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“”All toupées look fake; I've never seen one that I couldn't tell was fake.
It should be obvious that such a phrase can only be said about bad toupées — ones that look fake — and not actually all toupées. If the person uttering this phrase saw a convincing toupée, they wouldn't have noticed it at all! Hence it is a fallacy to draw such a conclusion from a horrendously limited evidence base.
The origins of the name are unclear, but it can be traced back to at least 2006 with a mention on a Skeptics Guide to the Universe podcast as a "name that fallacy" question and the Skeptical Medicine blog's list of fallacies attributes the phrase to Rebecca Watson.
 Relation to other fallacies and biases
The toupée fallacy in this form is a specific case of the far broader problem of generalizability, which is the question of whether specific observations can lead to generalised rules that must always hold true. So, in this illustration, trying to claim that all toupées look fake based on the ones that obviously do look fake doesn't work, and shows the problem of induction clearly. One can not draw the general conclusion that all toupées make the wearer look like an arse merely by pointing to the ones that do, because you have no idea about which realistic looking hair pieces might, underneath, be fake.
Toupées, in this analogy, that look "real" enough to be ignored and passed by undetected are often referred to as "silent evidence", and it is this concept of silent evidence that forms a key part of hindsight bias, the narrative fallacy, and what has been popularised by economist Nassim Taleb as "the black swan problem". The toupée fallacy, as stated above, is highly isomorphic with the statement "all swans are white", an assertion that can be shattered by the observation of even a single black swan. Similarly, the statement that all toupées look fake can be shattered by a toupée that looks convincing. While the black swan problem suggests that black swans are not observed mostly because they haven't happened yet, the toupée fallacy specifically puts evidence that would disconfirm it outside what people are looking for.
The fallacy and how it illustrates the problem of induction also exemplifies the need for falsifiable hypotheses in science. The assertion that "all toupées look fake" cannot be proved by only looking at hair pieces that look fake and restricting one's search for evidence this way - a method known in the skepticism business as confirmation bias. However, by searching realistic looking hair and finding that none of them happen to be fake hair pieces, we can build up confidence that toupées tend to look fake.
The fallacy was mentioned by name by Natalie Reed in response to the idea that all transgender women are easily discernible from cisgender women, even just with a passing glance in public. Such an observation must only have come from trans women (MTF) who are either mid-transition or happen to look — in the words of radical feminist Germaine Greer — like a "ghastly parody" of cisgendered women. Reed also spotted it in her own thinking, having once held the opinion that all trans women were batcrap crazy, happily ignoring the ones that simply passed by without drawing attention to themselves in that fashion.
The problem of induction is almost always well pronounced when generalising about demographics, and such things are easily influenced by selective reporting. For instance, it's quite likely that you've met a gay man who wasn't excessively camp, wasn't highly groomed, and didn't drop their sexuality into the conversation in the first fifteen seconds — but it's quite likely that if you did, you didn't notice (or care, or even go out of your way to find out) that they were gay. Simply looking out for a set of simplistic and basic traits like that can very easily enforce stereotyping, and confirmation bias happily fills in the rest.
Similarly, it's often argued that the news media will happily enforce confirmation bias by reporting on news that fits existing narratives. Hence, terrorists associated with Islamic extremism are likely to be shown on the news. This supports the stereotype of "all Muslims are terrorists" in a manner similar to affirming the consequent, and is a case of the toupée fallacy as people who happily accept this phrase won't be interested in Muslims who aren't also terrorists.
A variant (the Inverted Toupee Fallacy?) is along the lines of "Despite every advance in forensic science over the last (insert random number of your choice) years, the incidence of undetected murders continues to rise".
 See also