Bad logic, but good game theoory

John D. Cook writes:

Ad hominem arguments are bad logic, but good (Bayesian) statistics. A statement isn’t necessarily false because it comes from an unreliable source, though it is more likely to be false. (...) Some people are much more likely to know what they’re talking about than others, depending on context. You’re more likely to get good medical advice from a doctor than from an accountant, though the former may be wrong and the latter may be right.

This is true, but I don't think it's the most important reason why ad hominem arguments persist. After all, they are used also (and perhaps mostly) against reliable sources of information. The reason is game theory. Most interactions we face are signaling games of partial conflict. We talk not just to transmit information, but also to influence other people's beliefs and actions in ways that are beneficial to us. We talk to persuade more than to inform. (Of course, communicating information is a necessary condition of persuasion. You cannot persuade anyone by talking to them if they do not understand what you're saying. Language could not evolve if all human interactions were zero-sum--there wouldn't be enough coordination to establish a common understanding of messages.) Persuasion consists of sending messages of the form "given your preferences, you should do X because Y." The logical validity of such message is of course completely independent of the sender's identity; however, the truth value of the conclusion (that doing X is good for you) is not. If someone gives you a logical argument for why it's good for you to do X, it's perfectly rational for you to wonder why they want you to believe that. Perhaps it's good for them, not so much for you. In other words, it matters who it is that's telling you this, for strategic reasons. Their preferences are relevant information in terms of assessing the likelihood of the conclusion being true.

What separates ad hominem as good game theory from ad hominem as fallacy is whether you're using information about sender's identity to update your beliefs about truth value of the conclusion or about validity of the argument. Here's an example. Suppose you are a (benevolent and completely ignorant) dictator of a medium-sized country. You wonder if establishing minimum wage requirements would help low-skilled workers and, in the process of your wondering, you ask the opinion of an expert economist. The expert comes back to you with the standard microeconomic theory argument that enforcing a minimum wage higher than the market rate increases unemployment among low-skilled workers. You then find out that your expert owns a whole bunch of enterprises that depend on low-skilled labor. It's logically valid and perfectly rational for you to use that information to postpone your decision with respect to the minimum wage (for example, until you get more opinions from experts who have no stakes in the conclusion). But, it's a fallacy if that information causes you to conclude that microeconomic theory is wrong.

I knew it all along

Andrew Sullivan's blog pointed me to a magazine article about women marrying the wrong guys, where we can read the following:

According to recent research conducted by Jennifer Gauvain, a therapist in
Denver, 30 percent of now-divorced women say they knew in their gut they were
making a mistake as they walked down the isle--and kept walking anyway. Only a
handful backed out. The obvious question: If you know you're marrying the wrong
guy, why do it?

Actually, I think this raises at least two questions much more obvious than that. First, has Jennifer Gauvain, a therapist in Denver, ever heard of hindsight bias? Second, when she was conducting her study, did she already know in her gut that her research design is completely useless?

Otherwise known as 'placebo'

From The New York Times:

It has long been the standard practice in medical testing: Give drug treatment to one group while another, the control group, goes without.

Now, New York City is applying the same methodology to assess one of its programs to prevent homelessness. Half of the test subjects — people who are behind on rent and in danger of being evicted — are being denied assistance from the program for two years, with researchers tracking them to see if they end up homeless.

The city’s Department of Homeless Services said the study was necessary to determine whether the $23 million program, called Homebase, helped the people for whom it was intended. Homebase, begun in 2004, offers job training, counseling services and emergency money to help people stay in their homes.

But some public officials and legal aid groups have denounced the study as unethical and cruel, and have called on the city to stop the study and to grant help to all the test subjects who had been denied assistance.“They should immediately stop this experiment,” said the Manhattan borough president, Scott M. Stringer. “The city shouldn’t be making guinea pigs out of its most vulnerable.”

It's fascinating to see how much perceptions of abstract situations depend on completely superfluous details. No one calls on cancer drug researchers to stop experimenting and immediately give new, untested treatments to everyone; no one vilifies them for making guinea pigs out of people. The NYT article is titled "To Test Housing Program, Some Are Denied Aid;" if the article was about a medial trial, what would the title be? Would it contain the phrase "denied aid?"

