Most supporters of democracy embrace the ideal of majority rule.  The great Swedish economist Knut Wicksell started from a different ideal: Unanimity.  If your idea is so great, shouldn’t we all agree to it? And even if it’s only a great idea for 51% of the people, if it’s truly great then the 51% should be able to buy off the support of the other 49%.  

Under unanimity rule, everybody wins, every time.  Pareto efficiency in economics jargon (or is it sociology jargon?).  

It’s yet another example of the Coase Theorem: Regardless of who owns the property right–here, the right to stop change–if people are good at bargaining, then we should be able to get to an efficient outcome.  
Buchanan and Tullock, in the Calculus of Consent, wisely started from the Wicksell position and dialed back slightly (check out the legendary chapter 6 here, Alex’s PowerPoints on the topic here).  In real life, some people are grumpy holdouts–maybe they’re bad bargainers, maybe they’re just oddballs whose well-being we don’t place much weight on.  In cases like that, even if a deal is worth doing, you probably won’t insist on 100% agreement.  
But you’d probably still want more than a mere majority: So especially on big issues, a society that wanted to really make almost everybody better off would make government decisions with supermajority rule.  
There’s another reason to support supermajority rule: Credibility.  If you live by the one-vote majority, you die by the one-vote majority.  And when actions today depend on beliefs about future government actions, credibility matters a lot.   
In the realm of monetary economics, credibility has become an obsession in recent decades. The rational expectations revolution made monetary economists worry about how beliefs about the future influence behavior today.  And the problem of credible commitment by politicians and bureaucrats–usually known as the problem of “time consistency”–brought a more explicitly political edge to the issue of beliefs.  
Investors, savers, CEOs–all care about the likely future more than they care about the promised future. Promises are cheap, after all.  
I’m guessing the issue of credibility has kept Bernanke awake nights over the last four years.  The full story of his lobbying and cajoling and persuading other members of the Federal Open Market Committee (FOMC) remains to be written, but he appears to have succeeded at creating credible expectations that the Fed will stick with his policies whether he’s reappointed as Fed chairman or not.  
I could show you market based evidence of that, but I’d rather show you the mechanism that really illustrates Fed credibility: The Bernanke supermajority.  
Below is a chart from the FOMC’s economic projections report, a regular report that deserves your attention.  It shows the number of FOMC participants (voters and nonvoters) who think 2012, 2013, 2014, 2015, or 2016 is the right year to start raising short term interest rates: 
Looks like they’ve got a solid supermajority for 2015.  Of course, these are people forecasting their own future choices, and the best choice will change as the data change.  But (setting aside the issue of which FOMC members are allowed to vote in a given year) there’s a filibuster-proof supermajority behind extended easing.  
Someday, we may find out what Bernanke’s own preferences have been in recent years.  But in any case, since credibility is hard to gain and easy to lose, it’s worth sacrificing the best policy in order to get a credible policy.  And the credible policy isn’t the policy that squeaks through by one vote.