Category: Political Science
Popularizing Arrow’s Theorem II
Arnold Kling is not satisfied with Tyler’s popularization of Arrow’s impossibility theorem asking (in the comments) “what exactly did Arrow show was impossible?” Here is my attempt.
- Andy walks into an ice-cream shop and seeing that they have chocolate, strawberry and vanilla, orders chocolate. Before the vendor has a chance to scoop the ice cream she says, “Sorry, we are out of strawberry.” “In that case,” Andy says, “I’ll have vanilla.” Strange right? Yet however strange we might think this behavior is for Andy it is routine when groups make choices (just substitute Bush, Nader, and Gore for chocolate, strawberry and vanilla.) (Failure of IIA.)
- Andy likes sprinkles on his ice cream. Andy walks into the ice-cream shop and seeing that they have chocolate, strawberry and vanilla chooses chocolate. Before the vendor has a chance to scoop the ice cream she says “Today, chocolate comes with free sprinkles.” “In that case,” Andy says, “I’ll have vanilla.” Strange right? Yet once again it is easy to show that improving an option can result in a group rejecting that option (n.b. no psychology is involved in this result). (Failure of positive association.)
- Andy walks into a supermarket and is offered apples or bananas and chooses apples. Andy is then offered bananas or coconuts and chooses bananas. Andy is then offered apples or coconuts and Andy chooses coconuts. (A>B, B>C but C>A). Strange right? Not only is this strange, if Andy has preferences like this the supermarket can take all his money with a money pump. Once again, however, it is quite possible for groups to cycle in just this way even if every individual in the group has perfectly normal (transitive) preferences. (Failure of transitivity).
Paradoxes such as the above have been known for centuries. What Arrow showed is that no decision mechanism can eliminate all of these types of paradoxes. (n.b. Arrow’s theorem actually applies to any mechanism for aggregating any rankings not just voting and not just preferences.) We can tamp down some paradoxes but only at the expense of creating others (or eliminating democracy altogether.)
More generally, what Arrow showed is that group choice (aggregation) is not like individual choice.
Suppose that a person is rational and that we observe their choices. After some time we will come to understand their choices in terms of their underlying preferences (assume stability–this is a thought experiment). We will be able to say, “Ah, I see what this person wants. I understand now why they are choosing in the way that they do. If I were them, I would choose in the same way.”
Arrow showed that when a group chooses, there are no underlying preferences to uncover–not even in theory. In one sense, the theorem is trivial. We know or should always have known that a group doesn’t have preferences anymore than a group smiles. What Arrow showed, however, is that without invoking special cases we can’t even rationalize group choices as if leviathan had preferences. Put differently, the only leviathan that rationalizes group choice has the preferences of a madman.
Popularizing the Arrow Impossibility Theorem
Arnold Kling presents it as an under-popularized idea, so here is my attempt to popularize it:
Let's say you had two people on a desert island, John and Tom, and John wants jazz music on the radio and Tom wants rap. Furthermore any decision procedure must be consistent, in the sense of applying the same algorithm to other decisions. In this set-up (with a further assumption), there is only dictatorship, namely the rule that either "Tom gets his way" or "John gets his way."
Arrow's axioms, by invoking "the independence of irrelevant alternatives" (read: pairwise comparisons) require that all information in the problem be ordinal. A decision procedure such as: "Turn the radio (and allocate other resources) to which station makes the winner happier" is ruled out per se. Which person is happier cannot be expressed in the language of pairwise comparisons, which allow you to claim only that "John prefers jazz to rap" and so on. "Let Tom and John trade" also won't do, whether or not transactions costs are high. That's not a social welfare function as Arrow defined it.
I sense the above paragraph isn't a very charming popularization (it wouldn't make the Freakonomics movie), but let's continue.
That's a two-person example. With 17 persons, Arrow's clever method of partitioning shows that conflicted decisions ultimately must break down to one-on-one comparisons of different individual preferences, returning us to the island/radio example.
For a truly popular audience, you could go on about the difference between inter-profile and intra-profile social welfare functions.
I believe that a popularized version of Arrow's theorem, which explains where the main result actually comes from (strong IIA), is not very impressive to most people. That may be one reason why the theorem doesn't get popularized so much.
Here is one very good transparent version of a proof, which requires virtually zero mathematics. If you work through this paper, you will understand the theorem and where it comes from. Here is a related journal article.
