Bitcoin address X contains 1.06 bitcoin.

Let's say a miner sees two unconfirmed transactions broadcasted - the first one says to send 1 bitcoin from address X to address Y. The second transaction says to send 1 bitcoin from address X to address Z. Both transactions cannot be completed. This is a double spend.

My understanding is that Bitcoin miners can write their own miner software to choose which transaction to process in any way they wish. They could include in the next block whichever transaction has the higher fee, they could go with whichever transaction they received first, they could go with whichever one has more of the letter 'Q' in the destination address because they like the letter Q.

But in practice, how would this normally be handled by most miners' software?