Theocracies - those nations supposedly governed by God - are a strange animal in this world. Look at modern-day Iran, for example.
The Ayatollah in theory has the power to overrule the democratic institutions of the nation if he feels their actions run counter to Allah's will. That may be what happened in the recent elections there. It appears that many voters have challenged his supreme authority.
Historically, the Christian Church of the 1300's and 1400's had something of a similar hierarchy. The Pope had ultimate power to influence governments. Monarchs needed the Pope's approval for major decisions.
The popes, in those centuries, became more and more corrupt. They formed an international powerhouse that was subject to no one - but they were not ruled by God's principles. Their reigns were based on political alliances and manipulation that might make our heads spin today. Or not, considering our current politics.
When Moses led the people of Israel out of Egypt's slavery, we see a working theocracy. Moses met with God and conveyed God's commands to the people. God led the people.
However, when the Israelites finally reached the Promised Land of Canaan, the theocracy which continued soon collapsed. If you've ever read the book of Judges, you know the theme of that book is "each man did what was right in his own eyes."
More specifically, Judges shows us that we need a king. We don't do so well on our own. Often, theocracies have a Wizard of Oz look, where the show is impressive but it's all run by a guy behind the curtain.
How is God involved in government? Tomorrow, I'm going to search some biblical texts for principles to apply to our political leaders.