Isn't that the answer to all petitions? Petitions are just pleas to the king. It is in the king's prerogatives to ignore them.
What you need in a democratic society is not petitions, but acts of parliament.
"This split between "democracy" and "constitutional republic" is something being pushed more and more, but it's really a fantasy peddled by some US-based politicos with vested interests in devaluing the concept of democracy and making you accept the fact that you should be happy without it.
A "constitutional republic" is something defined by a set of laws with certain specific elements in common: having a constitution and being a republic (which is also quite a loose term, used to define "anything that is not a monarchy" -- Iran is also a constitutional republic, for example, albeit a theocratic one)."
Whole comment at https://news.ycombinator.com/item?id=3668684 See also https://news.ycombinator.com/item?id=8542546
Someone recently pointed out that California is as close to a direct democracy as we get in the US and look at what it's doing there: "Raise taxes? Nope! Fund schools: Yup!" People end up making decisions that benefit them in the short term while ignoring the global consequences. That's human nature and direct democracy assumes that everyone is an informed rational thinker.