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June 30th, 2022 (Revised: 7/2/2022) (Permalink)

When More is Less & Who are the Experts?


  1. Plato. The Republic, 488A-489A; Jowett's translation.
  2. Eric W. Weisstein, "Condorcet's Jury Theorem", Wolfram's MathWorld, accessed: 6/29/2022.
  3. Douglas O. Linder, "Criminal Procedure in Ancient Greece and the Trial of Socrates", Famous Trials, accessed: 6/29/2022.

Disclaimer: I don't necessarily agree with everything in these articles, but I think they're worth reading as a whole. In abridging them, I may have changed the paragraphing and rearranged the order of the excerpts in order to emphasize points.

June 26th, 2022 (Permalink)

Inflation and "Record-High" Gas Prices

Inflation in America increased to 8.6% last month, a level that we haven't experienced for forty years. An important aspect of that inflation is the price of gasoline, which has risen at a rate much higher than the overall rate of inflation, increasing by nearly 50% over the last year1. You don't need the news media to tell you that the cost of gasoline has gone up a lot this year: just fill up your gas tank and you'll be painfully aware of it. Nonetheless, the news media keep referring to "record" or "record-high" gasoline prices2. In what sense is the price a "record"?

The claim that gas prices are setting new records is based on an average of prices nationwide compiled by the American Automobile Association (AAA). According to the AAA, the current national average price for a gallon of regular unleaded gasoline is $4.903. The "record high" was actually set on the 14th of this month at $5.016, so it's not now at a record-setting price, but only about a dime away.

What the news media don't usually mention is that AAA's average measures nominal gas prices, that is, simply the price on the pump unadjusted for inflation. Inflation is money losing value over time―which it's been doing unusually fast for the last several months―so that a dollar today is not worth what it was yesterday. A dollar this year will buy less gas than it would have last year, let alone ten, fifty, or one-hundred years ago.

Given inflation, comparing prices from many years apart is comparing apples to oranges or, for a less hackneyed and fruity analogy, it's like comparing prices in American dollars with prices in Canadian dollars without taking the exchange rate into consideration. "The past is a foreign country", as L. P. Hartley wrote4. So, to compare today's prices to those many years ago, you should adjust for inflation5.

Adjusting for inflation, the previous record was set in 2008, when prices averaged $4.116, which is $5.49 in today's dollars7. Inflation is running so high currently that it's entirely possible that we'll see inflation-adjusted prices exceed $5.49 in the near future, which would be a real as opposed to a merely nominal record price.


  1. Aimee Picchi, "Inflation surged 8.6% over the last year — fastest since 1981", CBS News, 6/10/2022.
  2. For just one example: Chris Isidore, "Average US gas price hits $5 for first time", CNN, 6/13/2022.
  3. Gas Prices, American Automobile Association, accessed: 6/26/2022.
  4. L. P. Hartley, The Go-Between (1953), prologue. From Bartlett's Familiar Quotations, Justin Kaplan, General Editor (1992, 16th edition), p. 692.
  5. If you want to adjust prices for inflation, see: Elizabeth B. Appelbaum, "The Consumer Price Index and Inflation - Adjust Numbers for Inflation", Mathematical Association of America, 12/2004. The math is not difficult, but you can use the Bureau of Labor Statistics' online calculator, instead: "CPI Inflation Calculator", Bureau of Labor Statistics (BLS).
  6. Sarah Hansen, "5 Facts That Show How Painful Gas Prices Are Now", Money, 6/7/2022.
  7. I used the BLS calculator to adjust for inflation, with June of 2008 for the previous record, since the source gave the nominal price only for the summer of that year and not the month. I also used May of this year, which is the last month for which data is available, for the current price.

June 9th, 2022 (Permalink)

How to Get a Correction or Retraction in Ten Easy Steps

If, in the course of amateur fact-checking, you discover a factual error in a publication, what should you do then? You've received the benefit of not being misled by the error, but what about other readers or viewers who will not make the effort to check the mistaken claim? My suggestion is that you request a correction or retraction from the source that made the mistake, so that unwary people will not be misinformed.

What's the difference between a correction and a retraction? In a correction, the article itself may be edited to remove or correct the error, and usually a notice at the top or bottom of the article will notify the reader that a correction has been made. Sometimes, the article itself will not be corrected, but a correction appended at the beginning or end. Other times, the notice of a correction will appear on a separate corrections page, though this is not good internet practice.