A rainfall theory of democracy
From Stephen Haber and Victor Menaldo:
Why have some countries remained obstinately authoritarian despite repeated waves of democratization while others have exhibited uninterrupted democracy? This paper explores the emergence and persistence of authoritarianism and democracy. We argue that settled agriculture requires moderate levels of precipitation, and that settled agriculture eventually gave birth to the fundamental institutions that under-gird today’s stable democracies. Although all of the world’s societies were initially tribal, the bonds of tribalism weakened in places where the surpluses associated with settled agriculture gave rise to trade, social differentiation, and taxation. In turn, the economies of scale required to efficiently administer trade and taxes meant that feudalism was eventually replaced by the modern territorial state, which favored the initial emergence of representative institutions in Western Europe. Subsequently, when these initial territorial states set out to conquer regions populated by tribal peoples, the institutions that could emerge in those conquered areas again reflected nature’s constraints. An instrumental variables approach demonstrates that while low levels of rainfall cause persistent autocracy and high levels of rainfall strongly favor it as well, moderate rainfall supports stable democracy. This econometric strategy also shows that rainfall works through the institutions of the modern territorial state borne from settled agriculture, institutions that are proxied for by low levels of contemporary tribalism.
For the pointer I thank www.bookforum.com.
Stanley Fischer update
Formerly a famous macroeconomist at MIT, he now runs the central bank of Israel and he just won a Euromoney award for best central banker of the year.
Jacob Frenkel argues that Fischer's shekel-selling policies are unsustainable. Here is another account. Israel foreign currency reserves now exceed $66.3 billion, in part because of Fischer's decision to buy up so many dollars and keep down the value of the shekel.
Here, Fischer complains that the Israeli economy is dominated by a few families and excessively concentrated wealth. He wants the government to remedy this situation, although it is hard to tell which policy he is proposing.
Run for the Border
By perceiving state borders to be physical barriers that keep disaster at bay, people underestimate the severity of a disaster spreading from a different state, but not the severity of an equally distant disaster approaching from within a state. We call this bias in risk assessment the border bias.
More here. Amusingly, the authors show that making the border more salient by darkening the border lines on a map can make people feel even more protected.
Hat tip: Paul Kedrosky.
Expecting too much
Sometimes people hold an attitude which I call "expecting too much," even if they do not always articulate this view as such. Here are a few possible examples:
Some Germans: "Yes we know that the eurozone is problematic for some of the poorer countries. We expect that they get their fiscal house in order, and produce some major productivity gains, as we have done in the past. We expect this even if we don't quite tell them this."
Some Americans: "I expect my government to solve Problem X (fill in the blank, the list is a long one) without raising my taxes, and in the meantime I will refuse to countenance a tax increase. To support this attitude I am willing to sound fiscally unreasonable, if necessary."
Some economists: "It is a tough labor market, to be sure. Yet it is expected that you be willing to move around to get a job, as many immigrants do, or that you find a way to make a lower wage work for your life and for an employer. My grandparents managed that, why can't you?"
There are numerous other examples. Is "expecting too much" ever a reasonable attitude? A reasonable tool of motivation? A reasonable bargaining stance? A reasonable defensive strategy against institutions which will otherwise treat you unfairly or perhaps even rapaciously?
I find that expressions of "expecting too much," whether they are articulated as such or not, often send intellectual opponents, on the respective issues, into a fury.
"Expecting too much" is a frequent attitude among the American public today and it is rooted in common sense morality. To the extent "expecting too much" is a reasonable point of view, the public is wiser than its critics will admit.
I am still debating how much reasonable force there is behind this kind of argument.
Insider Trading is Legal for Congressional Insiders
Bloomberg: Your senator learns that a much- maligned weapons system now has enough votes for funding. Before the news gets to a reporter, he buys shares in the arms manufacturer for a quick, handsome profit.
What’s wrong with this picture? Nothing, according to the law…
U.S. senators, representatives and congressional staffers routinely attend high level, closed briefings or engage in conversations where secrets are disclosed that might send shares climbing or slumping if widely known.
That access lets them buy low and sell high based on material, non-public information, and they can do it without concern that their remarkable prescience will alert federal investigators of possible wrong doing.
Insider trading in Congress is not new. In 2004, I wrote about a study showing that the portfolios of US Senators "outperformed the market by an average of 12 per cent a year in the five years to 1998."
Hat tip: The Browser.
The culture that is Washington
Business is the most common academic major in the nation, representing one-fifth of all college degrees. And business ranks second among academic majors in the Washington area, but it's a distant second, representing 11 percent of the college-educated population.
Literature and languages rank third. Liberal arts and history rank fourth.
