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As we know bitcoin uses Proof of Work Concept and it introduces never ending long block chain and some other issues. Why is it not designed in a way to use consensus algorithms what ripple uses? What is reason for proposing the Proof of Work Concept when implementing the Bitcoin? Is there any special reason? or Is it a mistake happened when designing the Bitcoin?

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It's a good question. You will however find many subjective answers to that question. There are arguments both for and against PoW. Some people will disregard many of the arguments and only consider those supporting their own point of view. – kasperd Aug 1 '14 at 12:57

PoW, apart from securing the network, also provides a way to democratically distribute the initial coins. For systems like Ripple there's no real democratic way of distributing the coins.

Here's a comment by D. Schwartz specifically on this matter: Bitcoin without mining

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Bitcoin's PoW isn't democratic any longer—it requires an investment in specialized hardware and technical expertise. – alwillis Aug 5 '14 at 16:22

Why is it not designed in a way to use consensus algorithms what ripple uses?

A consensus algorithm requires that you can trust contributing nodes. Otherwise, you're open to a Sybil attack, where an attacker creates many dummy nodes. Ripple was built on the idea that you can establish trust in some entities, trust that they will not collude to defraud you.

Proof of work, as Bitcoin uses, has some advantages over this: proof of work does not require trust of any kind, and it doesn't require that you know anybody's true identities. Instead, you trust the proof that someone put a lot of work (time/money) behind establishing a block. Since Bitcoin aims to be a completely trustless, decentralized network, that allows some anonymity, it makes sense to use proof of work in it.

Of course, proof of work also has some disadvantages: a slow block time (say, a minute or more, to keep the orphan rate low) is necessary, which slows confirmations. It can be overtaken by someone controlling >50% of the network's hash rate. And it results in work just for the sake of work, wasting electricity. Also, while ideally each user/node would have an equal share (just their own CPU), ASICs (and their predecessors) instead focus this control in more-centralized miners.

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