Madsen Pirie's The Book of the Fallacy is now available in an online edition, thanks to the Adam Smith Institute. This is a public service both because it is free and because the paper version of the book is out of print and used copies are difficult to find.
Source: Madsen Pirie, "Logical Fallacies", The Adam Smith Institute
Acknowledgment: Thanks to Alex Singleton.
Update (7/21/2006): Unfortunately, it is no longer available online.
Update (7/21/2016): More good news: This book is now available in an updated, and more reasonably priced, edition under the title How to Win Every Argument. There's even a Kindle edition!
The Dangers of Blogging
The latest issue of Time magazine has a short interview with Jon Stewart, who is promoting a new book, which includes the following exchange:
"WRITING A BOOK IS SO RETRO. SHOULDN'T YOU BE BLOGGING OR SOMETHING?
"I can't. It's too hip. Then I'd have to get a BlackBerry, and I'm wired in, and next thing you know, I'm at a Black-Eyed Peas concert with a crack problem. I just can't go down that road."
This comment is also good:
"SOMETIMES IT FEELS AS IF WHEN THE STAKES GET HIGHER, THE QUALITY OF DEBATE GETS LOWER.
"Oh, I don't think there's any question about that. Now it's gone Malcolm X. It's gone 'by any means necessary.' I mean, how many campaigns do you remember where Hitler has come up a lot? If I were the Hitler people, I'd be raising a stink. I think he's gotta protect his legacy. He's gotta come out and go, Look, all right, you guys have your flaws but, hey, I was evil, baby!"
Sources: Jon Stewart & Lev Grossman, "10 Questions for Jon Stewart", Time, 9/20/2004
The most recent Gallup poll shows President Bush with a 13 point lead over Senator Kerry among "likely" voters: Bush with 55% and Kerry at 42%. The margin of error was ±4%.
Even with such a large margin of error, Bush's lead is well outside of that margin. However, this poll raises another issue concerning the confidence intervals determined by the margin of error, that is, the intervals from 51-59% for Bush and 38-46% for Kerry. As with most opinion polls, these intervals are based on a confidence level of 95%. This means that if 20 polls are conducted, one can expect the results to fall within these intervals 19 times; in other words, one can expect that 1 out of 20 polls will be off by more than the margin of error.
This point is relevant to the Gallup poll because it shows a considerable jump in support for President Bush, and another poll taken about the same time by Pew shows Bush and Kerry in a statistical tie. Which poll is right? There's no way of knowing for sure, but there have been more than twenty national polls taken during this campaign, so one would expect at least one of them to show inaccurate results just by chance. The Gallup seems most likely to be the black sheep.
Another issue has to do with the notion of a "likely" voter: what is a likely voter? "Registered voter" is a precisely-defined concept, but "likely voter" is vague. Gallup and Pew each has its own distinct definition of what a likely voter is, so that comparing the two polls is really comparing apples and oranges—that is, equivocating—which may account for the difference in the polls' results.
The Gallup poll may still be accurate for all that, but these considerations show that we should have much less than 95% confidence that it is.
- Carl Hulse, "Varying Polls Reflect Volatility, Experts Say", New York Times, 9/18/2004
- "Latest Presidential Polls Vary Widely", CNN, 9/17/2004
- The Big MOE, 9/3/2004
- (Added 9/23/2004) Mark Blumenthal, "More Divergent Than They Should Be?", Mystery Pollster, 9/22/2004. He's not really a mystery, since he identifies himself, but he is a pollster!
I've added a new quotation to the Quote…Unquote page. I've also added name tags to the quotes so that they can be linked to directly by the last names of the authors.
An Odd Puzzle
Three people go into a coffee house together and each orders a single cup of coffee. Each pours an odd number of packets of sugar into his or her cup of coffee. The total number of sugar packets that they use is eight. How is this possible?
The same three people go back to the coffee house on a later occasion, and each again orders a single cup of coffee. Each pours an even number of packets of sugar into his or her cup of coffee. The total number of sugar packets that they use in their coffee is seven. How can this be?
- Spinsanity has a report on a couple of Kerry contextomies in Rudy Giuliani's speech at the Republican convention. The most egregious example concerned Kerry's view of Israel's security fence:
" Giuliani said that, 'In October of 2003, (Kerry) told an Arab American institute in Detroit that a security barrier separating Israel from the Palestinian territories was a barrier to peace. Okay. Then a few months later, he took exactly the opposite position. In an interview with the Jerusalem Post he said, "Israel's security fence is a legitimate act of self defense."'
" [T]he first statement is taken dramatically out of context. Kerry actually said, 'I know how disheartened Palestinians are by the Israeli government's decision to build the barrier off of the green line, cutting deep into Palestinian areas. We don't need another barrier to peace.' As aides explained in the Jerusalem Post article Giuliani cites, Kerry was describing the route of the fence as a 'barrier to peace,' not the fence itself."
