why didn't democracy work at lord of the flies how did it go wrong and when did it go wrong and why

This is a pretty loaded question. Democracy never worked from the beginning because of human nature. The boys had not yet become entrenched in the adult world of right and wrong. Democracy was a "toy" to them; it was a role-play exercise that didn't last. Essentially, the boys didn't want a responsible leader. They wanted a dictator, someone to fear and obey. The essentials of society like shelters, fire....were abandoned for primal pleasures like hunting and play. Piggy, a symbol of order and democracy, is mocked and humiliated. Democracy takes much work and most of the boys had forgotten what that meant. Instead poor Ralph was left with a group of boys who delighted in chaos instead of order. In the end the conch or voting meant nothing. Instead the boys reverted to what Golding felt was humanities natural order, evil and chaos.

There was no adult to control the Beast. In the absence of "civilization," the boys were overcome by the Inner Beast within us all. We have laws and punishments, but Ralph could not be law and punishment all by himself. As Aslan says the evil and chaos are humanity's natural order. The whole purpose of society is to keep those in check. Mankind fails miserably at this, as evidenced by the "trim cruiser" at the end of the novel--which is merely a more sophisticated form of the war occurring on the island.