Inspired in parts by Result of a goverment where extra votes can be bought, earned, or lost? and in parts by actual political discussions:
Let's take a society similar to the current North American / Western European ones. Kinds of politically stable, democracies, multiple parties. Demographically, the rate of children per woman is somewhere in the 1.5 region. Society is receiving some population influx from outside, but total numbers are holding stable / mildly declining.
And now, we change the voting system slightly. Let children vote! Okay, not really. Let their parents vote for them until they are 18! One of them, at least - an appointed voter, needs to be a legal guardian. At 18, that vote goes to the now-adult. This applies directly after birth - no pregnant women voting for two, but it's instantaneous as soon as the birth is registered. When there's multiple guardians (like two parents...) and they can't agree on who votes for the child, nobody gets to.
How would this influence society / politics over the short and long term? Would we even see a big impact?