I have no idea if this experiment is actually methodologically valid or ethical. But if it isn't, it's certainly not because it treats people as lab rats or denies aid to the needy.

Strange beliefs involving numbers: When is a group overrepresented?

One of my hobbies is collecting bizarre and unusual examples of confused quantitative reasoning. Some innumeracies are very common (such as thinking that if an item's price has been discounted twice, first 50% and then 20%, it means that the overall discount is 70%), other ones not so much. Here's an example of the latter kind.

Poland has had presidential elections a few months ago. There were two candidates in the second (and final) round (Poland has a two-candidate runoff system). On election night, when polls were closed but votes were not fully counted, the media were of course talking about election-day polls. Those polls showed a stark contrast between the candidates' relative support among rural and urban voters. About 25% of one candidate's (Komorowski) electorate was rural, whereas the other candidate's electorate (Kaczynski) was reported to be 48% rural. The media concluded that Komorowski was overrepresented among urban voters while Kaczynski was overrepresented among rural voters. One blogger took issue with this interpretation, offering a quite creative argument against it:

The fact is that Kaczynski is represented equally by the whole country. Exactly equally. Because those 2 percent are just statistical error. Rural and urban electorates support Kaczynski equally strongly.

What's bizarre (and, to be honest, quite stupid) about this argument is the implicit assumption that a candidate's representation among different groups is equal if those group's shares in his electorate are equal. Which is absurd, of course; I mean, if some candidate's support was split 50%-50% between people under and over the age of 80, would you say that the candidate is equally supported by young and old voters? In a one-dimensional case, to claim that support is equal it has to be roughly proportional to the base rate. Since about 62% of Poles live in cities, Kaczynski is indeed overrepresented in rural areas.

Interestingly (or perhaps not), in the short passage I quote, the blogger makes two additional quantitative mistakes. First, he writes "2 percent" where he means "two percentage points." Second, he assumes that because the sampling error in the poll is at least 2 points it mean that the true rate is 50% rather than 48%. Sure, it could be 50%. But it's equally likely that it's 46%.

Three staggering mistakes in three sentences! (Yes, I do mean three. The second period mark is artificial.)

Non sequitur of the month: Stunning economics

This installment is inspired by a piece of breathtaking simple-mindedness exhibited by a writer for the Polish leftist site Krytyka Polityczna (it means "political critiques;" think of it as of Polish Huffington Post, with all applicable differences of scale of course). Some guy named Kapela has a review of the movie "The Social Network" in which he writes:

Where does Facebook's worth of 25 billion dollars come from? (...) it means that each account is worth about $50. How come I can't sell it then? I have over 1000 friends, which is more than average. So maybe my account is worth more than $50. No one wants to buy it though.

To clear things up first, the actually relevant reason you can't sell your account is that you don't legally own it; Facebook does. But let's imagine you would be legally able to sell your account. You still wouldn't actually be able to, and the reason is that your account isn't worth $50. It's worth next to nothing. Most of Facebook's revenue comes from selling ads. The possibility of reaching hundreds of millions of people is worth a lot to advertisers, so they are willing to pay a lot for it. The possibility of reaching "over a thousand" of individuals through one account, on the other hand, isn't worth a dime to advertisers, which means a single account would bring zero revenue, which means that it's worth about zero dollars. Now this isn't necessarily true of all accounts; I'm sure that if, say, Barack Obama were to sell his account on ebay, he could get a lot of money for it. But in those cases the account's worth is due in large part to things other than possible future revenue. Assuming that since 500 million accounts are worth $25 billion, 1 account is worth $50, is just dumb.

Elections bring out the stupid in people

So, elections are upon us. Ever heard the phrase "If you don't vote, you have no right to complain?" Always uttered with much self-righteousness and absolutely no reflection, it's one of the most blatant non sequiturs in circulation at the moment. There's absolutely no logic to it. The probability that your particular vote will be pivotal in terms of the outcome of state or national elections is so small that it's essentially zero. Given the fact that multiple millions of other voters turn out at the polls, the influence that your individual vote has on the outcome is zero, which is about the same as the influence you have on the outcome if you don't even bother to vote in the first place. Ergo, either everyone has the right to complain or no one does.

