Conjunction Fallacy, What’s Your Function?

August 25, 2012
Posted by Jay Livingston

The “conjunction fallacy.”  I've blogged about it before, but my beach reading yesterday was Thinking Fast and Slow by Daniel Kahneman, who discovered the concept – I nearly said, “who invented the concept”;  I'm still not sure which verb is more accurate – and the book has a chapter on this bit of twisted logic.

As Kahneman tells it, he and Amos Tversky were trying to show that heuristics, mental shortcuts, can replace logic even when logic is called for.  They went about this in the usual way of academic psychologists – they gave a quiz to undergraduates.  The quiz item that became famous was “the Linda problem.”  Students read or heard a brief description of Linda – “single, outspoken, concerned with social justice,” among other traits – and were then asked which conclusion about Linda was more likely

    a.  Linda is a bank teller
    b.  Linda is a bank teller and is active in the feminist movement [This was back in the 1980s.]

Nearly everyone chose “b.”

Wrong.  The conjunction of two events cannot be larger than either event.  “Feminist Bank Teller” cannot be larger (i.e., more likely) than “Bank Teller.”  Think of a Venn Diagram.

Hence, the conjunction fallacy.  Interesting that so many people can get it wrong, but I wonder whether it’s like some clever riddle or a joke – something with little relevance outside its own small universe. You’re never going to be having a real drink in a real bar and see, walking in through the door, an Irishman, a rabbi, and a panda.

Kahneman explains the fallacy as an instance of the more general problem of stereotyping or “representativeness.”  Linda in choice “b” fits with a plausible story, a stereotype.  She represents a more complete picture, and that picture overwhelms logical Venn-diagram reasoning.  Even when logic triumphs, it’s a struggle. Kahneman quotes Steven Jay Gould’s reaction to the problem.  Gould got the right answer, but

a little homunculus in my head continues to jump up and down shouting at me – “but she can’t just be a bank teller; read the description.”

I think Gould’s homunculus is miscommunication.  As I said in that earlier post about the conjunction fallacy (here), the question asked by researchers is sometimes not the question that people hear.  When I hear the question and the two choices, I don’t think of “a” and “b” as separate circles in a Venn diagram.  Instead, I picture a bank with its many tellers behind their counters.  One of them is wearing a large NOW button. Danny Kahneman taps me on the shoulder and whispers,”Which one is Linda?” I answer, “Most likely, she’s the feminist.”

Something else about this study bothers me.  Here’s Kahneman:

When I asked my large undergraduate class in some indignation, “Don’t you realize that you have violated an elementary logical rule?” someone in the back row shouted, “So what?”

I don’t usually have much sympathy for anti-intellectualism, especially at a university, but I have to admit that the backbencher has a point.  How might this fallacy ever come up in real life?  The scarcity of this fallacy may also be the reason it’s so difficult, even for Steven Jay Gould, to hear the literal question that the quizmaster is posing.  The other logical slips that Kahneman details in his book occur in many situations.  But what is the real-world function of the conjunction fallacy? 

Those other cognitive fallacies and shortcuts are often well-known, at least among cognitive psychologists, and Kahneman’s studies are attempts to specify the conditions under which they occur.  But the conjunction fallacy was new.  He had asked students the Linda question with something else in mind.  His assistant had gathered some of the questionnaires and left them lying in a tray

I casually glanced at them and found that all the subjects had ranked “feminist bank teller” as more probable than “bank teller.”  I was so surprised that I still retain a “flashbulb memory” of the gray color of the metal desk and of where everyone was when I made that discovery.

So the conjunction fallacy was a discovery.  But it was also an invention.  Kahneman created it, albeit unwittingly, with the Linda problem. 

At the end of each chapter of Thinking Fast and Slow, Kahneman offers short examples of how the ideas of the chapter might have real-world applications.  But the examples at the end of the Linda chapter are unrelated to the conjunction fallacy.  Linda seems to have no life outside of logic problems for psych students, much like the snee, the stoa, the edh, and other creatures whose existence, for most of us, is confined to crossword puzzles.