Source: "Deception Becomes All Too Conventional", Spinsanity, 9/7/2004
- An Associated Press report bizarrely quoted Arnold Schwarzenegger's convention speech out of context:
"Austrian historians are ridiculing Arnold Schwarzenegger for telling the Republican convention in New York that he saw Soviet tanks in his homeland as a child . Recalling that the Red Army once occupied part of Austria after the second world war, the California governor told delegates on Tuesday: 'I saw tanks in the streets. I saw communism with my own eyes.' One historian, Stefan Karner, told the Vienna newspaper Kurier: 'He could not have seen a Soviet tank in Styria.' Mr Schwarzenegger was born in Styria in 1947. But the Russians left the province in 1945, said Mr Karner."
Here's what Schwarzenegger said, in context:
"When I was a boy, the Soviets occupied part of Austria. I saw their tanks in the streets. I saw Communism with my own eyes. I remember the fear we had when we had to cross into the Soviet sector. Now, my family didn't have a car. But one day we were in my uncle's car. It was near dark as we came to the Soviet checkpoint. I was a little boy. I was not an action hero back then. But I remember. I remember how scared I was that the soldiers would pull my father or my uncle out of the car and I would never see them again. My family and so many others lived in fear of the Soviet boot. Today, the world no longer fears the Soviet Union, and it is because of the United States of America."
In context, it's clear that Schwarzenegger is not claiming to have seen tanks in Styria, but when his family crossed into the Soviet zone.
In the same article, there's an equivocation on the word "socialist", which can either refer to a relation between the government and the economy, or is the name of some political parties. The former is usually not capitalized; the latter often is. When Schwarzenegger said that Austria was socialist he apparently meant the former, not the latter.
A different version of this story includes explanations of Schwarzenegger's comments from his spokesperson, but when the fallacies are removed from the story there's not much left.
Update (9/9/2004): I've changed the Sources for this entry to include the original story and the later, corrected version, listed in chronological order below. Both are dated on the same day, but the version containing Schwarzenegger's spokeswoman's clarifications is later. It's a good thing that the AP changed it, but they should have just dropped it since there's really no story here.
- Roland Prinz, "Historians Criticize Schwarzenegger for Austrian History Gaffes", The Associated Press, 9/3/2004
- Roland Prinz, "Austrians Doubt Schwarzenegger's Memories", Sun-Herald, 9/3/2004
- "Schwarzenegger: No Country More Welcoming Than the USA", CNN, 8/31/2004
Via: "Austrian Media No Better Than Ours", Oh, That Liberal Media!, 9/5/2004
Check it Out
The New Scientist has an interview with philosopher Jamie Whyte, who has written a book titled Bad Thoughts: A Guide to Clear Thinking. I haven't read Whyte's book yet, so I can't directly recommend it, but it will go down on my "to read" list. I'll review it if the publisher will be kind enough to send me a review copy. I especially like this part of the interview:
"There is a terrible tendency to treat people as reliable sources of fact when in fact they are simply 'important' people or people who happen to be in the news. It is doubly perverse when you consider who gets counted as 'important'. For example, the victims of train accidents appear on television as authorities on rail policy and celebrities endorse presidential campaigns as though they are expert on politics. It's sheer insanity."
Source: "Get it right!", New Scientist
Via: "Outraged of Highbury", The Church of Critical Thinking, 9/6/2004
The Big MOE
Tim Carter writes in with the following criticism of the recent "Name That Fallacy!" weblog entry:
"On August 29th, you quoted poll results within the margin of error that concluded that Bush had a slight lead, and labeled it a fallacy of false precision. I disagree. A lead less than the margin of error does show a greater probability that the person with a lead in the sample has a lead in the group sampled. For a reporter to write this as saying that the person with the lead in sample has a slight lead in the race might be oversimplified to the point of inaccuracy for a peer-reviewed academic social science journal, but it is hard to see why this is a misleading way to get the point across in plain English to a general readership."
I'm not a statistician, Tim, so I can't give you an expert opinion. If there are any readers who are experts, I would be glad to post their responses. Also, I include below a number of expert Resources that you can consult. With that proviso, here's my explanation of why I think the example is fallacious:
Every measurement instrument has some limit to its precision; for instance, a weight scale might be accurate to the pound, but not to the ounce. Thus, if you weigh two items and the scale shows that one weighs a pound more than the other, then you can have confidence that the one really does weigh more than the other. In contrast, if you weigh two different items and the scale shows that one weighs 1 pound 6 ounces, whereas the other weighs 1 pound 9 ounces, then you shouldn't be confident that the one really does weigh less than the other. The scale is not that precise.