A retraction is more drastic than a correction, and you are unlikely to get one for a single mistake unless it undermines the thesis of the article. In a retraction, the entire article will be removed, with perhaps a note replacing it that explains the retraction. Articles are most likely to be retracted for extensive plagiarism or fabricated information rather than easily correctable errors.

  1. Don't request a correction over a difference of opinion: Only make such a request when a publication has committed a checkable factual error. If you're not sure whether something is a matter of opinion or of fact, then review the previous entries in this series on fact-checking1. If you're not sure whether something is a factual error, or whether it's a factual error, then don't ask for a correction. Be sure that you're on solid ground before contacting a publication. If it is a difference of opinion, then there are many ways that you can challenge the publication's claims: send a letter to the editor, add a comment to the article, or write and publish your own response. Don't waste your and the publication's time by demanding the correction of an opinion.
  2. Request a correction first: Have the courtesy to contact a publication and request a correction or retraction before you publicly criticize it for a mistake. Give it a chance to do the right thing. This warning includes adding a public comment to an article if the publication allows such a thing, so don't use such comments as a way to try to get a mistake corrected or an article retracted.
  3. Be polite: If you want to get a correction or retraction, don't insult the readers of your request or the publication for which they work. Don't call them ignoramuses, fools, or worse―they may actually be ignorant fools, but don't say so. Assume that they want to get it right. Don't use sarcasm to suggest that they are idiots, or that it is unlikely that they will honor your request―there's no better way to get them to ignore you. If you violate this rule your request is most likely to end up in the trash.
  4. Don't curse: This, of course, is part of politeness, but it may need special emphasis nowadays. If you curse at the person reading your request or the publication the person works for, your request will justifiably go in the trash.
  5. Be specific: Describe the error you want corrected exactly and precisely. If you just have some vague feeling that an article is mistaken, then you're not going to get a correction anyway, so don't bother asking for one.
  6. Be able to prove your case: Don't request a correction or a retraction unless and until you can prove the publication committed a mistake beyond a reasonable doubt. This is an unfair standard, but it is likely to be the one that you'll be held to. If there's any way for a publication to wriggle out of the need to correct or retract something, it will usually try to do so. Publications do not like to issue corrections or, especially, retractions. So, you need to have such a solid case that there's no wiggle room. If you can't prove your case, you can still request a correction or retraction, but don't expect one.
  7. Don't hold your breath: As I mentioned above, publications don't like to make public corrections, let alone retractions. This is true―perhaps especially true―of even the most prestigious and reputable institutions. So, don't be surprised if your request is silently rejected.
  8. If your request is granted, thank the publication and its representative: This, of course, is also a matter of politeness. However, we need to encourage publications to admit error and correct the public record, so thank them when they do so! Anybody can make a mistake, but they did the right thing despite the likelihood of public embarrassment, so they deserve praise and reward for doing so.
  9. If your request is denied or ignored, don't demand that your subscription be cancelled: In the lapidary words of William F. Buckley, Jr.: "Cancel your own goddam subscription!"2
  10. Go public: If you did all of the above, and the publication still does not correct or retract its mistake, publicly embarrass it! There are, of course, many ways that you can lay your case before the public. About the only thing a publication likes less than issuing corrections or retractions is being publicly shamed for getting something wrong. If the publication allows comments to its articles, you can add your correction of it to the comments. You can contact a rival publication, especially one with a different political slant, which may be eager to point out the mistakes of its competitor. Just as we need to reward those who do the right thing, we need to punish those who do not. Let's make it easier and less painful to admit error than not to.


  1. In chronological order:
  2. William F. Buckley, Jr., Cancel Your Own Goddam Subscription: Notes and Asides from National Review (2007)

June 7th, 2022 (Permalink)

Crack the Combination II

The combination of a lock is three digits long. Here are some incorrect combinations:

  1. 054: Two of the digits are correct, one is in the right position, but the other is in the wrong place.
  2. 754: Two digits are correct but both are in the wrong positions.
  3. 742: Two of the digits are correct, one is in the right position, but the other is in the wrong place.

Can you determine the correct combination from the above clues?

WARNING: May cause brain-teasing.

June 4th, 2022 (Permalink)

Cite or Site?

A report in the The New York Times from fifty years ago about a water main break contained the following sentence: "A portable toilet unit on the construction cite also fell into the hole in the street.1" The toilet, of course, was on a construction site.

"Cite" is a verb, most commonly occurring in scholarly writing, which means to point to a source of supposed evidence for a claim or a quote2. In this weblog, I often cite sources for the information and quotes that I write about.