At any rate, I have recently stumbled upon an original rephrasing of this peculiar argument due to a Marc Hedlund writing for O'Reilly.com. Hedlund starts with a simple paraphrase of the original:

Once, many years ago, I was waiting in line at the Post Office on election day. One postal worker asked another if she had voted, and the second responded, "Hell yes, I voted. If you don't vote, you can't bitch, and I am not giving up my right to bitch!"

So far so bad. Therefore, Hedlund decides to make it worse by inventing his own analogy of the problem:

I was thinking about that the other day when trying to decide whether to buy a new iPhone 4 or wait to see what happens with Verizon at some point in the future (...) If you're buying an iPhone 4 tomorrow, you already know AT&T is almost universally considered the weakest aspect of the phone's experience. You're signing up for that (...) So here's the deal: if you buy that phone right now, you're giving up your right to bitch about AT&T for the next two years. No, I mean it! Complaints will be returned to sender unread.

(...)

I'm undecided about what to do, myself. I'll probably cave. But if I do, I won't bitch, and you shouldn't either. The single strongest message you could send to Apple and AT&T would be to vote with your wallet against AT&T's crappy service. If you don't vote, then you're getting what you paid for.

OK, so this is actually a slight variation on the original, because what Hedlund seems to be saying is that you have the right to complain about Obama if and only if you voted for McCain. If you voted for Obama, you can't complain because you got what you've signed up for, and if you didn't vote at all, you can't complain because blah blah blah whatever (I'm not sure what the argument is there).

However, none of this changes the fact that Hedlund's is one of the worst analogies in the history of bad analogies. If I decide to buy an iPhone instead of a Verizon-based smartphone, i will have an iPhone. If I decide to buy a Verizon phone, I will have that. See where this is going? What happens to me phone-wise depends on my decision and my decision only. By contrast, if I decide to vote McCain, I may get McCain for president, but then again I may not. I may get Obama. What happens to me president-wise depends not just on what I do, but also on what about 215 million other people do. 215 million people on whom I have no influence whatsoever. In other words, while I decide what type of phone I will use (or if I will use any type of phone at all, for that matter), I do not decide what type of president I will use. That is decided for me. Sometimes I will like the outcome, and sometimes I will not, but either way the fact is that I did not choose the outcome. Tell me again, then, what exactly does the act of voting have to do with the right to complain?

Now because people have full control over what phone they use, they tend to choose between phones based on which one they think will be best for them. In other words, if they buy an iPhone and not a Verizon phone, they do it because they like iPhone's features so much that they are willing to get over its inferior signal reception; if they buy a Verizon phone, they do it because they value signal reception so much that they are not willing to sacrifice it for additional features. Hedlund suggests a novel reason for making a choice like that: if you don't like Apple's crappy phone service, buy Verizon in order to induce Apple to change their strategy. Actually, perhaps this is a good analogy of voting after all: thinking that your individual decision as to where to allocate $300 can change the behavior of a corporation whose annual revenue is some $43 billion is just as delusional as thinking that your individual vote matters for an outcome of an election with over 200 million participating voters. If you're forgoing iPhone 4 because you want to change Apple's strategy with respect to phone service, you have a serious problem with respect to your grip on reality.

Things depend

xkcd comments on using unconditional probability in situations when what's relevant is conditional probability:

Happens all the time. How many times have you heard someone say "Sure, the probability of winning the lottery may be very small... but someone wins it nonetheless!" Or take a more ominous example: Alan Dershowitz's claim, made during O. J. Simpson's trial, that since less than 1 in a 1000 women abused by their partners are also killed by them, the fact that Simpson abused his wife doesn't make it much more likely that he killed her. Makes me wonder how many people were falsely convicted or acquitted because of erroneous arguments like this not having been exposed.

Where does the something that everything must come from, come from?

