Simple version that is what mining does.

Also what is "first" and "second" with a distributed network.

I send transaction A to you (and thus half the network)
I send transaction B (a double spend of A) to someone else (and thus half the network).

Now half the network thinks A is "first" and half thinks B is "first".  So each half thinks the other is invalid.

Starting to see the problem.

Have you even read Satoshi paper? 
From what I've read so far, the second transaction will be considered invalid. My currency will do the same.
I'm not sure what Bitcoin does to prevent both products delivered, but you certainly will be given a bad rating as a costumer, thus losing trust from other potential sellers.

Thank you for your criticism!
[/quote]