April 22nd, 2019 (Permalink)
What's wrong with the following headline?
Poll: 39 percent say Mueller failed to prove Trump campaign did not collude with Russia1
Let's start with the poll question. Why was this question asked when it was? The poll2 ended before the report on the Mueller investigation was released, so no member of the general public had been able to read it at the time of polling3. Why ask people for their opinions on the results of an investigation before they can have read the report?
Here's another recent headline that's relevant:
Who Really Cares About Mueller Report? New Poll Finds One-Third Of Voters Don't Even Know Who William Barr Is4
This is a report on the same poll as the previous headline, but focusing on a different question that shows just how little many of those polled know.
Here's the poll question whose results are reported in the first headline: "Do you think the Mueller investigation proves Donald Trump’s campaign did not collude with the Russians during the 2016 campaign, or does it not prove that?5" This is a confusing question given that the choices offered for answering it are: "Yes", "No", and "Don't know".
At this point, we need to look at some erotetic logic, that is, the logic of questions and answers. I'll try to keep it as brief and non-technical as possible, but some technical language is unavoidable. To start with, the poll question is a disjunctive one, that is, one of the form: "Is P or Q the case?" Disjunctive questions are not yes-or-no questions since to answer "yes" would merely affirm that one of the disjuncts is the case; answering "no" rejects both disjuncts, thus denying the presupposition of the question.
For example, suppose you feel a draft and ask: "Is the door or the window open?" An answer of simply "yes" is likely to be annoying since all that the answer tells you is that one or the other is indeed open, but you want to know which. In contrast, if the answer is "no", you'd assume that neither door nor window was open. Instead, a direct answer to a disjunctive question is any one of the disjuncts, so to answer the question directly is to say either: "The door is open" or "the window is open"6.
An additional point about the poll question is that the second disjunct is the negation of the first, so that the question has the more specific logical form: "Is P or not-P the case?" To answer this simply "yes" or "no" would be either to truly affirm a tautology or falsely deny it.
To adapt the previous example, suppose that you ask: "Is the door open or is it closed?" If the answer comes back: "yes", you'll probably be angry at the answerer since, again, you want to know which. In these sort of situations, people usually assume that a "yes" answer means that the first, affirmative disjunct is the case, and a "no" means that the second, negative one is.
I assume that most of those who answered the poll question assumed that a "yes" answer affirmed the first disjunct and a "no" affirmed the second, which is equivalent to denying the first. The 39% referred to in the first headline, above, are those that answered "no" to the poll question5.
So, probably most of those who took the poll were able to decipher this question, despite its logical problems. Nonetheless, potential confusion could have been easily avoided simply by rewording the three possible answers to something like: "Yes, it proved no collusion", "No, it did not prove no collusion", and "I don't know".
I did a double take when I first read the headline because of its two negations: "not" and "failed". They are not a double negation that simply cancels out, as the negation of "failed" has wide scope and "not" has narrow scope. In other words, "not" negates only the predicate "colludes with Russia" whereas "failed" negates the claim that "Mueller proved Trump campaign did not collude with Russia".
As a general rule, one should use as few negations as possible―either one or none―since multiple negations are hard to cognitively process. One way to eliminate the narrow scope negation is realize that to prove no collusion is to exonerate, so the headline could have been reworded as follows:
Poll: 39 percent say Mueller failed to exonerate the Trump campaign of collusion with Russia
This is easier to understand, but yet another problem lurks here, namely, the word "failed". This word can't be blamed on an editor, since the article under the headline begins: "Almost 4 in 10 Americans think special counsel Robert Mueller's investigation failed to prove President Trump's campaign did not collude with Russia….1" Nor are the pollsters to blame for the occurrence of the word "fail" in the headline since, as we have seen, the poll question did not use that word.
You cannot "fail" at something unless you try to do it. For instance, I did not fail to climb Mount Everest since I never even tried. What reason do we have for thinking that Mueller tried to exonerate the Trump campaign? Since when was it his job to prove that Trump did not collude with Russia? Did the writer of the article presume that the Trump campaign was guilty of collusion and that Mueller's job was to prove its innocence? What happened to the presumption of innocence7?
These considerations lead to a final revision of the offending headline:
Poll: 39 percent say Mueller did not exonerate the Trump campaign of collusion with Russia
The news media like polls because they are manufactured news: instead of waiting for something to happen, just commission a poll and no matter what the results you get instant news. In this case, the poll question was premature, badly worded, and the article shouldn't have focused on it. Moreover, the article gives the false impression that the purpose of the Mueller investigation was to exonerate the Trump campaign.