The "margin of error" (MOE) is a way of quantifying the level of precision of a survey. Specifically, it quantifies sampling errorthere are other kinds of error that can affect polls, but they can't be quantifiedwhich is the error in a random sample of a population when the sample is unrepresentative of the larger population. For instance, in a sample of adult Americans it could be that just by chance every single person sampled is a registered Republican; this is not very likely to happen, but it can't be ruled out. Such sampling errors can, of course, result in survey results that are unrepresentative of the larger population; for instance, in the biased sample of Republicans, it would not be surprising if the overwhelming majority of the sample supported President Bush for re-election.
The MOE is usually stated as "±N%", which then determines a "confidence interval". For instance, if a candidate's support is 45% in a poll with an MOE of ±3%, then the confidence interval is 45%±3%, that is, the interval from 42% to 48%. This means that we can be confident that the candidate's support amongst the whole population is somewhere between 42% and 48%; however, we can't be confident that it is exactly 45%.
How confident are we entitled to be that the result for the population falls within the confidence interval? In American polling, it is traditional to use 95% confidence in determining confidence intervals and, therefore, this number is often omitted in news reports of polls. However, one needs to know the confidence level in order to determine the MOE, since the confidence level and MOE are directly related: as the confidence level decreases, the MOE also decreases, so that the confidence interval gets smaller. In other words, if you want to get more precise results, then you have to sacrifice some of your confidence in their correctness.
Given this background, I can finally address your criticism directly, dealing first with where we agree. There is nothing magical about the confidence level of 95%. I don't know why this level is typically used for American polls, though it may be because it is what is usually considered "scientifically significant". However, for many practical purposes, a confidence level of less than 95% would be adequate. In the example that you are criticizing, it might well be that the poll results would be significant at a lower confidence level. However, there is no guarantee of this, and on this point we begin to disagree.
It's misleading to report the MOE of a poll, and then to treat results within the margin as significant. If reporters disagree with the confidence level chosen, they should choose a lower confidence level and refigure the MOE. Currently, all major media outlets that I have seen, including those which commission polls, report the MOE provided by the pollster. Since the MOE is a way of quantifying how precise a poll's results are, to ignore a given MOE is to treat the poll results as if they are more precise than they are, which is the fallacy of fake precision.
Furthermore, the way that polls are currently reported is often self-contradictory. The story will say in one paragraph that candidate A leads candidate B by 1%, then in the next paragraph we are told that these results could be off by 3% either way. That lead disappeared fast! This inconsistency is the result of journalists treating the MOE as if it were a meaningless number, which I suspect for many of them it is.
Source: Name That Fallacy!, 8/29/2004
- Darrell Huff, How to Lie with Statistics (W.W. Norton, 1954), Chapter 4: "Much Ado about Practically Nothing"
- Pam Hunter, "Margin of Error and Confidence Levels Made Simple", iSixSigma
- Thomas Lang, "Margin of Ignorance", The Campaign Desk, 8/4/2004
- John Allen Paulos, A Mathematician Reads the Newspaper (Doubleday, 1996), pp. 152-153.
Source: Joan Vennochi, "The Women Who are Eyeing Kerry's Seat", The Boston Globe, 8/24/2004
Answer to the Odd Puzzle: The first person used one packet of sugar, which is an odd number. The second person also used one packet, which is an odd number. The last person used six, which is an odd number of packets of sugar to put in a cup of coffee!
Source: Paul Sloan & Des MacHale, Challenging Lateral Thinking Puzzles (Sterling, 1993), Puzzle 4.4.
Answer to the Even Odder Puzzle: The first person put two packets of sugar in his or her coffee, which is an even number. The second person also put two packets of sugar in his or her coffee, which is an even number. In addition, the third person put two packets of sugar in his or her coffee, but also put a single packet of sugar into the first person's cup. Thus, they each put an even number of packets into their own cup, but a total of seven were used.
Acknowledgment: This puzzle was suggested by the following alternative answer to the Odd Puzzle sent in by Michael Koplow:
"Here's my solution. It explicitly states what your solution silently assumes: that 'his or her cup' means his or her own cup:
"A puts a packet into his or her own cup. A also puts a packet into B's cup. B also puts one packet into his or her own cup, and C puts five packets into his or her own cup. The packet that A puts into B's cup is not covered by the statement of how many each puts into his or her own cup, but it is covered by the statement about the total number of packets.
"Is there anything wrong with assuming that 'his or her cup' means 'his or her own cup'? Only in trick questions of the type you find on some web sites. Without shared assumptions about what things mean, it would be very difficult to communicate."
In order to rule out Michael's solution, the puzzle would have to be worded so that the total packets used are the total of those that each person puts in his or her own cup, excluding any that they may use for some other purpose such as spiking their neighbor's cup.
Of course, Michael's solution and the puzzle based on it don't play upon the ambiguity of "odd", but they do illustrate another logical boobytrap, namely, rules of thumb. It is a rule of thumb that people do not put sugar in other people's cups of coffee, but there are exceptions.