Can a four-year old participate in the Rite of Election?
==
Is the four-year old also receiving confirmation and first communion at the Vigil? If not, then the four-year old is not a catechumen and is not becoming one of the elect.
There are some precocious four-year olds who would qualify, so maybe you have one. But if it is just baptism at the Vigil, then the child may come to the Rite of Election as anyone else would, but will not be signing the book or listed among the elect.