In his new book "The Grand Design," Stephen Hawking writes:

Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist. (...) It is not necessary to invoke God to light the blue touch paper and set the universe going.

Naturally, the statement caused quite an uproar and a lot of polemics from apologetics. It may just be my bad luck, but quite honestly I have not read one single response to Hawking's claims that would be in any way insightful, or even intelligent for that matter. Every single defender of religion that I've read argued against Hawking using some version of the famous First Cause Argument: Whatever begins to exist has a cause, therefore the Universe has a cause, the "First Cause" of everything there is. Apologetics identify the First Cause with God.

Newsflash: The First Cause argument is logically flawed. As in: it's wrong. It commits the fallacy of "begging the question" or, in much less fancy terms, simply assuming what it's trying to prove. Suppose everything that exists must indeed have a cause. Then it does follow that the Universe must have a cause. But what caused the First Cause? You just assumed that everything must have a cause, so the First Cause must have one too. What is it? The Mother of All Causes? And who's her mother? In other words, if everything that exists must have a creator, then who created the creator? Note that you're not allowed to say that God exists without having to be created because "that's His nature." That's not an argument; it's a hand-wave. We might just as well assume that the Universe created itself out of nothing because "that's its nature."

But some response pieces are even more confused that just relying on the First Cause Argument, and I'll write about one of those. It's an essay by Pawel Lisicki, editor-in-chief of one of the largest daily papers in Poland, "Rzeczpospolita." Referring directly to Hawking's above quote, Lisicki writes

Both creation and spontaneity (...) are concepts that are well-defined only in the realm of personal metaphysics and religion. Only a person, an agent (...) who has free will and ability to reason, can be spontaneous.

Strike one for monumental ignorance. Spontaneous appearance of things uncaused by an intelligent agent is directly observable. Certain particles have been observed to appear spontaneously, out of absolutely nothing. The price mechanism causes millions of unconnected individual decisions to coordinate into one huge resource-allocating machine which does not have a conscious designer. Further, Lisicki writes

In Christian thought, being able to create something is an attribute of God (...) only through analogy and metaphor can we also talk of human creation. Impersonal, spontaneous creation as a cause that the world exists is a self-contradictory concept.

Strike two for ignorance coupled with pretentiousness. Lisicki says that impersonal spontaneous creation is a self-contradictory concept, and that's because... it's inconsistent with the definition of creation that he is using! In other words, he clearly has no idea what "self-contradictory" even means; he's just pretentiously throwing the term around because it makes him sound all smart and everything. To top things off, the definition he's using makes his reasoning perfectly circular. Effectively, Lisicki's entire argument is this:

I've just assumed that everything that exists has been created. I've also defined "creation" as something only God can do. Therefore, the Universe has been created by God.

That's all of it, really. How completely uncritical of your own beliefs do you have to be to think this is actually a sound argument?

Beautiful experiments in social science: Reversing the implication

People tend to make the logical error of reversing the implication, i.e. believing that "If A then B" implies "If B than A." A clever experimental design devised by psychologist Peter Cathcart Wason showed how often that mistake is made. Here's the design:

You are shown a set of four cards placed on a table, each of which has a number on one side and a colored patch on the other side. The visible faces of the cards show 1, 2, red and blue. Which card(s) should you turn over in order to test the truth of the proposition that if a card shows a 2 on one face, then its opposite face is red?

Answer given by more than 90% of participants: 2 and red. Correct answer: 2 and blue. The incorrect answer clearly stems from reversing the implication.

An imperfect argument

What would political debate (or, for that matter, any debate) look like if its participants truly internalized the fact that arguing to the effect of "You are accruing personal gains from publicizing your arguments, therefore your arguments are wrong," is a fallacy?

Reversing implication: you really can't do that

One of the most common fallacies is that of reversing an implication. An implication is a statement of the form 'If A then B,' where A and B can be any statements whatsoever. Now reversing implication is an incorrect belief that 'If A then B, then if B then A.' Implication is not symmetrical, and it's easy to come up with an example that would make it clear. Suppose we have the following implication: 'If Roger Federer is the best tennis player in the world, then he is the best tennis player in Europe.' Reversing this implication you'd have 'If Roger Federer is the best tennis player in Europe, then he is the best tennis player in the world,' which is clearly not true. You just can't reverse an implication; in fact, the only valid conclusion you can get from 'If A then B' is 'If not-B then not-A' ('If Roger Federer is not the best tennis player in the world, then he is not the best tennis player in Europe').