"Fake news" is "news" that reports things that aren't true, so this isn't fake news. Rather, it's junk news―the journalistic equivalent of junk food: fast, cheap, and low in nutrition.
- Chris Mills Rodrigo, "Poll: 39 percent say Mueller failed to prove Trump campaign did not collude with Russia", The Hill, 4/18/2019.
- "Fox News Poll", Fox News, 4/18/2019.
- The first sentence of the story under the headline reads, in part: "…according to a Fox News poll released a day before a redacted version of the report was slated to be made public."
- Daniel Moritz-Rabson, "Who Really Cares About Mueller Report? New Poll Finds One-Third Of Voters Don't Even Know Who William Barr Is", Newsweek, 4/18/2019. More precisely: 30%; see question 13 in the poll report, linked to in note 2, above.
- See question 23 in the poll report, linked to in note 2, above.
- Unless, of course, the correct answer is: "I don't know." If the question is based on an incorrect presupposition, the answer is: "Neither".
- The presumption of innocence is not just a legal or ethical presumption but a logical one as well: the burden of proof is not on President Trump or his administration to prove that it did not collaborate with Russia, but on those who make that accusation.
April 15th, 2019 (Permalink)
Charts & Graphs: The IRS Baked Two Pies for Tax Day
The two pie charts below appear near the end of the booklet of instructions1 for filling out and filing the 1040 tax form put out by the Internal Revenue Service that is due today. The charts serve no purpose in helping figure taxes, and most taxpayers probably ignore the page where the charts occur in the rush and hassle of preparing a return. Instead, the charts give information on what percentage of the government's income comes from income taxes, and what those taxes pay for.
These charts are three-dimensional pie charts which, as I've pointed out previously2, can be misleading. These are particularly bad examples of this type of chart since the angle from which the "pies" are portrayed is quite acute. This means that the areas of the pies are distorted, so that some look larger in comparison to others than they should. Furthermore, these are "deep dish" pies with thick edges that make the wedges facing the viewer appear to be larger than similarly sized wedges at the back of the pies, whose edges cannot be seen.
For instance, in the "Income" chart, the wedge for "Corporate income taxes" looks almost the same size as that next to it for "Borrowing to cover deficit", despite the fact that the former is only 7% of the pie while the latter is 17%. Similarly, the wedge for "Social security, Medicare,…" behind them represents almost a third of income, but appears to the eye to be about a quarter.
In the "Outlays" chart, the wedge facing the viewer representing "National defense,…" appears to be considerably more than 20% of the pie. In contrast, the largest segment, labelled "Social security, Medicare,…", is over twice the percentage of that for "National defense,…", but doesn't appear to be twice the size.
I don't suppose that these charts were intentionally constructed to mislead, especially since the percentage for each segment is included next to its label. However, there's not much point in baking a pie chart if you have to read a bunch of numbers in order not to be fooled. Instead, a couple of tables listing the parts and their percentages would have conveyed the same information with no risk of misleading the reader. If we must be served with pies, then the angle from which we view them should be close to 90°.
- P. 112. See also: "Major Categories of Federal Income and Outlays for Fiscal Year 2017", Internal Revenue Service, accessed: 4/14/2019.
- Charts & Graphs: Three-Dimensional Pie, 5/5/2013.
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March 31st, 2019 (Permalink)
With tax day rapidly approaching, here are some ways to spend your time instead of filling out forms:
- Benjamin Mazer
To answer the title question: Yes, at least if they want to be so credited. This is one little way that journals could incentivize people to point out errors. Currently, there is little or no incentive to do so, and sometimes actual disincentives. It is the possible existence of such disincentives that makes me add the proviso rather than just answer the question affirmatively. Such perverse incentives are one reason why so many bad studies get published, and reversing them would be one small way to help ameliorate the problem.
[Arizona State Representative] Townsend says her opposition [to compulsory vaccination] is rooted in her experience. The legislator’s 22-year-old daughter has significant medical problems that she blames on a vaccine she received when she was 10 months old. She says no scientific evidence will convince her otherwise. “My entire life has been a struggle, and it’s been nothing compared to my daughter’s struggle, and it’s been due to the shots she got at 10 months old,” she said. “You can have 10 years’ worth of daily articles saying vaccines do no harm and I won’t believe it because it happened to us.”
