In the context of the Drivechain proposal, for UTXOs in miner-controlled escrows to be spent, they have to be voted on by each block over a large number of blocks, right?

Now, how are these votes made and where are they computed? I think the votes are somehow written in the block coinbase, but how exactly? It's not like there's much space there. And then each full node has to keep a table of what transaction has how many votes and verify against that whenever a transaction is included in the block?