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Inspired by the app development process , I found a way to measure the user scale of Apps.
Because of the network lantency, the more online users work together, the faster they pick up distributed information in the network. And I called that the ability of “network dispersity”.What if we use that ability to compete generating blocks?
First, I think this ability can't be improved by enhancing the performance of a single machine or using more electric power, and the second, there are a huge number of Apps and their developers could join the mining competition.
If we do it right, it may be another consensus method of the fully distributed systems other than POW and POS.

In this protocol, I use the transaction broadcast as the "distributed information" and the miners(App developers) make their users pick these signals as fast as possible. As the first miner who answers a transaction, his account will be stored in that transaction. Those stored accounts will become the basis of the mining competition for the later blocks.

That process can be considered as the process of voting as well. To quote the article, it is

I will explain it with more detail.
The mining competition is shown below:
https://raw.githubusercontent.com/yj1190590/POnD/master/res/competition.jpg

Isn't it the opposite? In a decentralised system, the lesser users there is, the lesser hops is needed for the information to be passed around and the faster it would be.
It doesn't exactly ensure security, if I'm reading you right. Whomever having the most number of phones would be able to choose whichever transaction to include.

It is also impossible for app developers to add such mining malwares into their apps without significant backlash.
So whomever that has the fastest internet connection is the winner? How do you know who is the fastest if you don't rely on a central server?

If the user picks up the signal successfully, the account of the owner will be stored in the transaction and his job is done.There is no hop happened.

Isn't it  exactly what  the miners do when they win the right of generating block?

The malware's noly job is to answer some signals nearby.

It doesn't affect the fairness if some App's users have the fastest internet connection, that's also the ability to win the competition. Actually It doesn't matter if they don't even have any latency at all , by collaborating with the message sender.  Refer to [disabled]
 And we don't need to know who is the fastest.

Gossip protocol converges in O(logN) where N is the Number of participants.

I don't quite understand that formula but I am pretty sure that the Gossip protocol is not related. ;D

Oh.
Well when you said this
I assumed you were going to use a gossip protocol to broadcast information across nodes.

I have drawn a picture which might explain the competition process.
https://bitcointalk.org/index.php?topic=3267633.msg34050880#msg34050880 (https://bitcointalk.org/index.php?topic=3267633.msg34050880#msg34050880)

I have just heard about it before. Now I have known about it. But I still don't understand the principle.  ;D

Are there anybody who can build a mathematical model of the theory and find the formula between the user number N and the probability P of meeting the target?
I really appreciate.

I think they are in direct proportion, but I don't have the mathematical skills to prove it.

updated with new node names. ;D
and revised.
[disabled]