Miner Extractable Value (MEV) is a big topic in the life of Ethereum users, and it creates an additional revenue source for the miners.
Is MEV possible on the Bitcoin blockchain as well? And if yes/no, why and is it being used?
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In Bitcoin, transactions generally¹ have immutable self-contained outcomes—they boil down to a list of inputs spending existing UTXOs, and a list of outputs to be created. All the amounts involved are independent from the position in the block, or even what block a transaction gets into.
In Ethereum, especially transactions interacting with more complex smartcontracts, some of the values of transactions are dynamic. If you e.g. place a market order on a decentralized exchange, you may get more or less for your money depending on whether other transactions call the same contract before you. Since miners see transactions before they are confirmed, they can front-run such transactions. This is how they can extract value by reordering transactions.
¹ Arguably, miners could hypothetically benefit in scenarios where there are multiple transactions with competing outcomes, e.g. the closing of a Lightning channel. In some such situations, a miner could perhaps benefit from not including a transaction in their block or doing something else than picking the transaction with the highest feerate. This could potentially lead to some form of MEV on Bitcoin, but if the incentives of such second-layer protocols are properly designed, I would expect them to remain negligible exceptions.
No, in Bitcoin most miners simply choose the transactions with the highest fees.
The order of transactions just has to be valid (eg, transaction that spends a UTXO of another transaction in the same block has to be placed after the transaction it spends). As long as it is any valid order, which particular order is not particularly important.