What's the opposite of "at the expense of"?
Solution 1:
Other answers provide good specific answers to the question. However, I believe it's worth noting/answering that the most common phrasing is still to focus on the cost to others, not the benefit, when stating something is unfair. This answer should be taken in the context of the other answers.
They're doing X at the expense of Y.
In the majority of situations, such as newspaper articles, you will not see them writing the benefit of the situation as being unfair. Instead, they will focus on the disadvantage to everybody else.
While it wouldn't be wrong to write:
They're building new schools in FancyRichArea, to the sole benefit of a small number of elite students.
What you'll tend to see is:
They're building new schools in FancyRichArea for a small number of elite students, at the expense of existing schools in desperate need of funding across the country.
The general use of these kind of statements is to bring people onto the side of the writer, and get them upset at an apparent injustice. To do this, it is often more effective to write about how the situation affects their readers adversely, and not just write about the unfair benefit given to non-readers.
Again, I appreciate this does not directly answer the question. But it is information I feel that is important to the context of answers given here, that is not fitting to be given in a comment.
Solution 2:
They're doing X to the unfair advantage of G.
Collins:
to one's advantage
phrase If you use or turn something to your advantage, you use it in order to benefit from it, especially when it might be expected to harm or damage you.The government have not been able to turn today's demonstration to their advantage.
COBUILD Advanced English Dictionary. Copyright © HarperCollins Publishers
Usage examples:
Solution 3:
Consider the phrase for one's own profit:
The social media giant has been publically busted for not holding up its agreement with users to not sell information about its members or allow companies to mine Facebook data for their own profit.
Source: Face the Face, Posted By Babs Delay on April 4, 2018, 11:00 AM
I think we do need efforts targeting particular companies, agencies or individuals who are corrupt and are horribly worsening the situation for their own profit.
Source: Clearing Hurdle, Children's Lawsuit Puts Federal Government on Trial for Climate Change Inaction, Posted March 14, 2018
Solution 4:
Perhaps you could slightly re-arrange your example to insert the phrase "one-sided"
They are doing X, and this is having a one-sided benefit for G's health."
Among the definitions listed for one-sided given by Collins are:
- favoring one side; uneven or unfair; prejudiced
- considering or favouring only one side of a matter, problem, etc
- having all the advantage on one side
Notice also the synonym unilateral, if you want to go a little more formal.
Solution 5:
Disadvantage
When something is to the advantage of one, it is usually to the disadvantage of the other.
When something is to everyone's advantage, it's progress.