how likely is a 51% attack or sybil attack within bitcoin and under what conditions can we make it less likely.
under conditions of decreasing number of profitable miners/pools which is why we are talking about this (reactively again of course)..your first question is impossible to know for certain without access to unknown info about the miners. too many varriables
there's no way of telling if all pools are owned by the same person, then it's not collusion or 51% attack, it's a sybil attack
The Byzantine problem deals with a minority of actors or signal throwing off the consensus of the system or majority. If you can't determine how many actors even exist in the first place, you're probably always going to lose this test.
The only way is to audit them yourself, which is the purpose of the voting mechanism in DPoS, to audit the block validators for sybil.
whats it been like 2 years now that we've been preaching this magic called math?
just like how bitcoin is all about big numbers giving us security, the math behind this "late in the game" "global stage degree of decentralization" becomes more complex and indeterminate once you cross the threshold where mining pools start to coalesce due to unprofitability. and of course.. couple that with the fact that you could never know what the other guys are thinking and gaming, etc... there are just too many variables to analyze as accurately as you could when you were describing a system with a total number of nodes that did not exceed the total number of your fingers and toes.
in bitcoin's younger days, it was more transparent and easy to see that its initial centralized small community of 1 then 2 then 3...etc..had grown into a global, and of course, more decentralized organism... this was a gigantic feat but mathematically simple to prove that the network had obviously become more decentralized than it had been after genesis.. but then how to you measure the change in decentralization on a global scale? That's where Bitcoin2.0 forked and we started building the first gargantuan global scale smartchain that had to be more physically (based on HARDWARE LOCATION) decentralized... thats of course when then things got fuzzy...
not from all the hookers and blow, but because: once bitcoin was at the physical size of a global hardware unit, and all the big money has been made from the growth phase (and halvings instead of doublings due to the fact that it is a deflationary currency), then the maintenance phase takes over (you want a deflationary currency, then this is what you get)(deflation)...now you have to maintain the mainframes that are unprofitable without the continuing influx of new cash from new users...Just like how the oil drillers stopped opening up new wells when the oil price crashed last year, nobody opens bitcoin mines anymore either in this identical deflationary economic scenaro..
So like Chuck ponzi in search of his next buck... without continuous growth, more miners turn off their unprofitable rigs and leave it to the big guy who just might be your brother......
people will claim there are incentives against a big hash man owning several pools that make up the majority of hash rate. This is obviously false. There are no incentives against him taking this course of action, since he can do so in secrecy, there are only incentives against him making double spends. I would argue that even if he isn't double spending the security model is broken. If you accept this security model, there's no reason to not accept a security model of one guy always having 90% hashrate out in the open (not trustless, they can double spend at any time).
Bitcoin was born, and grew up strong, then became weak in its old age, unable to support itself under the strain of unprofitability. .. ... please buy BTC to keep another miner alive... help them pay for their electricity to run the fans that are keeping his house from catching fire... or like rOach says, pitch your burnt out ASIC in the garbage can with all the rest of your underutilized technological masterpieces that were only useful for a blink of your lifetime and be still and know that Satoshi and Co. control the majority of the bitcoin mines...
and who knows.. maybe he always did (its impossible to prove otherwise)
http://i3.cpcache.com/product/697015910/be_still_know_that_i_am_god_surgeonpng_classic_th.jpg?height=225&width=225(hint.. its not the size that counts here)