Quote from: smooth on July 01, 2015, 07:43:34 PM

Quote from: Peter R on July 01, 2015, 05:08:44 PM

Quote from: rocks on July 01, 2015, 05:02:05 PM

Quote from: justusranvier on July 01, 2015, 04:28:42 AM

From the perspective of a Bitcoin user, every possible thing that can go wrong with Bitcoin can be categorized into one of two failure modes:

A payment you belive to be valid, isn't (double spend)
You are unable to perform a payment that you want to perform (denial of service)

Exactly, great way to put it.

+1. Justus, I've been reading some of your work and I really like your push to clearly and precisely define the cryptocurrency terms we're using. Here's what I had jotted down yesterday, which sort of jives with the two points you made above:

Bitcoin is decentralized if no entity exists with the ability to costlessly double-spend or bar valid transactions from the blockchain.

Thoughts?

I like your approach to clearly define terms but i don't like your approach of effectively redefining decentralized as a binary term when it has been generally understood to be fuzzy. This sort of redefining of terms can easily lead to confusion or deliberate obfuscation.

For example, by your definition, there being a miner or pool with 50%-1GH of the hash rate would still be considered a decentralized system, but in practice such a miner could trivially increase his hash rate or collude with any other miner and then costlessly double spend or block. Likewise, a 50%+1GH pool that attempts to block might find that some miners leave and the ability to block is lost. By your definition this would not be decentralized but in practice it would be since ability is so fragile.

i prefer to view decentralization more along the lines of a continuous metric such as https://en.wikipedia.org/wiki/Shapley%2dShubik_power_index

The entities with the highest scores not only indicate whether the system is decentralized (your usage) if <1 but also how decentralized (common usage). The approach is not perfect here since there are different kinds of votes. Pool operators control important infrastructure and have some influence but their votes are not measured directly in hash rate.

Further, one can likely construct a single metric along the lines of https://en.wikipedia.org/wiki/Herfindahl_index (but not exactly that) which would characterize the presence of entities with relatively high Shapley-Shubik scores.

I like the approach, but a lot depends on how you value various metrics.

For example with mining pools, how few is too few where it starts to be a problem? Is going from 30 major pools to 20 major pools a reduction in Bitcoin's decentralization? I'd argue no because as long as miners have a range of pools to choose from, they will be able to select a pool that reflects their preferences. But when does this start to become an issue and how much of an issue? i.e. Does going from 20 major pools to 10 represent a significant issue or a slight one? When does it start to become a red flag issue? 5? 3? Personally I think 10 is probably enough, 5 is problem and 3 is a real problem. But that's just opinion and we can all make our own models to support various opinions.

So metrics are useful, but I think defining the objectives, as justusranvier did above, are key. The objectives at least puts a framework around what is an opinion based discussion.