In contrast, "site" is usually a noun meaning "place", as in "web site" or "construction site"3. Given that the two words are pronounced identically, they are easy to confuse. Oddly, only two of the books I usually check, and sometimes cite, warn against such confusion4, though it seems to be a common error. In my experience, the most common mistake is to misspell "cite" as "site", though the confusion obviously can go in the opposite direction, witness the Times example.

Since "cite" is a verb and "site" is usually a noun, it's possible that a grammar checking program will catch confusion of one for the other. However, "site" can also be used as a verb meaning "to place", which means that a grammar checker may not catch it. My old copy of Microsoft's Word program flagged "cite" in the above example, and one online program automatically changed it to "site", though another did not. So, I would suggest that you test whatever program you usually use to see whether it would catch this mistake. If not, you can either upgrade your program or add this distinction to your mental software.


  1. Martin Gansberg, "Subway Flooded by a Broken Main", The New York Times, 9/28/1970. I found this example in the following article: "'Cite' vs. 'Site' vs. 'Sight'", Merriam-Webster, accessed: 6/4/2022.
  2. "Cite", Cambridge Dictionary, accessed: 6/4/2022. For instance, this note cites the entry for "cite" in the online Cambridge Dictionary.
  3. "Site", Cambridge Dictionary, accessed: 6/4/2022.
  4. They are:
    • Mignon Fogarty, Grammar Girl's 101 Misused Words You'll Never Confuse Again (2011), p. 29
    • Robert J. Gula, Precision: A Reference Handbook for Writers (1980), p. 209

June 2nd, 2022 (Revised: 6/4/2022) (Permalink)

The Signal in the Noise

First target

Quote: "To understand error in judgment, we must understand both bias and noise. Sometimes…noise is the more important problem. But in public conversations about human error and in organizations all over the world, noise is rarely recognized. Bias is the star of the show. Noise is a bit player, usually offstage. The topic of bias has been discussed in thousands of scientific articles and dozens of popular books, few of which even mention the issue of noise. This book is our attempt to redress the balance."1

Title: Noise
Second target

Comment: I was put off this book for several months by the title. While it's obvious that it's not a book about "noise" in the everyday sense of the word, it's not clear what it is about. There is a technical meaning of "noise" from information theory2, which is usually contrasted with "signal". Initially, based on the title, that's what I thought the book must be about, but at least two of the authors did not seem to be connected to information theory.

The phenomenon discussed in this book seems not to be "noise" in the information theory sense. "Noise", in that sense, refers to interference in a message, that is, something from outside that corrupts the message. For instance, static on a telephone line is "noise", and so is literal noise when you are trying to hold a conversation in a loud, crowded room. The message is the "signal", and "noise" is anything that interferes with or corrupts the signal.
Third target

In the Introduction, the authors use diagrams to explain what they mean by "noise". Suppose that we're shooting a gun at a target; the first target, shown to the above right, is what we were aiming at, that is, to have all of the bullet holes grouped as closely together as we can get them in or near the bull's-eye.

In contrast, the second target to the above right shows that we have consistently missed the bull's-eye, though at least the holes are close together.

In the third target, above right, the holes are at least centered on the target, but they are widely spaced with only one close to the bull's-eye.
Fourth target

Finally, the fourth and last target, right, is the worst performance. The holes are not centered on the bull's-eye and are widely dispersed.

There are two distinct phenomena demonstrated in these four diagrams, which I'll call "accuracy" and "precision". Accuracy is the closeness of the bullet holes to the bull's-eye, whereas precision is the closeness of the bullet holes to each other. So, in the first target, we see both accuracy and precision: the bullet holes are close to the bull's-eye, and they are grouped close together. In the second target, we have precision, because the holes are closely grouped, but the shooting is inaccurate. The third target shows accuracy in that the holes are centered on the bull's-eye, but the shooting is imprecise. Finally, the fourth target shows neither accuracy nor precision: the holes are spread out and uncentered on the bull's-eye.

Interestingly, I recently purchased a book published ten years ago that uses the same target analogy:

…[P]recision is not accuracy. Let's go to a rifle range. Accuracy means that the average location of all of our shots is in the bull's-eye; precision means all of our shots hit close together. If all our shots hit the bull's-eye, then our shooting is both precise and accurate. If all of our shots cluster in a dime-size hole far from the bull's-eye, then our shooting is precise but not accurate. If all of our shots are centered on the bull's-eye but evenly distributed over the entire target, then our shooting is accurate (on average) but not precise.3

The only thing missing from this description is the last target, in which the shooting is both inaccurate and imprecise.