Nonetheless, reversing implications is pretty much bread and butter of political dispute. Let me give a concrete example. On August 1, 1944, Polish anti-Nazi resistance called the Home Army (Armia Krajowa) started an open battle with Nazi troops stationed in Warsaw; the battle is known as the Warsaw Uprising (Powstanie Warszawskie). I will not get into the details of the Uprising here, as I am planning a whole series of posts on this fascinating topic in the very near future. For now I'll just talk about one fact about it: when Poland succumbed to Soviet rule soon after the war was over, the official line of communist propaganda with respect to the Uprising was that it was an insanely careless endeavor that brought more harm than good. The reason that communists were saying this was purely cynical: they hated the Uprising because it was a last-ditch effort anti-communist population of Warsaw to try to prevent the city from being taken over by the Soviets. Of course, I don't share those motivations; but I do indeed believe that the Warsaw Uprising was a tragic mistake, and that, even in its terrible post-war situation, Poland would probably have been better off if it had not happened.

I cannot count the times when, after sharing this belief of mine in a face-to-face or an online discussion, I have been called a communist for having this opinion. But it should be clear that those of my critics who were using this argument were committing the fallacy of reversing an implication. We have 'If one is a communist, then one believes that Warsaw Uprising was a mistake.' From this, my critics were concluding that 'If one believes that Warsaw Uprising was a mistake, then one is a communist.' Fallacious reasoning, clear as day. And the interesting part is those were all people smart enough that, if they were presented with the Roger Federer example given above, would no doubt understand that reversing implication is invalid reasoning. Yet in this particular context they were completely unable to realize that they were making the same silly mistake.

The naturalistic fallacy, subtle style

Via PZ Myers: An adjunct professor at the University of Illinois Kenneth Howell has written an email to his students in which he defended the Catholic position on homosexuality. Here's an excerpt:

But the more significant problem has to do with the fact that the consent criterion is not related in any way to the NATURE of the act itself. This is where Natural Moral Law (NML) objects. NML says that Morality must be a response to REALITY. In other words, sexual acts are only appropriate for people who are complementary, not the same. How do we know this? By looking at REALITY. Men and women are complementary in their anatomy, physiology, and psychology. Men and women are not interchangeable. So, a moral sexual act has to be between persons that are fitted for that act. Consent is important but there is more than consent needed.

This reasoning is an instance of the naturalistic fallacy, albeit in a somewhat subtler form. In its naive version, the naturalistic fallacy states that what is natural is moral and vice versa. This is grotesquely absurd: rape and murder are natural, for example, so they would have to be adjudicated as moral. Howell doesn't go as far as to say that morality and naturalness are equivalent; he adds consent as another criterion for judging an act to be moral. More precisely he (seems to be) saying that consent is a necessary, but not sufficient, condition for an act to be qualified as moral. (IOW, all moral acts are consensual but not all consensual acts are moral.) To fulfill the morality definition, an act must be consensual and natural (as he says, "be a response to REALITY").

But this definition is absurd too. I'm sure any of my readers could come up with an indefinite number of examples of consensual acts that pretty much everyone on the planet agrees are not immoral but which nonetheless are highly unnatural. To give just one example: If he's consistent in his beliefs, Howell must think that flying in an airplane is immoral. It doesn't matter that people do it voluntarily; flying is not appropriate for people. How do we know this? By looking at REALITY. There is nothing in human anatomy or physiology that would suggest humans are meant to fly. So, a moral act of flying has to be left to species that are fitted for that act.

More broken windows

Few weeks ago I've written about a particular example of the broken window fallacy; here comes another one. Bozeman, MT has recently suffered a hail storm which damaged many buildings. Of course, the local paper reported this as good news: "Storm Boosts Bozeman Economy"!

