Majority

I think I've given my opinion on this elsewhere already, but as for these sentences:


1-1. These days a vast majority of children avoid chickenpox.
1-2. These days the vast majority of children avoid chickenpox.

In (1), the proximity of 'children', clearly a countable plural, makes the singular ring strange, even though we know that 'majority' is a singular noun.


2. Most people don't think it is good as it is/stands, but a/the majority don't want to get involved (in it).

Similarly here, with 'people'. All of your other word choices are OK.


3. A two-thirds majority is needed/required to override a veto.

Here, majority is comfortably singular, and I notice that you do not question it. The alternate verbs that you offer are non-native to me.


4-1. He won the governorship by a (small/narrow) majority of 1500.
4-2. He won (by) a small/narrow majority of 1500 at the gubernatorial election.

All of (4) seem acceptable to me, except for the adjective for 'governor'.