Explication needed in White Paper fees section

[jamesray1]

https://github.com/ethereum/wiki/wiki/White-Paper#fees

Context:

1. A transaction leads to k operations, offering the reward kR to any miner that includes it where R is set by the sender and k and R are (roughly) visible to the miner beforehand.
2. An operation has a processing cost of C to any node (ie. all nodes have equal efficiency)

1. The miner does pay a higher cost to process the transaction than the other verifying nodes, since the extra verification time delays block propagation and thus increases the chance the block will become a stale.

2. There do exist non-mining full nodes.

(1) provides a tendency for the miner to include fewer transactions, and (2) increases NC; hence, these two effects at least partially cancel each other out.

How do they partially cancel each other out? Be more explicit.

(1) C_miner > C_verifying node. N*C_miner is more likely to be higher than R so the miner will include fewer transactions. (2) Assume N is the total number of nodes so is higher with non-mining nodes, thus NC increases. I still struggle to see how they cancel each other out.

[Enigmatic331]

I too am having issues understanding this section of the whitepaper. Perhaps I am just missing something?

[foogunlana]

@jamesray1 @Enigmatic331 It's not 100% clear to me either but perhaps this could help:

(2) Means that not all nodes collect the reward, so while NC increases due to an increase in nodes, the reward per miner doesn't fall with each additional non-mining node.

I think the ambiguity comes from the inequality R > NC which is fine, but doesn't differentiate between N_m (miner), and N_n (non-miner) and also C_m and C_n.

Perhaps it could also look something like: R/N_m > (N_m*C_m + Nn*C_n)/(N_m + N_c).
Think that helps?

[jamesray1]

Yeah I looked over it again and I am still not sure if I fully understand it. I think the effects partially cancel each other out because the miner pays a higher cost than non-miners to process each transaction, while there are non-mining full nodes, so the total network cost of processing each transaction also increases. Therefore, because the total network cost increasing also negatively impacts non-mining nodes (as well as miners being impacted by higher costs than non-mining full nodes), the two effects partially cancel each other out, so inequality in the network is minimised.

[jamesray1]

Well someone removed the "clarification needed" tag without doing anything about this issue.

[jamesray1]

I readded a "How?" tag.

[jamesray1]

@vbuterin may you please clarify this?

[gftea]

I think it may be due to below:
miner's expected reward is kR/N, the NC increase, so the sender has tendency to increase R, so (1) and (2) cancel each other

[mattbonnell]

To correct the minor typos in @foogunlana formula:
R/N_m > (N_m*C_m + N_n*C_n)/(N_m + N_n)