Evol-psych Goes to the Polls

August 23, 2012
Posted by Jay Livingston

National Review has long been the most important voice on the right.  When NR publishes something, I suppose they mean for us to take it seriously. 

In the Aug. 27 issue, they publish Kevin Williamson’s evolutionay-psychology view of the election and why Romney deserves to win.

Elections are not about public policy. They aren't even about the economy. Elections are tribal, and tribes are . . . ruthlessly hierarchical. Somebody has to be the top dog.

You can read the whole thing here, but (trigger warning) you may find it not just silly but deeply offensive, especially if you think that women have the power of thought and reason.

What do women want? The conventional biological wisdom is that men select mates for fertility, while women select for status.

You want off-the-charts status? Check out the curriculum vitae of one Willard M. Romney . . . boss of everything he's ever touched.

Romney is the alpha-male.  Why?  First, because he made a lot of money.  And second, because the Romney has more sons and grandsons.  I am not making this up.

It is a curious scientific fact . . . that high-status animals tend to have more male offspring than female offspring, which holds true across many species, from red deer to mink to Homo sap. The offspring of rich families are statistically biased in favor of sons — the children of the general population are 51 percent male and 49 percent female, but the children of the Forbes billionaire list are 60 percent male. Have a gander at that Romney family picture: five sons, zero daughters. Romney has 18 grandchildren, and they exceed a 2:1 ratio of grandsons to granddaughters (13:5). . . . He is basically a tribal chieftain.

And by the same reasoning, Obama is a pussy.

Professor Obama? Two daughters. May as well give the guy a cardigan. And fallopian tubes. [Professors are, by definition, wimps.  No alpha males teach Con law.]

How does this matter in the election?

From an evolutionary point of view, Mitt Romney should get 100 percent of the female vote. . . . the ladies do tend to flock to successful executives and entrepreneurs.

You can’t argue with logic like that.  The only trouble is in the evidence.  Obama consistently polls 12 points higher than Romney among women. 

Oh, those foolish women, thinking about a candidate's policies – how these might affect them, their children, and their country – rather than his wealth and the gender of his offspring. 

FWIW, in 1992, a wealthy candidate with lots of sons (four, and two daughters), with warrior credentials (a navy pilot) ran against a candidate, also a former law professor, with only a daughter, far less wealth, and no military credentials.  Maybe the Bush campaign had signs saying,  “It’s the evol-psych top dog status, stupid.”

(HT: Mark Kleiman, who notes that even from the evol-psych perspective, among male voters, Romney should be getting killed, electorally and maybe literally:  “Admiring alpha males is purely a female trait; the other males mostly want to kill them, or at least replace them.”

The Budget - Whose Benefits?

August 20, 2012
Posted by Jay Livingston

I mentioned Niall Ferguson in the previous post.  I had not realized that his anti-Obama essay  (“Hit the Road, Barack”)  was Newsweek’s cover story and was stirring up much dust.

No wonder. 

Welcome to Obama’s America: nearly half the population is not represented on taxable return – almost exactly the same proportion that lives in a household where at least one member receives some type of government benefit. We are becoming a 50-50 nation – half of us paying the taxes, the other half receiving the benefits.

The first part of the first sentence is technically wrong – even those who do not pay taxes and who get the EITC file a return.  And it is true that 46% of earners pay no federal income tax.  That doesn’t mean they pay no taxes – there are payroll taxes and sales taxes – just no income tax.

It’s the second sentence, the applause line, that’s misleading.  Is all that tax money really going to the less wealthy half of the people?  The federal budget shows where the tax money actually goes.  Here’s the New York Times chart.  I have outlined in red the categories that benefit mostly those who pay no income tax.

