The phrase "almost no authority" is correct and usable in written English.
It can be used to describe a situation where there is very little power or control held by an individual or organization.
Example: "In this chaotic environment, the manager had almost no authority to make decisions."
Alternatives: "barely any authority" or "little to no authority."
In practice, Mr. Tsvangirai's party has had almost no authority to change the fundamental structure of Zimbabwe.
In "Max's Bedtime," first published in 1985, the authority figure is a figure with almost no authority.
The ruling generals have defied a week of protests to reiterate, more forcefully than ever in the last two days, that they expect to yield almost no authority to the new Parliament, and might claim special permanent powers under the new constitution that the Parliament is to write.
In polls, millennials say they trust almost no authority figure to do the right thing most or all of the time: not Congress, not the president, not the Supreme Court, not the media, not Wall Street and definitely not federal, state or local government.
But under the 1996 Communications Act, the FCC has almost no authority to regulate Internet access or content.
The trouble is simply that the BBM data is all handled in Canada in RIM's datacenters, and without a local node on Indonesian, Saudi Arabian, Indian, or other soil, those governments have almost no authority over the information.
The school has almost absolutely no authority over your parents.
For example, if you have a blog post with high authority from dozens of inbound links pointing to it (let's call that post A) and another blog post with almost no page authority (post B), you can boost post B's authority by linking to it from post A, and post A's authority will drop by a similar amount.
But the group had almost no enforcement authority and operated largely out of public view.
Haiti today is an occupied country, with almost no legitimate authority.
The move would mean the FCC would have almost no oversight authority over broadband providers like Comcast, Verizon, and AT&T.