In contrast to "accuracy" and "precision", the New Book's terms are negative, that is, they call inaccuracy "bias" and imprecision "noisiness". So, in those terms, the first and third diagrams show unbiased shooting, and the third and fourth are noisy. The first diagram has unbiased shooting with little noise, the second is biased but not noisy; the third is unbiased but noisy; and the last is both biased and noisy.

As indicated by the title and the Quote from the Introduction, above, the book is concerned with noise rather than bias, that is, with imprecision instead of inaccuracy.

Subtitle: A Flaw in Human Judgment

Comment: How is noise a "flaw" in human judgment? Noise has multiple causes, many of which come from outside of us. I could see calling it a "problem" for human judgment, but calling it a "flaw" makes it sound as though it is a mistake that comes from within. I guess I'll see whether the authors make good on the subtitle, or perhaps it was foisted on them by the publisher.

Authors: Daniel Kahneman, Olivier Sibony & Cass R. Sunstein

Comment: Kahneman is, of course, one half of the team of Kahneman & Tversky, famous for its work on cognitive biases. I'm unfamiliar with the second author. Cass Sunstein is the co-author, among other works, of Nudge, which I was highly critical of shortly after it came out almost fifteen years ago4. That book was about trying to exploit human biases for allegedly paternalistic reasons, and I hope this book is not about trying to manipulate people in order to reduce noise―see the General Comment, below.

Summary: According to the Introduction5, the book is divided into six parts on the following topics:

  1. The difference between bias and noise: it argues that some areas of human judgment are noisy―I, for one, don't need any convincing. In fact, I would go farther by pointing out that some areas are so noisy that the results are random. See Philip Tetlock's work on political prognostication6, for example.
  2. Occasion noise: when an individual person's judgments are unreliable.
  3. Predictions, which are notoriously noisy: for example, consider the predictions over the last couple of years of the course of the coronavirus epidemic; they were both biased and all over the place, that is, noisy. If plotted on a target, the results would look like the fourth target, above.
  4. Human psychology: the sources of noise in individual judgments.
  5. Practical advice on noise abatement.
  6. What is the right noise level? The authors suggest that it is not zero noise, which is probably right at least for practical reasons.

The Blurbs: The book is favorably blurbed by Robert Cialdini, author of Influence; Annie Duke, author of Thinking in Bets; Jonathan Haidt; freakonomist Steven Levitt; and the aforementioned Philip Tetlock.

Date: 2021

Comment: This book is from last year, so it's not brand new, but I'm just getting around to reading it for reasons explained in the first Comment, above.

General Comment: Keeping in mind that I've read only the Introduction so far, my only misgiving about this book is that it appears to emphasize precision over accuracy, and I don't think that noise reduction should be an end in itself. Certainly, if we find ourselves in the situation represented in the third target, we would like to reduce the noise so that we get closer to the first target. However, suppose that the situation we find ourselves in resembles the fourth target, where there is both bias and noise, which is the most common situation. Why should we want to go from the last target to the second one, that is, reducing noise without improving accuracy?

The situation illustrated by the second target may actually be a worse one than the last target in that the precision of the shooting may give a false impression of accuracy. As the authors point out7, if we look at the backs of the targets we can't tell the difference between the first and second, which is often the situation we're in since we don't know exactly where the bull's-eye is.

In particular, I'm skeptical about the value of a program to reduce the noise in social and political judgments, since this may result in a misleading conformity. The easiest way to reduce imprecision in judgment is to compel people to conform through social pressure such as shunning and threats to one's livelihood or even life. Such pressure can create a factitious "consensus", such as that about the lab leak hypothesis or Hunter Biden's laptop.

These are just preliminary questions and doubts that occurred to me as I read the Introduction and, hopefully, the book will address and answer them adequately.

Disclaimer: I haven't finished reading this book yet, so can't review or recommend it. However, its topic interests me, and may also interest Fallacy Files readers.


  1. Pp. 5-6. All page references are to the new book.
  2. George Markowsky, "Information Theory", Encyclopaedia Britannica, accessed: 5/10/2022.
  3. Lawrence Weinstein, Guesstimation 2.0 (2012), p. 344. I adopted the term "precision" from this passage in place of "reliability".
  4. See: Fallacy Files Book Club: Nudge, Introduction, 5/12/2008, and subsequent installments.
  5. Pp. 8-9.
  6. Philip Tetlock, Expert Political Judgment (2005).
  7. P. 4.

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