It probably wouldn't
Allowing a 2 or 3 or even a 10 year old to vote means more uninformed voters. People of that age can in no way grasp the platforms or issues at hand.
What happen is that their parents, guardians or other adults would simply have them vote the way they want to.
So in essence, the more kids you have the more times you can vote.
Since that usually balances out between party lines it is doubtful it would have any major or lasting impact.
Now lowering the voting age to a more reasonable age would probably play a small part as sometimes certain demographics are swing votes in elections. When its old age pension, medical issues for instance the seniors can usually swing the vote one way or another. When its minimum wage, free education, etc its the young voters that can have an impact.
If for example, we say, as is the case in Nepal where the voting age is 16, every adult citizen has the right to vote, that will not be sufficient to change politics. Registering to vote, having a voting booth easy to get to, having ballots that are easy to read and understand and mark, having enough voting stations to prevent long lines, having voting days and hours that maximize the opportunity to go and vote, having a vote counting system that is transparent and guaranteed to reflect the actual count of the votes, and most of all having voter education so people are motivated and go and vote. All of these provisions are necessary for assuring the public that those who win elections actually are the people that won.
I don't think it would make a huge difference if even a baby could vote. The parents would vote on the child's behalf cancelling out any benefit gained. The other people voting would also vote on their kids behalf so there may be more votes cast but it will be a minimal impact on the outcome of the election.