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Anarchy is a system without the need of a central authority.
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Anarchy as in greek anarchia which translates to "without rulers" this however does not mean that there are no rules. There is a big difference between a person or a group or persons setting rules (thus beeing rulers) or a mutual aceptance of a certain set of rules.
I disagree with Foxpup that this contradicts capitalism (as in you own what you own and can trade it to anyone you like).
Democracy is not an economic system. It is a politic ideal. In fact it doesn't exist because it is too easy to corrupt in any system.
This ideal existed once for few years in Athens but it has been corrupted and we never got close to it since.
It was far from ideal in Athens, mainly because only citizen could vote and thus the minority.
Perfect democracy (as in consensus not majority) is the same as perfect anarchy. If everyone has the same rights you dont have anyone above you and thus no ruler.
But lets get back to the topic, which is p2p not political systems if I remember correctly.
p2p has political and economic impact.
Everything of relevance has impact.
It is against capitalism.
p2p itself is not against anything. If you think so, please explain why. Because the way you just say "its like this" we can not argue with you.
Think about the millions of music and movies downloads.
Thats refering to the bittorrent protocol I assume? What about them? They changed the way to music industry thinks about distrubuting music and the same downloads will revolutionize the film industry. The current distribution system is outdated. Why cant I pay x amount of currency to watch HBO from e.g. Jamaica? Or just the show I want to see? This makes no sense with the internet.
Anarchy is a system without the need of a central authority. Network resources can be anything: software, video files, audio files, images, e-books and of course COINS!!! Bitcoins are DATA. And like any other data can be shared equally through the network.
The blockchain is shared equially amoung all full nodes. The "coins" are allways in the blockchain you only hold a private key, which is the right to spend certain coins.
Bitcoin IS NOT 100% P2P!!! Only some functions are p2p. Not all functions.
Which functions are not? Why are they not p2p? What do you think is p2p?