What happen to a blockchain in the case of decreased security constraints?

Main forces which drives/limits blockchain:

1) Security. More secure network forces to downgrade number of nodes in network.

2) Decentralization. More decentralized network forces to increase number of nodes in network

This two forces, which are very desired in blockchain, are rather against each other.

Let’s define that scalable network is such one, which is secure and decentralized in the same time. Also it is important that, in a scalable network, security and decentralization is linear proportional to the number of nodes n (Fig 1). In Fig 2) it is shown how the current blockchain (eg. Ethereum or Bitcoin) is behaving in the case when the security is maintain perfectly, but with the cost of decentralization. In this case decentralization is linear proportional with only for some small value of n, and after all it is proportional only to logarithm of n. This is because each node, when would like to preserve security, have to save and operate each transactions, or blockchain state, and possesses limits to some operations per second or to value of space on hard drive. One can also say that the single node is the bottleneck, this is because security is fully preserved, so each single node has to operate whole blockchain parallel with others nodes. My proposition in previous article, “What is the problem now with scalability of Ethereum network and how to cope with it?”, was the hybrid Q-Network in which security will preserved up to some value (eg. 99%), but then decentralization is hold likely linearly with number of nodes n (see Fig. 3).

In conclusion, one can understand, that in order to get almost scalable network, one should to go on compromise between security and decentralization. It is easily seen that releasing some small amount of constraints on security (means some error to be accepted), will bring us the scalable network (blockchain).

Fig 1) The Scheme of truly scalable network (blockchain). The light green field is showing the value of network, which should be proportional to n*n. The security and decentralization are just independent from each other, so are described by different dimensions.

Fig 2) The scheme of non-scalable network (blockchain). The security is preserved, but decentralization is propagating with log(n), rather than n.

Fig 2) The scheme of almost-scalable hybrid Q-network (blockchain). The security is preserved up to b% and decentralization is propagate also linearly with b*n.