The Times chose very faint colors that make the writing hard to see.  The square in the lower middle,  “Income Security,” includes unemployment insurance, retirement benefits for civilian and military, food stamps, TANF, and several programs.  The squares in the upper right are Medicaid and CHIP.
(Go to the Times, here, for an interactive version of the chart.  You can also click on“Hide Mandatory Spending” to view the parts of the budget that can actually be cut.)

Niall Ferguson is an intelligent and well-informed man, a Harvard professor, and he has lived in the US for several years now.   You would think that he’d know that most of the federal budget goes to Social Security, Medicare, and the Pentagon – programs that benefit all Americans (including Paul Ryan’s mother) and do not “benefit mostly those who pay no income tax.”  Anybody who reads a newspaper or listens to the news a couple of times a month must know this.

I can understand why Ferguson would write something like this – he obviously intended to write  a campaign screed against Obama, not a thoughtful, accurate news article.  To that end, he echoes the Romney ad, the one that says Obama

Quietly announced a plan to gut welfare reform by dropping work requirements. Under Obama’s plan, you wouldn’t have to work. You wouldn’t have to train for a job. They just send you your welfare check.

Not true, of course, but that’s not the point.  The point is that YOU (you hardworking, taxpaying good person) pay tax money that Obama gives to THEM (the lazy recipients of government benefits, the bad people). Neither the ad nor Ferguson says what color YOU and THEM are, but we know, don’t we?  It goes without saying.

There are many more errors and contradictions in Ferguson’s piece; that's to be expected.  But what is Newsweek’s excuse for not fact-checking it?


(For fact-checks of the Ferguson article, see, for example, Business Insider, The Atlantic, and Slate .  Other critiques should not be hard to find, Noah Smith’s, here,  for one.)

Vacation

August 20, 2012
Posted by Jay Livingston
Cross-posted at Sociological Images

As I speculated years ago (here and here), it may be hard for Americans to imagine a world where the law guarantees them at least 20 paid vacation days per year. But such a world exists. It’s called Europe.* 

Americans are the lucky ones. As Mitt Romney has warned us “European-style benefits” would   “poison the very spirit of America.” Niall Ferguson, who weighs in frequently on history and economics, contrasts America’s “Protestant work ethic” with what you find in Europe – an “atheist sloth ethic.”

The graph is a bit misleading. It shows only what the law requires of employers. Americans do get vacations. But here in America, how much vacation you get, or whether you get any at all, and whether it's paid – that all depends on what you can negotiate with your employer. 

Since American vacations depend on what the boss will grant, some people get more paid vacation, some get less, and some get none. So it might be useful to ask which sectors of our economy are beehives of the work ethic and which are sloughs of sloth. (Ferguson’s employer, for example, Harvard University, probably gives him three months off in the summer, plus a week or two or more in the winter between semesters, plus spring break, and maybe a few other days. I wonder how he would react if Harvard did away with these sloth-inducing policies.)

The Wall Street Journal recently (here) published a graph of BLS data on access to paid vacations.

(Click on the chart for a larger view.)

Those people who are cleaning your hotel room and serving your meals while you’re on vacation – only about one in four can get any paid vacation days. And at the other end, which economic sector is most indulgent of sloth among its workforce? Wall Street. Four out of five there get paid vacation. 

How much paid vacation do we get? That depends on sector, but it also depends on length of service.  As the Journal says,

Europeans also get more time off: usually a bare minimum of four weeks off a year. Most Americans have to stay in a job for 20 years to get that much, according to BLS data.

All this is by way of announcing that posts to the Socioblog for the rest of the month may not be frequent, and they may arrive faintly scented with salt air, sunscreen, and sand.

’Cause down the shore everything’s all right.**

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* The graph is from five years ago, but I doubt things have changed much.  The US still has no federal or state laws requiring any paid vacation days.

** The song, though associated with Springsteen, was written by Tom Waits.