My own supplement to various resources on logical fallacies.
In many cases below, I will refer to the H-1B work visa controversy, as it is one that I am highly familiar with, having been a major critic of the program. Thus it provides an easy source of examples for me.
In a nutshell, here is the issue: The tech industry wants Congress to increase the yearly cap on new visas, saying there is a tech labor shortage. The critics counter that there is no shortage, and that the employers simply want a source of cheap, immobile labor. This is in turn related to the issue of international graduate students at U.S. universities, who tend to be hired as H-1Bs after graduation, a typical reason the foreign students come to the U.S. for study.
NOTE CAREFULLY: The fact that someone uses bad arguments for or against a certain issue does NOT imply that his/her stance on the issue itself is wrong. H-1B, for instance, is a complex issue, and reasonable people may disagree with each other on it.
Here are a few common examples:
There really is no such thing as "the" economy, and most policies will have winners and losers. Who are the members of each group? And even for the winners, to what degree do they "win"?
If you buy a shirt made abroad, how much does it save you? The answer is typically pretty minor, something like 5%, and many Americans may consider that a poor trade for the loss of U.S. jobs. Meanwhile the shirt manufacturer wins big, as that 5% may be a hefty portion of the company's profit margin. If the latter had been, say, 10%, before shipping the work overseas, the 5% labor savings would raise profits by approximately 50%.
In the H-1B debate, most if not all of the pro-H-1B research is conducted by analysts with vested interests in H-1B or with financial ties to the industry, often undisclosed in the research reports.
Sometimes the financial interests are "hidden in plain sight," such newspaper op-ed pieces by immigration lawyers.
University presidents often speak in favor of the H-1B program. You might think that they are neutral, but international students are generally charged higher tuition, thus form a revenue source. Graduate students and post docs get stipends far lower than in industry, thus saving the universities money; since the wages are unattractive to U.S. citizens and permanent residents, foreign students fill the gap.
I will not get mathematical here, and it is not necessary. The issues involve simple common sense.
"My father smoked his whole life, but he never got cancer. I don't believe the research that says cigarettes cause cancer."
The research only showed a TENDENCY for smokers to develop cancer, or in the formal term used, smoking increases the RISK, i.e. the probability, of cancer. It didn't say everyone will get cancer.
Another example: I recently heard a debate on NPR as to whether unlimited contributions should be allowed to political candidates. The Yes side pointed to the fact that in 2014, Rep. Eric Cantor of Virginia lost his primary election to a relative unknown, in spite of having greatly outspent his opponent during the campaign. The Yes side offered this as "proof" that campain money has no effect. But actually, there is no BINARY effect; spending more increases one's chance of winning, but certainly doesn't guarantee it.
This is a variant on the famous post hoc, ergo propter hoc fallacy, which says, "B happened after A, so A must have caused B." The point in this variant is that just because a pattern was found in the past doesn't mean it will hold in the future; conditions may have changed.
For instance, U.S. government economic stimulus programs arguably worked well in the 1960s. But what about today? We now literally have a different world -- globalization. We shouldn't take it for granted that the old methods will still work now.
The pro-H-1B entities like to point to awards, portraying the H-1Bs as typically brilliant. Let's look at an example, the COPSS award in statistics, one of my research fields.
The Wikipedia entry says,
The COPSS Presidents' Award is given annually by the Committee of Presidents of Statistical Societies to a person under the age of 40, in recognition of outstanding contributions to the profession of statistics. It is arguably the most prestigious award in statistics, the Nobel Prize of Statistics.
I fully agree. These are really brilliant people, and the U.S. is fortunate to have them, natives and immigrants alike. In most cases, I'm very familiar with, and highly impressed by, their research work.
Of the awardees, I count 30 who have gotten their PhDs in the U.S., 10 of which did so as foreign students, i.e. 33%. The pro-H-1B people would point to this as indicating general brilliance of the foreign students. Here their fraction is number of foreign awardees / number of awardees.
Yet 50% of all PhDs in statistics in the U.S. are granted to international students. In other words, a smaller percentage of foreign students reach "superstar" status than the corresponding figure for Americans. So the proper fraction to use is number of awardees in the group / number in the group, the group being foreign students in one case and Americans in another.
A famous example is the UC gender bias lawsuit. Plaintiffs pointed to data showing that the admissions rate to grad school was lower for female applicants than for men. In other words, there was a negative correlation between the variables Acceptance and Female. However, subsequent analysis found that a third variable, Department, needed to be taken into account, because it turned out that the women were generally applying to more selective departments than men were. Once this was accounted for, it was found that the women were actually MORE likely to be admitted than men.
This is a statistical philosophy under which the analyst is permitted to formally inject his/her own gut feelings about the subject at hand. Needless to say, this can produce deep biases, whether consciously or not. Unfortunately, the popularity of such methods is on the increase.