This is an amazingly similar statement to one from over ten years ago by another vaccination opponent:
"I know what happened to my son after he got his MMR shot," [Mary Wildman] told me. "I have no doubt. There's no way they'll convince me that all these kids were not damaged by vaccines."1
What about the kids and adults damaged by this invincible ignorance? Here are a couple of articles about them, though I don't suppose they would convince these closed-minded people:
- Mona Chalabi, "How measles outbreaks have spread amid the anti-vaccine movement", The Guardian, 1/31/20192.
- Jami Ganz, " He contracted measles at age 30 — and he blames anti-vaxxers for 'spreading fear' and 'ignoring the facts'", MSN, 3/8/2019.
March 30th, 2019 (Permalink)
New Book: Thinking in Bets
…[T]his is not a book about poker strategy or gambling. It is, however, about things poker taught me about learning and decision-making.1
Annie Duke is not the usual suspect for a new book citation on this weblog; here's how she describes herself in her book's Introduction:
When I was twenty-six, I thought I had my future mapped out. … I had graduated from Columbia University with degrees in English and psychology. I had attended graduate school at the University of Pennsylvania, where I won a fellowship from the National Science Foundation, earning a master’s and completing my doctoral course work in cognitive psychology. But I got sick right before finishing my dissertation. I took a leave of absence, left Penn, got married, and moved to a small town in Montana. Not surprisingly, my NSF fellowship didn’t cover my cross-country experiment in adulting, so I needed money. My brother Howard, a professional poker player…, suggested I check out the legal poker games in Billings. … My plan was to earn some money during this break from school, stay on the academic path, and continue playing poker as a hobby. My temporary break turned into a twenty-year career as a professional poker player. … To say that I had strayed from the academic path might seem like an understatement.1
I don't play poker, so I'd never heard of Duke before I somehow stumbled across this book, whose subtitle is: "Making Smarter Decisions When You Don't Have All the Facts". I would only add that you never have all the facts so the book should cover all decision-making.
The title "Thinking in Bets" seems to be a way to emphasize the importance of thinking in terms of probabilities. This also seems to be the point of the title of the first chapter: "Life is Poker, Not Chess". Poker differs from chess in two ways: luck plays a role in poker, but not in chess; you can't see the cards your opponents are holding in poker, but you can see all of your opponent's pieces and their positions in chess.2 Thus, poker is more like life than chess is, since both chance and ignorance play a large role in what happens in life.
Reading a book is a bet: you bet your time, attention, and effort in hopes that the rewards that you receive will be worth it. There's uncertainty in that you won't find out whether the book was worth it until you've made the effort. I haven't read this book yet, so I don't know whether it's worth reading, but based on what I've looked at so far I would bet on it.3
- Annie Duke, Thinking in Bets: Making Smarter Decisions When You Don't Have All the Facts (2018), "Introduction".
- Duke makes this distinction in the following interview: "Poker Champion Annie Duke on Making Smart Bets in Life, Politics, and Football", Reason TV, 2/20/2018. This is not to say that uncertainty plays no role in chess: you can't read your opponent's mind, so you can't be certain of his or her future moves. Also, the game is so explosive combinatorially that it's practically impossible, even for supercomputers, to look more than several moves ahead in a game.
- I also based my decision on the following interesting interview with Duke about this book: "Annie Duke: 'Thinking in Bets'", Talks at Google, 6/21/2018.
March 12th, 2019 (Permalink)
Last month, "Three-Card" Monty*, the carnival con artist, shamelessly attempted to swindle a young couple on Valentine's Day using a pair of tricky dice! Now, he's back in his booth on the midway, but this time he has three strange dice.
Imagine that you approach Monty's booth and see on the counter before him three cubical dice: one colored red, the second white, and the third blue.
"As you can plainly see," Monty says to you, "these are three unusual dice. As you probably know, a standard die has one through six dots on its six faces. The number of dots on these dice range from one through nine, instead. Moreover, each of these nine numbers appears twice, both times on the same die. The numbers are distributed in such a way that each die has different numbers on its faces than the other two, so no number is shared among them. This means that when two of the dice are rolled against one another, they never tie. In every other way these dice are the same as standard dice: they're not loaded or gimmicked in any way.
"The first die has the numbers two, four, and nine, twice each on its six red faces. The second, white die has, instead, the numbers one, six, and eight. Finally, the last, blue die has the numbers three, five, and seven. The numbers on each die total thirty.
