal, where k<1. In effect, Nreal is reduced to Neffective and similarly the number of transaction is reduced too (since most pools pay above a certain threshold instead of paying at each block found). Alike, many bitcoin users/traders (including those who are not necessarily miners) hide behind exchanges that act as super-nodes too.
If one assumes k=1 in early days, it would be interesting to see the curve broken in two parts (or three parts I can see more than one inflexion points) and from there to firstly compute the proportional coefficient(s) for best fit on sqr(N) while k=1, then to use the same coefficients for computing k for later/present times.
By further including a k=f(t) in the model it may open it for exciting correlations and perspectives.

In the above I fully agree k would be the coefficient for small-world effect and k=f(t) would model the world getting smaller (from bitcoin viewpoint). Maybe instead of abandoning Metcalfes model altogether one may try to k-adjust it so as to correlate the price with transaction volume/ no. of addresses, which are imho very good input parameters.
So, in essence, my proposal would be to consider Metcalfe's adjusted model as a second tool to predict price variation and eventually to increase confidence in the logistic model during times when price under-perform instead of repeatedly questioning the validity of initial assumptions.
Please comment/criticize.

Id take this opportunity to thanks for the great work done and published here! I think this is one of the best if not the best thread of the entire forum. Very clean, accurate and at high standards my sincere congratulations! Great contributors too!
With your permission I will have some questions on the subject/logistic model but Ill take some more time to go again through it.

Best regards,