It's futile to explain why this type of thinking is outrageously stupid; the broken window fallacy is undead, it will go on forever. I think it is interesting though that the believers in this fallacy apply their belief rather selectively: some disasters boost, others not so much. Why, for example, do we not see anyone trying to tell us how the Gulf economy has been boosted by the oil spill? I mean, think about all the new jobs it has generated.

A parasite calling kettle black?

Through Ed Brayton, I've learned about David Jungerman, a Missouri farmer who had recently painted his tractor trailer with the message: "Are you a producer or a parasite? Democrats - party of parasites." This is murderous irony since most farming in the U.S. is inefficient and sustainable only because of government subsidies (a.k.a. handouts); Brayton quotes the Kansas City Star which determined that Jungerman himself has received over a million dollars in farm subsidies since 1995. The paper goes on to say

"That's just my money coming back to me," Jungerman (...) said Monday. "I pay a lot in taxes. I'm not a parasite." (...) Jungerman said he put up the sign to protest people who pay no taxes, but, "Always have their hand out for whatever the government will give them" in social programs.

To this Brayton replies

Sorry, still doesn't fly. I bet he hasn't paid a million dollars in taxes in the last 15 years.

Both Jungerman and Brayton are missing the point here. You can be a net income tax payer and still be a "parasite." For example, there are plenty of indirect farm subsidies which work as price distortions; basically, the government pays to inflate prices of goods sold by farmers and to deflate prices of goods bought by them. So it is very well possible that not just Jungerman's farm subsidies money, but his very income, is in fact a handout. Of course there's no way for me to know if this is actually the case. My point is that just because someone is a net income tax payer does not mean he's a "producer."

An then of course there's a broader point, which everybody is missing, not just Brayton. That point is that just because someone is a hypocrite does not necessarily mean that what he's saying is false.

Elections bring out the worst in people

I hate elections, especially the time right before and right after the actual voting. People get very passionate about politics, and when people get passionate, they tend to abandon clear thinking. The sleep of reason breeds monsters, said Goya, and in case of the height of electoral campaigns those monsters are fallacies. Here is (an incomplete) list of fallacies that "pop up" in the media every time a democracy holds elections.

1) Tribalism. As such it's not a fallacy per se, but it leads to fallacies. People stricken with the tribal mode of thinking tend to believe that their favored candidate is right about everything he says while the other one is wrong about everything. If the candidate they oppose says that two plus three is five, or that it's wrong to eat babies, tribal leaders on the other side automatically disagree or at least try to argue that the other side doesn't really believe what it says.

2) Hypocrisy about tribalism. Tribal disputes always come very crudely disguised as policy debates; but usually anyone with a clear mind can see that those who talk about policies have no interest in finding out what actually works.

2) Ad hominems. Those are ingrained in tribalism, and their most ubiquitous form is assuming that everyone who disagrees with you on policy issues has bad intentions.

3) Belief that "each vote counts." No elections have ever been decided by a single vote, or anything remotely close to a single vote. The probability that your vote will decide which candidate wins national elections is smaller than the probability that you will win the lottery.

4) Religious attitude towards the belief that each vote counts. Those who point out that a single vote does not, in fact, matter, are faced with much sanctimonious indignation. Also, whenever you are arguing that the probability of anyone being a swing voter is essentially zero, some defender of the "each vote counts" doctrine will inevitably counter by saying "What if everyone thought that way?"--as though that reply had any logical relevance.

5) Projection. Part of a whole package of fallacies stemming from people trying to read information from data that simply does not contain it. Polling numbers tell you who people voted for; it tells you nothing about why they voted for this guy and not that guy. It's extremely annoying to hear pundits trying to explain, right after the polls closed, that people voted for Obama mainly because of the economy or because they were tired of the war in Iraq. Before having reliable survey data, it's impossible to tell. Or, another example: how many times have you heard that Obama beat McCain because he ran a much better campaign? A lot, probably. But that's something we can't know, because we have no control: we don't know what Obama's numbers would have been if his campaign was weaker. It could have been the campaign, sure; but it could have been the economic meltdown just as well. We know that, all else equal, the incumbent party does well when the economy is good, and does poorly when the economy is weak. I could have been the case that, in the fall of 2008, the economy was in such terrible shape that McCain would have lost to a fire hydrant. We just don't know.

