The attacker can do that (even with a minority of the PoW). It is good to see that my prior explanation was coherent enough that you pondered that possibility, so I know I have made progress in my elucidation of my block chain design.

But anyone today could create a fork of Bitcoin and use it for paying from themselves to themselves, but no one does that because it is pointless.

As I explained, in my block chain design all the users who are (or their client is automatically) concerned about following the protocol which enforces honesty, will not be on the attacker's chain which has violated the protocol, because the objectivity of the protocol is not subjective.

To recap, a majority PoW attacker with approximately 49 - 99% (49% because the network wastes some of its PoW mining the orphaned chain per the white paper I linked in my prior post) of the systemic PoW resources normally in Satoshi's design has the ability to win every block announcement (thus blacklisting the minority PoW from the longest chain of PoW), because the attacker can ultimately build a longer chain which orphans all the block solutions produced by the minority. However I have stated that if we change Satoshi's protocol so that every announced block solution which is not challenged by another block solution within the reasonable propagation window (e.g. 6 seconds), must be based off the previously propagated block solution. Thus the attacker can no longer blacklist the minority PoW from the longest chain of PoW.  (With 99 - 100% majority of the PoW resources, an attacker can defeat the security in my design as well).

For n00b readers (not you monsterer), please understand the Bitcoin 101 concept that due to the randomness in the Poisson distribution, an attacker with < 100% of the PoW resources can't produce the first block solution every block period if the attacker is required to start his computation of each block at the same time as everyone else in the network. An attacker can produce a longer chain with a majority of the PoW resources, but only if the attacker is allowed by the protocol to ignore the minority's PoW solutions that occasionally (not a majority incidence) arrive faster than the attacker can produce the next block. Satoshi's design does not require the attacker to build his next block off the propagated block. Satoshi's design allows the attacker to build his chain hidden. This is the major design error of Satoshi's design, that enables selfish mining and the 51% attack. I correct Satoshi's design error. I believe this is the first explanation of any where of my aforementioned rule as a solution. If anyone can cite a prior art on this point, please do. Probably there is a post (or posts) from the 2010 - 2011 timeframe on this forum (or in 2013/14 discussions about the selfish mining white paper) that has some similarity to my point. I would be very interested in reading such posts if anyone can find such.

There are reasons that Satoshi's design can't incorporate my aforementioned rule which defeats selfish mining and the 51% attack:

• The attacker could put a double-spend in his chain, thus he can not follow a rule which forces him to base his chain on the announced chain which contains a double-spend. In Satoshi's design, there is no objectivity about which double-spend in which chain came first (i.e. there is intra-chain objectivity but no inter-chain objectivity). Whereas, my design is different because PoW has a dual role, one of which is to confirm nominations for "confirmation nodes" (the nodes which do the transaction confirmations distributed thus enabling the 1 second confirmed transactions, not 0-confirmation insecurity of Satoshi's design). Thus my rule is that nominations from the propagated block have to be included in the next propagated block, thus defeating the selfish mining and 51% attacks, but Satoshi's design can't do this rule because it doesn't have the concept of nominations. Note that unlike transactions, nominations of "confirmation nodes" can't conflict because they are accumulative. My design can't just be grafted onto Bitcoin, because it requires a radical hard fork which necessities changes throughout the ecosystem of clients (thus virtually impossible to accomplish).
• Satoshi's design has no mechanism to constrain the variance of the propagation. Afair, Satoshi's white paper doesn't even talk about P2P network design (other than the SPV client suggestion) in the propagation context and the propagation design issues. All that design work has been done ad hoc over the past years, where I showed with my recent paper that Maxwell et all still haven't even addressed DDoS (which it is synergistic with propagation due to amplication as I explained my recent paper) in the scaling up scenario. I will not explain my entire design now.
• Satoshi's suggestion of SPV lite nodes are too lite to guard the network. Recent comments from the Hong Kong Bitcoin scaling conference (which I really wanted to attend but I am just too overloaded with my illness and trying to get a coin launched) show that Bitcoin lead core dev Wuille at al are thinking more about Segregated Witness and user clients that are in between the power of a full node and an SPV node, as is the case in my proposed design. But afaics, they are a probably a long way from realizing all the issues and then realizing they can't realistically graft this onto Bitcoin and it will instead need to be a side-chain (since those guys work for Blockstream).