Just an interesting concept for the future, though A.I is still in its infancy, it is likely that A.I will eventually be at the forefront of technology, but also could be important factors in many other regions such as entertainment, economy and such. But could an A.I be a better leader?

Lets look at the advantages:

1. Could solve thousands of problems per second, maybe even more in the future.

2. Never requires sleep or break, meaning increased efficeincey.

3. If connected to the internet, it would allow to communicate with anyone near instantly.

4. Isn't biased or corrupt or has a specific political agenda, meaning the best solution to the problem then the solution which benefits them.

Though it is possible that it could be hacked, have an error or could shut down if there is a power cut, it could be a very good leader.

The only issue with AI type governance is that you entirely remove the human element of emotion. Politics require the ability to utilize compassion in certain decisions, the ability to pick apart the layers of a situation that is teeming with emotion, subtle inferences, and double meanings. While a straightforward, logic only approach could benefit some situations I don't see it being a fix-all. 

Take the situation of the soccer team trapped in the cave. Humans saw children, our future, trapped and in great harm. To those looking at the situation, there was only one course of action, to immediately begin setting up a rescue operation. During the course of the rescue, a ridiculous amount of money was spent and one very skilled individual died. While it is sad that someone died, the mission was accomplished and the children are safe.

If an AI was to make the call would a rescue operation be called for? Would it have been the logical approach? AI works on logic, statistical probability, and calculates all of the available variables to determine the most efficient outcome. Risking the lives of dozens of highly trained, extremely valuable members of society, for the lives of some children who may not achieve success to the measure that amounts to the cost of their rescue, is not logical. Statistically speaking most the kids combined will not earn and contribute back into society enough to return the investment that went into rescuing them. So an AI could have easily determined that leaving them in there without rescue would the most efficient and logical approach. Humans, on the other hand, have the benefit of compassion, value for life, and the ability to dream big and say what-if.  We can accept that despite the statistical likelihood, any one of those children has the capacity and the chance to go on and change the world. 

Would AI be a better leader than a human? I would say that answer is strictly dependant on how you are measuring the success of a leader. If its strict efficiency, cold and calculated decisions without compassion or empathy, then I would say yes. If its about pushing the peoples of the nation to dream big and strive against all odds to achieve the thought-to-be unachievable...well, thats where Humans come in and where Humans will need to stay.