The phrase "a relatively small majority" is correct and usable in written English.
It can be used when discussing a situation where a majority exists, but the majority is not significantly large compared to the total group.
Example: "In the recent vote, a relatively small majority supported the new policy, indicating that opinions were quite divided."
Alternatives: "a narrow majority" or "a slight majority".
Despite the government's relatively small majority, its chances are boosted by the fact the SNP is unlikely to take part in the vote, as it affects only English schools.
Trump's protestations that his agenda is being hampered by the Republicans' relatively small majority in the Senate and by Democratic opposition are at odds with his criticism of then-President Barack Obama for blaming Republican obstruction for hindering his policies.
Multimodality approaches have been of some benefit in prolonging the survival of very highly selected subgroups of patients, but they have had a relatively small impact on the majority of patients diagnosed with this disease (Sterman et al, 1999).
Firstly, this study involved a relatively small number of participants, the majority of which were male, so this limits its generalizability.
Readers were advised that women living without a spouse — the new majority — included "a relatively small number" whose husbands were temporarily away from home serving in the military or out of town working, or who were institutionalized.
A relatively small number of companies receive the vast majority of the money from this program.
Decisions continued to be made by a relatively small group of high-ranking nobles, the majority of whom were now clients of the retired emperor rather than the Fujiwara regent.
First, this study was limited to a relatively small cohort of trauma patients with the majority of persons requiring less than 24 h stay in hospital.
And the increased inequality undercuts real growth because a relatively small group of people who get the majority share of benefits cannot spend and consume enough to drive overall growth, and the mechanism creates a positive feedback loop, in which means things get driven further and further in an "adverse" direction.