6) Ecological fallacy. This one is rampant right after the results are turned in as well. Suppose that this time around, Democrats had more young people as well as more Hispanic people voting for them than they did four years ago. You will then inevitably hear someone concluding from this that more young Hispanics voted Democratic. But this conclusion does not follow: without seeing individual data, we don't know if its Hispanics or Whites or Blacks who were younger than usual.

And so on; there's more, much more. It's possible that I will update the list if something else comes to my mind. To wrap the post up, a disclaimer: I only hate elections in an absolute sense, not in a relative sense. That is to say I hate elections, but I hate viable alternatives even more.

Why did JFK want to send cloned dinosaurs into space?

A brilliant quote from Randall Munroe:

(...) if you read [JFK's] speech at Rice, all his arguments for going to the moon work equally well as arguments for blowing up the moon, sending cloned dinosaurs into space, or constructing a towering penis-shaped obelisk on Mars.

The quote is a mouse-over in Munroe's equally brilliant cartoon. It's probably the best (and definitely funniest) example of a fallacy that is ubiquitous in all debates, public or private: refusal to take responsibility for logical consequences of one's own beliefs. If you claim that A, and if it can be shown that A implies B, then you are also claiming that B, whether you like it or not. It doesn't matter that you didn't intend to claim that B, that you disagree with B, or whatever. If you don't like the consequences of your beliefs that have been shown to you, your only logically valid line of defense is trying to show that the consequences you don't like do not really follow; you are not allowed to just say "But I've never said that." For example, I think that if you're saying it's wrong to discriminate based on race, you're also saying that it's wrong to protect American jobs from foreign competition; and if you're saying that manufacturers should have legal power to set asking prices of the goods they manufacture, you're also saying that Amazon.com does not provide any useful services. If you don't like these conclusions, you have to either attempt to show they do not follow from your premises, or else rethink those premises.

If xkcd is right and JFK's arguments for sending people to the moon are equally good as arguments for sending cloned dinosaurs into space, then JFK was indeed in favor of sending cloned dinosaurs into space, whether he realized it or not.

Non sequitur of the month: personal communication

I'll describe this month's entry in abstract terms first, then provide two examples. Suppose you have two sets A and B. They're both non-empty and they overlap; other than that, no additional assumptions about them are made. Our non sequitur of the month is the following implication:

If the number of elements that belong to the intersection of A and B constitutes x percent of the number of all elements of A, then it also constitutes x percent of the number of all elements of B.

This is true if and only if A and B are exactly equal in size (or, as a special case, if they are one and the same set). But no such assumption was made, so it is definitely not true; in fact, it is a stunning non sequitur.

I've encountered this baffling mistake in two real-life contexts; describing those may help highlight how incredibly wrong this reasoning is. First context: There are studies trying to estimate the percentage of homosexual men among pedophiles. Any study that comes up with such an estimate (say 10 percent) will invariably be quoted somewhere in the media as saying that 10 percent of homosexual men are pedophiles--as if it were the same thing. Second context is a guy I knew named Bob (not his actual name). Bob is a very successful individual. He holds a Ph.D. in one of the social sciences, and among many things he does for a living is teaching a course in quantitative research methods at an Ivy League university. One of Bob's research interests is the connection between homelessness and foster care. There's research out there estimating that roughly 20 percent of youth that "age out" of foster care experience a significantly long spell of homelessness. Bob is convinced that this means that 20 percent of homeless people have aged out of foster care. I am not making this up; both myself and several other people have asked him to articulate his conviction as clearly as possible, and it is indeed how I've just described it. All attempts to show him the absurdity of said conviction have failed miserably.

Think about what this logic implies. Suppose 5 percent of smokers get lung cancer; this means you should believe that 5 percent of people with lung cancer are smokers. If 95 percent of men have a high school diploma, then 95 percent of people with a high school diploma are men. If half of the cats are black then half of all black things are black cats. Etc., etc. I think the sheer stupidity of this particular non sequitur is clear enough by now.

