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I am trying to understand the below statements and also the intuition behind burning ether. Could you elaborate on the below statements from https://ethereum.org/en/developers/docs/intro-to-ether/.

Burning the base fee prevents various ways block producers could manipulate it otherwise. For example, if block producers received the base fee, they could include their own transactions for free and raise the base fee for everyone else. Alternatively, they could refund the base fee to some users off-chain, leading to a more opaque and complex transaction fee market.

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You'll find some of the motivations in EIP-1559. I've highlighted some sentences to make them more clear.

An important aspect of this fee system is that miners only get to keep the priority fee. The base fee is always burned (i.e. it is destroyed by the protocol). This ensures that only ETH can ever be used to pay for transactions on Ethereum, cementing the economic value of ETH within the Ethereum platform and reducing risks associated with miner extractable value (MEV). Additionally, this burn counterbalances Ethereum inflation while still giving the block reward and priority fee to miners. Finally, ensuring the miner of a block does not receive the base fee is important because it removes miner incentive to manipulate the fee in order to extract more fees from users.

Also you'll find a more lengthy discussion in the EIP-1559 thread https://ethereum-magicians.org/t/eip-1559-fee-market-change-for-eth-1-0-chain/2783

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