"limits the influence" is a correct and usable phrase in written English.
It can be used to describe a situation where something or someone has a restricted or diminished effect on something else. Example: The strict regulations on advertising for unhealthy foods limit the influence of marketing on people's food choices.
"That really limits the influence of a lot of people who used to play a big role in all of this".
We need to have a campaign finance structure that limits the influence of the special interests and restores confidence in our democracy".
There have been some changes, including a recent law that bars candidates with criminal records from running for office for eight years, and a campaign finance law, scheduled to take effect this year, that limits the influence of corporate money.
[Capitol Tonight] Campaign finance groups plan to increase pressure on state lawmakers to stop fund-raising outside their districts, which advocates say limits the influence of the lawmakers' own constituents.
This complexity, as well as the fact that it limits the influence of political parties, probably accounts for its infrequent use; it has been used in Northern Ireland, Ireland, and Malta and in the selection of the Australian and South African senates.
The Engine also limits the influence of any single one of your Diggs.
This transformation limits the influences of the most unreliable decision bit to only one syndrome element.
The design presented in this paper offers a stiff construction, which limits the influences of floor vibrations on the measurement.
The city's program was always intended to limit the influence of moneyed contributors.
Breyer asserts that the Constitution permits Congress to limit the influence of these wealthy political insiders.
This, he hopes, would end corruption and limit the influence of regional bosses.
