A bitcoin is a crypto-signed message.
The blockchain is an archive of signed messages.
If you could find a trusted centralized entity to determine what transactions...
You can't trust an entity that is held accountable by no one.
Of course, I'm just saying the problem that Bitcoin solves in a novel way with mining is the very specific double-spend problem, everything else it does doesn't need a blockchain. (well, maybe initial coin distribution too)
If you could find a trusted centralized entity to determine what transactions, and in what order, should go in the blockchain, you wouldn't need mining at all.
Or you could find a decentralized entity that determines who puts what transactions in the chain, without mining.
If you can figure out how to do that and be sybill-attack resistant you can be the next Satoshi.
Expanding on my last message, actually, come to think of it, we don't need a one-to-one relationship... and maybe spam isn't as big of an issue.
Lets suppose we want to start a pure alt-coin. Lets assume the initial coin distribution problem is solved, and multiple participants have coins they want to create transactions for. Like Bitcoin they can broadcast their transactions on a flood-fill P2P network, letting everyone know about them.
Anyone is then allowed to build a block consisting of a merkle tree of transactions, hashed with a header that includes a reference to a parent block. They broadcast this block on the alt-chain P2P network, and simultaneously broadcast a specially marked Bitcoin transaction including the hash of the block on the bitcoin P2P network. Dos attacks can be avoided by dropping nodes that transmit blocks without submitted the associated Bitcoin transactions.
Unlike Bitcoin the rule is that multiple parallel blocks, that is blocks with the same parent block, are allowed. Transaction validity however is defined by being in the block whose marked transaction in the bitcoin block chain is first. Transactions that are found to be invalid can be ignored simply ignored, and blocks with excessively large numbers of invalid transactions can be ignored in their entirety. You'll may also still want some sort of payment-based rule to discourage creating huge numbers of blocks, such as a mandatory fee, maybe tied to the average transaction fee on the bitcoin network. You can determine if your peers are hiding transactions from you by just scanning the bitcoin blockchain, although come to think of it this mechanism is susceptible to griefing by creating bogus marked transactions...
This does do a decent job at minimizing the extra junk left in the Bitcoin blockchain though by allowing transaction combining. It's also possible to "merge-mine" multiple such alt-chains with just one transaction.
Oh, and here's another idea: going back to the "highest-paying block wins" it'd actually be possible to solicit donations to pay the fee. The proposer of a block would create a transaction template and solicit signatures from the donators. The interesting thing here is donators can donate to multiple candidate blocks that they are happy with, and only one block would ever get accepted as the others would look like double spends. Griefing is of course possible, just like similar coin-mixing proposals, but solutions to the latter may be solutions to the former. Again, I dunno if this is actually useful, but maybe someone will come up with an application for the idea.
