What is the role of government?

Some ideas:

1. Government should represent its people’s preferences and interests via the democratic process. This seems nice, but it is the most clearly flawed.  First, nobody seems to really believe that politicians should blindly follow the desires of their citizens.  The populace is ill-informed, often wanting many incompatible things at the same time (lower taxes, but more government services).  It is often fickle, and can be easily swayed into extremes.  Elected officials are supposed to listen to their people, but also to lead them in the right directions when the situation demands it, and to play to their better angels. 
2. Government should represent its people’s enlightened interests via the democratic process. This seems to be the sort of default position that many people hold now.  Elected officials are expected represent the interests and preferences of their constituents and also the national or state interest.  But they are expected to represent a sort of enlightened interest of their citizens, or what their citizens should want.  This is a nice concept, but the devil is in the details.  How should politicians decide what is in the best interests of their people?  This is just too subjective.  To believe that government should follow the interest of its citizens is to allow government an ethical role. You are allowing government to decide what issues should be prioritized over others. 
3. Government should attempt to maximize the lives and health of its citizens. The appeal of this role for government (and the next) is that it is neat and objective.  Ethics can (mostly) be removed from the picture, and government can adopt a utilitarian attitude in policymaking, with maybe some tweaks around the edges.  I find this to be the most compelling role for government, but perhaps that is because I am most interested in health policy.  Or maybe vice versa.  In any case, this seems like the best way to find an objective role for government as well as a compassionate role for it. 
4. Government should attempt to maximize the prosperity of its citizens.  I like this role for many of the same reasons as the previous role.  It is perhaps the most objective, and many would say that it is closest to what policymakers try to do.  A compelling argument could probably sway me to switch from #3 to #4.  I currently come down on the side of #3 because I think that health and life is a more worthy objective than prosperity.  Prosperity is good, and it leads to good outcomes such as better health, but I think it’s less valuable in itself.  An argument could be made though that many (say, professional football players) value prosperity over a few extra years of life (although I would argue that status plays a larger role than wealth in that decision). 
5. Government should attempt to maximize the happiness of its citizens.  In a simpler world, this would be my favorite.  Happiness is a great ideal to strive for, and one can argue that there are objective metrics, but I’m skeptical.  I’ve never been convinced by any of the attempts to objectively measure happiness.  Some of the techniques are clever, and they are better than nothing, but none seem sound enough that I would feel comfortable building broader government policy around them.