Garett Jones  

Buchanan: Seeing With New Eyes

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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."

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CATEGORIES: Public Choice Theory



COMMENTS (8 to date)
jsalvatier writes:

(I say this as someone who is much more anti-voting than most people for Caplanian reasons).

Arrow's Impossiblity Theorem is often over interpreted. People often interpret AIT as 'good voting systems are impossible', but what it really means is that 'voting systems that meet AIT's criteria are impossible', AIT's criteria don't map directly to goodness. For example, it totally rules out randomized tie breakers, as well as anything attempting to measure preference strengths. Taking into account preference strengths seems like an important feature of a voting system to me.

AIT certainly suggests that a good voting system is not trivial to design, but it doesn't mean it's impossible to design one.

(see http://blog.tyrannyofthemouse.com/2010/10/setting-arrows-impossibility-theorem.html for more)

Chris writes:

So James Buchanan was a genius because he understood a point made in Robert Dahl's 1956 "Preface to Democratic Theory?

blink writes:

The thoughts on Buchanan's take are worthwhile, but the post is so vague as to mislead. What does it even mean to "guarantee" that voters won't "hate the outcome"? Or for one to be "unanimously disliked"? (Unanimity can't be taken in Arrow's sense...) How about "democratic utopianism"? Aie, but there are good ideas buried beneath the sloppy language.

Jim Rose writes:

this was a great insight by buchanan. what is so wrong with instability?

Garett Jones writes:

Just returned to a computer; I edited the first and second paragraphs for clarity.

Thanks to blink for noting my ambiguity in the initial version.

Buchanan saw an argument that democracy might not be quite so dangerous after all.

Or, as the cliche has it, democracy is the worst system ever invented...except for all the rest.

Arthur_500 writes:

Hmmm, maybe I still miss your point(s) but democracy was de-bunked by the ancient Greeks.

When the US Constitution was written the idea of democracy was thrown out immediately as the tyrany of the majority.

Maybe there is a place for democracy. Maybe when we sit down to dinner the majority gets the meal they desire. However, in government, and elsewhere, fairness is lost in a democracy.

Buchanan and others recognized the important of protecting the miniority. Does Arrow's Theorem indicate laizzez faire governing will balance out in the end? If so then what is the appropriate sample size to see it balance out?

Craig Yirush writes:

But why is unanimity necessarily tyrannical? Is the fact that the overwhelming majority of Americans today reject racism or slavery or religious bigotry a bad thing? Would you be upset if a clear majority of Americans were opposed to rent-seeking or deficit spending? Is there really a benefit in having a diversity of bad or immoral ideas?

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