Consensus of the order of transactions. A could sign two messages: "I, A, send my bitcoin to B" and "I, A, send my bitcoin to C". There needs to be global cons

Consensus of the order of transactions. A could sign two messages: "I, A, send my bitcoin to B" and "I, A, send my bitcoin to C". There needs to be global consensus whether the bitcoin ends up with B or C, otherwise the coin would be effectively duplicated and it wouldn't work as money. And further messages that A might sign in the future should not be able to retroactively change the recipient -- e.g. if we used a rule "the first recipient in alphabetical order wins", then A could take back the money months later by signing "I send my bitcoin to myself". So bitcoin instead uses "the first transaction to be put into a mined block wins", and thus needs a global consensus for the order of mined blocks.