Some corrections and clarifications:
Bitcoin utilizes a proof of work (PoW) system and works in the following manner,
1. A set of transaction is bundled into a memory pool (mempool)
2. Miners verify each transaction in the memory pool by solving a mathematical puzzle
3. The first miner to solve the puzzle is awarded with newly mined bitcoin also knows as block reward
4.The verified mempool now addressed as block is attached to the block chain.
1. The "mempool" holds
all unconfirmed transactions. A miner selects a portion to be added to their next block.
2. PoW is not verification. It's purpose is simply to add a cost to mining. Transaction verification is done before the PoW step.
3. More accurately stated: The "block reward" includes transaction fees plus the "subsidy".
Proof of Stake
Under this method there is no need to solve a mathematical puzzle instead, a creator of new block is chosen based on their stake. Stake is the number of coins/tokens one possesses. Under this system all tokens/coins have been already created so there is no block reward instead the miners would get a transaction fee
Many PoS coins include a subsidy in addition to transactions fees. Unlike Bitcoin, they have permanent inflation.
Security
PoW – Forking of blockchain is not desired as it is unhealthy for a network and can lead to instability. Under PoW system if a blockchain is forked miners will have to chose between the blockchains or if they plan to support both blockchains their computational power has to be split. As a result from an economic perspective forking is generally discouraged under a PoW system
Branches in the blockchain can add some minor instability, but it is not necessarily "unhealthy". The instability is minor because miners are motivated to choose one branch to follow.
PoS – This system does not inherently discourage forking and therefore when the blockchain is forked it can possibly result in a problem knows as “nothing at stake”. This essentially happens when a validator/miner receives a duplicate copy of their stake for a newly forked blockchain and he is able to sign off on both forks and potentially claim twice the amount of transaction fees as a reward and double spend their coins. A participant is not required to increase his/her stake to validate transactions on multiple blockchains and results in no economic incentive preventing the nothing of stake problem in the PoS system.
The "nothing-at-stake" problem occurs because validators are not motivated to follow a single branch (unlike PoW). They can choose to follow
every branch and the result can be serious instability. A miner following multiple branches does not receive extra rewards, but they can potentially use the instability to spend coins that that they ultimately don't own.
Centralization
PoW – High risk of centralization mainly due to the reason mining being a expensive process and therefore reserved predominantly for large scale operations. This is contrary to the main principle advocated by blockchain technology which is the concept of decentralization
PoS – A fairer concept in which the amount of network control granted is directly proportional to the the amount invested in the token/coin.
PoW – Larger-scale mining has an advantage, but it does not preclude small miners. The degree of centralization depends on the ability of larger miners to reduce their costs more than smaller miners.
PoS – PoS can be just as centralized. For example, 10 addresses control 50% of the EOS tokens.
