The phrase "administrations rather than" is correct and usable in written English.
It can be used when comparing or contrasting two different subjects, emphasizing a preference for one over the other.
Example: "The committee decided to focus on policies that benefit local communities and support small businesses, prioritizing community initiatives and administrations rather than large corporations."
Alternatives: "governments instead of" or "authorities as opposed to".
But until after the Civil War, the spoils system under which federal employees came and went, depending upon party service and changing administrations, rather than meritorious performance, was much the vogue and the prevalent basis for governmental employment and advancement.
They said that the governor's office had taken far more cases to arbitration than previous administrations, rather than reaching settlements for lesser penalties, but that they were hamstrung by an arbitration process that was part of the collective bargaining agreement.
On nearly every page, there is a scene that feels as if it could have taken place during the Bush and Obama administrations rather than those of McKinley and Roosevelt.
Jonathan Powell, former chief of staff to Tony Blair, is writing an update of Machiavelli's "The Prince": "It is based on examples from the Blair, Bush and Clinton administrations rather than 15th Century Florence".
In China, he went out of his way to woo President Xi Jinping, going so far as to suggest that the trade deficit with the United States was the fault of past American administrations rather than of China itself.
His particular complaint is that recent US administrations, rather than providing international leadership as in the age of the Marshall Plan and the Peace Corps, have been distracted by wasteful and sanguinary wars of no clear purpose and suspicious of multilateral institutions such as the UN.
"The problem is with regulations around administration rather than with vouchers," said the association's director general, Andrew Johnson.
Naive as well to hope that a Labour party would be "an effective administration" rather than a "government".
