As I see it extradition is quite an infringement on a persons liberty and should thus be treated in some form of legal process (like say, warrants for searching someones home). If this process is handled in the state where the crime is committed or where the accused lives, or both, matters less as long as it is the same for everyone.

Thinking about it, I think I prefer it to be handled in both states - one issuing the warrant, the other trying it - as both state apparatuses are involved in the infringement of liberty.

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