"Wouldn't you agree that they are evenly matched? I offer you an even money bet that the die I select will beat yours. That is, each of us will put up a dollar, each will roll his die, and the die that comes up with the highest number wins. Moreover, to be perfectly fair to you I offer you the first choice: you may select any one of the three dice and I will take one of the remaining two. What could be fairer than that?
"So, my friend," Monty finished, "which die do you choose?"
Is the bet that Monty is offering you fair? Should you accept or reject his wager? Assuming that you accept it, which die should you choose?
* In case you don't know Monty: he is a trickster, but he always speaks the exact truth. However, this does not mean that he necessarily tells the whole truth. Also, while he is a sharpster, he prides himself in not doing any sleight-of-hand. For previous puzzles involving Monty, see:
March 8th, 2019 (Permalink)
Rule of Argumentation 41: Be as definite as possible!
Before proceeding to this month's rule, I want to mention something that I should have explained earlier in this series, probably in the introduction: Each of these rules is a heuristic or "rule of thumb". In other words, there are exceptions to all of them, that is, situations in which you should not follow them, but such situations are exceptional.
Previous rules in this series were rules that governed the overall process of arguing: appealing to reason, acknowledging one's own fallibility, and focusing on arguments themselves rather than arguers. This is the first rule that deals with the content of argumentation. It says that the claims and arguments you make should be as definite as possible.
In order to be as definite as possible myself, I will explain what I mean by both "definite" and "possible":
- Definiteness: Most words, phrases, and even sentences in natural languages are ambiguous, that is, they have more than one meaning. The word "definite" itself is such a word, but one of its many meanings is "unambiguous", and that's how I mean it in this rule2.
One problem with ambiguity is, of course, that an ambiguous claim or argument may be misunderstood by your partner in argumentation or your audience. As a result, you may find that you and your partner are arguing past one another, and your audience may reject your arguments and claims because they misunderstand them. If your partner or audience raise questions or objections that make no sense to you, this is a sign that they may be misinterpreting something you have asserted. If such a situation arises, try to track the ambiguity to its source and correct it.
Not only may others misunderstand your arguments if you are not sufficiently definite, but you may even misinterpret them yourself. Ambiguity gives rise to a whole class of fallacies in which a word, phrase, or sentence occurs in both a premiss and the conclusion with different meanings. Such an argument may give a superficial appearance of cogency, but it actually changes the subject.
In order to avoid ambiguity, it's useful to be aware of the ways in which language can be ambiguous, of which there are two principal ones3:
- Lexical Ambiguity: This is the ambiguity affecting individual words and phrases, which can lead to fallacies of equivocation.
- Grammatical Ambiguity: This is ambiguity affecting phrases and whole sentences that results when their grammatical structure can be interpreted in more than one way. When it produces fallacies, such ambiguity is called "amphiboly".
There are also two types of definiteness needed to avoid ambiguity:
- Local: By "local" definiteness, I mean that the individual words, phrases, and sentences that you write should be univocal within their context, that is, they should have a single meaning.
- Global: In order to avoid fallacies, it is not only necessary that each occurrence of an individual word, phrase, or sentence should have a single, definite meaning, but that these meanings should be consistent across the context in which they occur. In other words, if a specific word has a definite meaning in one place, then it should have that same meaning in any other place it occurs. So, it's not enough that each occurrence be definite in meaning, but the meaning needs to be consistent across different occurrences.
- Possibility: Because of the pervasive ambiguity of natural languages, it is usually not possible to be perfectly unambiguous. However, it is usually possible to be as unambiguous as needed in a given context. For this reason, the rule is not to be perfectly unambiguous, but to be as definite as you can. So, you needn't try to be perfectly definite, but only as definite as required in the situation you find yourself in to avoid misunderstandings and fallacies.
Next Month: Rule 5
- Previous entries in this series:
- Rules of Argumentation: Introduction, 11/18/2018
- Rule of Argumentation 1: Appeal to reason!, 12/14/2018
- Rule of Argumentation 2: Be ready to be wrong!, 1/26/2019
- Rule of Argumentation 3: Focus on claims and arguments!, 2/13/2019
- Unfortunately, there doesn't appear to be a synonym for "unambiguous" lacking a negative prefix, so I choose the ambiguous "definite" so as to remain as affirmative as possible in this rule.
- For more on the types of ambiguity, including subtypes and examples, see the entry for the fallacy of Ambiguity.
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