The Ethereum network is permissionless, like Bitcoin’s; no central entity controls either the production of Ether or is involved in their transfer. In its current release (HOMESTEAD), Ethereum uses a Proof-of-Work algorithm (‘Ethhash’) like Bitcoin’s, but with two modifications to reduce the risk of mining centralization:
The algorithm operates with a protocol favouring nodes using computer memory rather than ASICs (Application-Specific Integrated Circuits) to discourage formation of ASIC-using mining pools.
Nodes producing orphaned blocks, or that include orphaned blocks in the blockchain, receive a reduced block reward to encourage them instead to continue with the latest block in the Ethereum blockchain.
Proof-of-stake is one of the two most commonly used blockchain consensus algorithms (together with Proof-of-work). In Proof-of-stake, new blocks are said to be ‘forged’ (or ‘minted’) rather than ‘mined’. Under Proof-of-stake, the node selected to create the next block is chosen through a pseudorandom process that depends partly on the wealth in its associated wallet (i.e. in its staking pool). As the selection is pseudorandom, no node can predict its turn in advance. A certain number of coins are kept in the staking pool to purchase block creation chances.
Proof-of-stake has the following advantages over Proof-of-work, it does not consuming significant computing power, reduces the risk of malicious attacks as it discourages centralized mining pools and as block-generators own coins, those ‘guarding’ the coins also own them (this is not necessarily the case in Proof-of-Work).
‘Nothing at Stake’ - Precisely because there is no cost in voting for multiple blockchain histories (as opposed to just one), a block-generator experiences no deterrent against working on multiple blockchains. This can prevent the consensus from forming, and increases the risk of ‘double spend’.