The phrase 'influence on decision' is correct and usable in written English.
It implies that something has had an effect on a decision being made. For example, "Bill's positive attitude had a positive influence on my decision to take up a new job."
On the other hand, some of the green building rating criteria have immense influence on decision makers to choose only one between various sustainable building technologies.
And in one of the first studies on researchers' influence on decision makers in Mexico, in 1994, Trostle et al. (1999) interviewed both researchers and decision makers about the relationship between health research and policy in the programme areas of AIDS, cholera, family planning and immunization (Trostle et al. 1999).
From their current influence on decision making to their future purchasing power, children represent a powerful force in the marketplace.
"Ahmad Chalabi, Kanan Makiya, all of these people became media stars, but their influence on decision making was next to nothing.
Faghihinia and Mollaverdi (2012) presented a multi-criterion decision-aided maintenance model with three criteria that have more influence on decision making: reliability, maintenance cost and maintenance downtime.
This paper presents a multi-criterion decision-aided maintenance model with three criteria that have more influence on decision making: reliability, maintenance cost, and maintenance downtime.
Nonetheless, it concluded, "no critic of W.H.O. has produced any direct evidence of commercial influence on decision-making".
A subsidy is not ipso facto a bad thing (Cassandra loves the subsidised French TGV trains…), but it can clearly have a malign influence on decision-making.
Ultra-rich philanthropists and their foundations have increasing influence on decision-making and are setting the global health and agriculture agenda in developing countries, according to a major study (pdf).
Beyond these achievements, the experience of the past seventy years has made it clear that reform and adaptation to the times is always necessary in the pursuit of the ultimate goal of granting all countries, without exception, a share in, and a genuine and equitable influence on, decision-making processes.
One reason for the increased interest is that regret has a significant influence on decision-making.
