This makes me wonder what the laws are for people with dual citizenship. Do you have to pay taxes to BOTH countries? Probably not, because then the only way to escape US taxes would be to renounce your citizenship. That sounds difficult.
By law you can have RESIDENCE (which is different from citizenship) only in ONE country. So, that's where you pay your tax.
There are ways to avoid that requirement as well. Only if you are staying for more than 181 days (out of 365), you need to pay taxes. You can spend 122 days each in three different countries to avoid paying taxes.