Full Idea
The veil of ignorance ensures that the original position is fair, but it also guarantees that agreement will be unanimous (which would be impossible if each person insisted that justice should match her own conception).
Gist of Idea
The veil of ignorance ensures both fairness and unanimity
Source
Tuckness,A/Wolf,C (This is Political Philosophy [2017], 4 'Original')
A Reaction
Not clear about this. If I choose very cautiously, but others choose very riskily, and they win, why I should I fall in with their unanimity? That can only be if we agree to be unanimous in backing the result. Like a democratic election?
Book Reference
Tuckness,A / Wolf,C: 'This is Political Philosophy' [Wiley Blackwell 2017], p.85