The data show "that D.C. is less business-focused than the country as a whole," said William Frey, a demographer at the Brookings Institution.
The full story is here.
*The Gold Standard at the Turn of the Twentieth Century*
The author is Steven Bryan, a historian, and the subtitle is Rising Powers, Global Money, and the Age of Empire. This book offers a great deal of previous unpresented information on the operation of the gold standard in Japan, Russia, Turkey, and Argentina, based on original rather than secondary sources. Here is a summary paragraph at the end of the book:
The connection between nineteenth-century great power politics, empire building, and militarism and the gold standard was obscured after World War I in the rush to reinstate the form of the gold standard while ignoring its substance and the varied rationales and motivations that had supported it. Despite the rose-colored hues of nostalgia that flourished after the war, the gold standard did not exist in some magical land separate from the rest of the late nineteenth-century world. For better or worse, the gold standard was as much a part of the age of empire as it was of the age of industry.
Here is the book's home page. Here is the p.99 test applied to the book.
Markets in everything
"The Republic of China (Taiwan)" has delivered to the municipality of Suchitoto, El Salvador two hundred packages of food, four wheelchairs, and a selection of musical instruments. The accompanying ceremony was attended both by the Chinese ambassador and the mayor of Suchitoto. Similar donations have been made to Santa Ana y Mejicanos and there are plans for visiting other locations as well.
*Washington: A Life*, by Ron Chernow
When the news from Boston reached Mount Vernon around New Year's Day, Washington deplored the methods of the tea party, even if he loathed the tax on tea. It was the next step in a fast-unfolding drama that would fully radicalize him. The administration of the bluff, portly Lord North had decided that Boston should pay for the destroyed tea and that Parliament should assert its supremacy, cracking down on harebrained schemes of independence now beginning to ferment in the colonies…the tea party convinced many British sympathizers that colonial protestors had become a violent rabble who had to pay a steep price for their inexcusable crimes.
I read only a few hundred pages of this book. The level of quality is high, but I find Alexander Hamilton's life much more interesting. This book does have an especially good discussion of Washington's contradictory attitudes and behavior toward his slaves.
Which is the country most likely to elect a Palestinian President?
El Salvador, here is some evidence, namely they already have done so and in the 2004 election both candidates were of Palestinian background. Belize has had a half-Palestinian President, so that would be an alternative pick, and the country has a fair number of Palestinians in politics and business.
The Charter 08 document
It helped Liu Xiaobo win a Nobel Peace Prize. Here is one good paragraph of many:
Protection of Private Property. We should establish and protect the right to private property and promote an economic system of free and fair markets. We should do away with government monopolies in commerce and industry and guarantee the freedom to start new enterprises. We should establish a Committee on State-Owned Property, reporting to the national legislature, that will monitor the transfer of state-owned enterprises to private ownership in a fair, competitive, and orderly manner. We should institute a land reform that promotes private ownership of land, guarantees the right to buy and sell land, and allows the true value of private property to be adequately reflected in the market.
Hat tip goes to Matt Yglesias.
Rereading *The Road to Serfdom*
Given all the recent fuss, I picked it up again and found:
1. It was more boring and less analytic on matters of public choice than I had been expecting.
2. Although some of Hayek's major predictions have been proven wrong, they are more defensible than I had been expecting.
3. The most important sentence in the book is "This book, written in my spare time from 1940 to 1943…" In those years, how many decent democracies were in the world? How clear was it that the Western powers, even if they won the war, would dismantle wartime economic planning? How many other peoples' predictions from those years have panned out? At that time, Hayek's worries were perfectly justified.
4. If current trends do turn out very badly, this is not the best guide for understanding exactly why.
It's fine to downgrade the book, relative to some of the claims made on its behalf, but the book doesn't give us reason to downgrade Hayek.
Canada’s budget triumph
From a new paper by David Henderson:
A federal government runs a large deficit. Deficits are so large that the ratio of federal debt to Gross Domestic Product (GDP) approaches 70 percent. A constituency of voters have gotten used to large federal spending programs. Does that sound like the United States? Well, yes. But it also describes Canada in 1993. Yet, just 16 years later, Canada’s federal debt had fallen from 67 percent to only 29 percent of GDP. Moreover, in every year between 1997 and 2008, Canada’s federal government had a budget surplus. In one fiscal year, 2000–2001, its surplus was a whopping 1.8 percent of GDP. If the U.S. government had such a surplus today, that would amount to a cool $263 billion rather than the current deficit of more than $1.5 trillion.