Phrase for group with no actual power
A blue ribbon commission is a group of people appointed by elected officials to study a problem but with no ability to actually implement any changes. At the end of months of deliberation they write a report which is (usually) ignored.
Often times it's a way for the Government to act like it is addressing the problem without actually pushing forward any policy changes that could be controversial.
On a larger scale you could refer to a "Puppet Government" which has power in name only, but is actually controlled by another state.
[both links are to Wikipedia]