One of the starting points for public choice theory was Kenneth Arrow’s Impossibility Theorem. Arrow proved that as long as people are diverse in their opinions, and as long as everyone’s opinion counts, it is impossible to create a voting mechanism that guarantees that voters won’t unanimously hate the outcome. Arrow proved that democracy failed a very elementary test.  

Some further implications of the Impossibility Theorem: 
1. Agenda control matters. The outcome of parliamentary voting procedures depends on how you set up the order of the vote. So who sets the order of the vote is critical: The vote for Speaker of the House or Senate Majority Leader is probably the most important vote taken in every Congress. 
2. You want an open primary followed by a runoff between the top two? Congratulations, you might just be giving the governorship to the candidate almost everyone hated. 
3. Democracy–even holding voter opinions constant, even with honest open voting–has multiple possible outcomes, and it’s possible for the final outcome to be unanimously disliked. 
Arrow’s result lowered the relative status of democracy. An outsider might suspect that James Buchanan would embrace such a result; that he would draw on Arrow’s Theorem to emphasize the chaotic, untrustworthy nature of democracy. 
Wrong wrong wrong. Buchanan saw Arrow’s theorem as a reason to trust democracy even more. In his short essay Politics Without Romance, Buchanan said he saw the chaotic multiple equilibria of democracy as a strength not a weakness (emphasis added): 
[A]ny attainment of political equilibrium via majority rule would amount to the permanent imposition of the majority’s will on the outvoted minority…My concern, then and later, was the prevention of discrimination against minorities rather than stability of political outcomes.
Buchanan saw Arrow’s Theorem as a solution to a problem raised by America’s founders: how can democracies avoid the tyranny of the majority? Well here’s one way, Buchanan said: Just let democracy behave normally. As long as people are diverse enough in their views for Arrow’s assumptions to hold, then the factions holding power will change relatively often. His words: 
Would not a guaranteed rotation of outcomes be preferable, enabling the members of the minority in one round of voting to come back in subsequent rounds and ascend to majority membership? 
Where other economists–including myself–had seen Arrow’s Theorem as an indictment of democracy, as a reducing the scope for democratic utopianism, Buchanan saw an argument that democracy might not be quite so dangerous after all. 
I can only presume that when, as a young scholar, he first read Arrow’s result, his reaction was entirely different from that of the rest of us. We read the result, ground out the mathematical proof for ourselves, and dialed back our faith in democracy.

When Buchanan saw the same proof, I can imagine that he grinned slightly, the slight grin so many of us have seen over the years. 

“Now,” he might have thought, “things might not turn out so bad after all.”