**Yes, you can make a Robot Overlord**
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The question of whether an algorithm could be constructed that spits out laws and policies to govern a human society is not at issue.  The complexity of such a thing is mind-boggling but I don't doubt that it can be done.  We have algorithms that can make decisions extremely quickly (such as high frequency traders) and we have algorithms that can make sense of unbelievable mountains of data (such as [Yahoo!][1] [Hadoop Cluster][2]).  We already have plenty of compute power in the form of Amazon Web Services, Microsoft Azure, Google Compute Engine and others.  How to synthesize all that data into something that can say "make this law, here" is another matter.  It's definitely computable, just not easy.

You would need data sharing agreements with access to almost everything about a person's economic life, including but not limited to credit card usage, tax returns and debt load.  If you had this for every person in a 1st world country, you'd have a really really good idea of how the economy is going.  Combine this info with all the research from economic statics researchers (Thomas Piketty is a good place to start.)

**But Acceptance is hard**
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The primary issue with this is getting humans to accept such leadership.  So either a large change in mindset will need to happen based on a long period of successes by algorithm controlled leaders where people literally say "I welcome our new robot overlords!" or control shifts in the background to where no one sees it.  The former approach is certainly difficult and may ultimately fail.  The latter approach while sneaky, has a better chance of succeeding because it doesn't have to outright face political scrutiny.  A political leader just needs to follow the advice of the Robot Overlord and they will make the optimal decision based on available data.

A sociologist and a political scientist could probably give you a better idea of all the factors that go into how humans make political and economic decisions. 

  [1]: http://www.hadoopwizard.com/which-big-data-company-has-the-worlds-biggest-hadoop-cluster/
  [2]: http://hadoop.apache.org/