There are errors in reasoning that are subtle: it's easy to make them if one is not careful enough, and even if avoided, it's easy to understand where the mistake originates. None of the non sequiturs of the month fall into that category. Try as I might, I cannot come up with a plausible line of reasoning that could lead to them.

The mother of all fallacies

Well, not really. Nothing is ever the mother of all anything. But, whenever politics and/or economics is being discussed, there is one fallacy that seems to be much more common than all the others: it's the Nirvana fallacy, i.e. belief that if some policy solution isn't perfect, it's useless. Or, to put it another way, comparing a policy proposal not to its best viable alternative, but to a perfect state of affairs.

Healthcare debate provides an example. Most of its participants, regardless of what they're arguing for, seem convinced that it's possible to build a system in which everyone is taken care of; they just disagree on what that system should look like. But, alas, it's not possible; at least not now, not with the income levels our economies generate as of today. In any system we can have right now, there will be people dying due to lack of adequate healthcare. In a purely market system, this will happen because providing healthcare is very expensive, and some people will not be able to afford the market rates (we see this happening right now in the U.S.). In a purely government-run system, this will happen because when the government controls prices of medical services, those prices will be set either below or above market clearing rates (most likely way below)--and both those situations generate shortages of supply and decrease of quality (we see this happening right now in Poland).

Scarcity is a fact of life. There are three ways of dealing with that fact. First, we can keep increasing our income and wealth, thereby decreasing scarcity in some areas of life by making things cheaper and cheaper to buy. Second, we can complain to whoever it is we think invented the world. Third, we can simply pretend it doesn't exist--and this is precisely what most of the political debate does.

Non sequitur of the month: "either-or" means "fifty-fifty"

Very frequently I experience an urge to write a post with no other purpose than to just mock some piece of extraordinary stupidity that I've encountered in the media. I try to fight that urge, as writing posts that do nothing but attack an easy target is kind of cheap. However, sometimes the temptation is just too strong. For one thing, shooting fish in the barrel can occasionally be fun. For another, psychologists tell me that it's unhealthy to suppress anger, and non sequiturs make me extremely angry. I take them very personally.

Therefore, in order to channel that anger, I decided to start a periodical feature called "Non Sequitur of the Month." In it, I'll try to present truly spectacular errors in reasoning. Fireworks of stupidity, if you will. And since pretty much any fallacy can in principle be stated as a non sequitur, I don't anticipate having trouble keeping things going.

First up is one Anna Cieślak, a journalist working for the second-largest Polish daily newspaper, Rzeczpospolita (title means "The Republic"). She has a blog, and on that blog, there's a post on unemployment. The very first two sentences of that post, in translation, read

From the micro point of view, i.e. from the point of view of an individual, it makes no practical difference whether the unemployment rate will climb to 12.5 or to 13.5 percent. You'll either get fired or you won't, and therefore your risk of becoming unemployed is 50 percent anyway.

Yes, you read that right. Apparently, the author believes that whenever the outcome variable is binary, it necessarily means that each alternative occurs with probability one-half. I should immediately start playing lottery; since I can either win the jackpot or not, it must mean that I have a fifty percent chance of winning.

This is truly a remarkable, monumental piece of stupidity. I believe the first entry in the Non Sequitur of the Month category may well turn into a non sequitur of the year.

Peak ignorance

Via the Economic Way of Thinking blog I came across this graph:

Let's think about this for a moment. As of now, oil is bought and sold on the world market, and demand for it is at least somewhat elastic (it's not the only possible source of energy). So how can demand possibly exceed supply, as the graph shows will inevitably happen? As far as I know, this can only be the case if someone can manage to keep oil prices below the market-clearing rate. Is that the prediction here, that by 2010 there will emerge an entity powerful enough to enact price controls in the world oil market? Or is it just that the Peak Oil advocates don't really know what they're talking about?

Added: Michael Munger is less kind, calling it Peak Idiocy.