De Finetti’s Game: How to Quantify Belief

August 15, 2011 by 9 Comments

What do people really mean when they say they’re “sure” of something? Everyday language is terrible at describing actual levels of confidence – it lumps together different degrees of belief into vague groups which don’t always match from person to person. When one friend tells you she’s “pretty sure” we should turn left and another says he’s “fairly certain” we should turn right, it would be useful to know how confident they each are.

Sometimes it’s enough to hear your landlord say she’s pretty sure you’ll get towed from that parking space – you’d move your car. But when you’re basing an important decision on another person’s advice, it would be better describe confidence on an objective, numeric scale. It’s not necessarily easy to quantify a feeling, but there’s a method that can help.

Bruno de Finetti, a 20th-century Italian mathematician, came up with a creative idea called de Finetti’s Game to help connect the feeling of confidence to a percent (hat tip Keith Devlin in The Unfinished Game). It works like this:

Suppose you’re half a mile into a road trip when your friend tells you that he’s “pretty sure” he locked the door. Do you go back? When you ask him for a specific number, he replies breezily that he’s 95% sure. Use that number as a starting point and begin the thought experiment.

In the experiment, you show your friend a bag with 95 red and 5 blue marbles. You then offer him a choice: he can either pick a marble at random and, if it’s red, win $1 million. Or he can go back and verify that the door is locked and, if it is, get $1 million.

If your friend would choose to draw a marble from the bag, he preferred the 95% chance to win. His real confidence of locking the door must be somewhere below that. So you play another round – this time with 80 red and 20 blue marbles. If he would rather check the door this time, his confidence is higher than 80% and perhaps you try a 87/13 split next round.

And so on. You keep offering different deals in order to hone in on the level where he feels equally comfortable selecting a random marble and checking the door. That’s his real level of confidence.

The thought experiment should guide people through the tricky process of connecting their feeling of confidence to a corresponding percent. The answer will still be somewhat fuzzy – after all, we’re still relying on a feeling that one option is better than another.

It’s important to remember that the game doesn’t tell us how likely we are to BE right. It only tells us about our confidence – which can be misplaced. From cognitive dissonance to confirmation bias there are countless psychological influences messing up the calibration between our confidence level and our chance of being right. But the more we pay attention to the impact of those biases, the more we can do to compensate. It’s a good practice (though pretty rare) to stop and think, “Have I really been as accurate as I would expect, given how confident I feel?”

I love the idea of measuring people’s confidence (and not just because I can rephrase it as measuring their doubt). I just love being able to quantify things! We can quantify exactly how much a new piece of evidence is likely to affect jurors, how much a person’s suit affects their persuasive impact, or how much confidence affects our openness to new ideas.

We could even use de Finetti’s Game to watch the inner workings of our minds doing Bayesian updating. Maybe I’ll try it out on myself to see how confident I feel that the Ravens will win the Superbowl this year before and after the Week 1 game against the rival Pittsburgh Steelers. I expect that my feeling of confidence won’t shift quite in accordance with what the Bayesian analysis tells me a fully rational person would believe. It’ll be fun to see just how irrational I am!

Filed under Math, Psychology, Rationality

Ethics of the sex tape

August 10, 2011 by 41 Comments

A friend was telling me last week about a celebrity sex tape that he particularly enjoys. I’m not going to help publicize this tape, for reasons that should become clear from reading my post, but I can sketch out the rough details for you: The woman is a young singer, publicly Christian, and she’s having sex with a married man. The tape was stolen (or hacked, I’m not sure) and leaked to the public. It’s theoretically possible that she leaked it herself for publicity, I suppose, but it seems unlikely given the cheating and the Christianity — it definitely tarnished the public image she’d carefully constructed for herself, in addition to being humiliating simply by virtue of it being a sex tape.

So I asked my friend if he feels any guilt about watching this tape, knowing that the woman didn’t want other people to see it, and we ended up having a friendly debate about whether there was anything ethically problematic about his behavior. Of course, the answer to that depends on what ethical system you’re using. You could, for example, take a deontological approach and declare that it’s just a self-evident principle that we don’t have a right to watch someone else’s private tape. Or alternately, you could take a virtue ethics approach and declare that enjoying the tape, after it’s already been leaked, is exploiting someone else’s misfortune, which isn’t a virtuous thing to do.

But my friend and I are both utilitarians, at heart, and neither of those lines of argument resonated with us. We were concerned, instead, with what I think is a more interesting question: does watching the tape harm the woman? As my friend emphasized, she’ll never know that he watched it. (At least, that’s true as long as he downloads it from Bit Torrent, or some other file-sharing site where the number of views of the video aren’t recorded such that she could ever see how much traffic it’s gotten.)

I agreed, but was still reluctant to conclude that no harm was done. Do I necessarily have to know about something in order for its outcome to matter to me? If you tell me about two possible states of the world, one in which everyone has seen my awful humiliating sex tape, and one in which no one has, I’m going to have a very strong preference for the latter, even if people behave identically towards me in both potential worlds. So maybe it makes more sense to define “harming someone” to mean, “helping create a world which that person would not want to exist, given the option,” rather than “causing that person to experience suffering or disutility.” My friend’s decision to watch the tape harmed the woman according to the first, but not the second, definition.

Then my friend advanced what I had to admit was a pretty clever argument:

“Well, presumably the reason she doesn’t want people to see her tape is that she assumes it will make them think worse of her. But I am totally non-judgmental about sex, and don’t think worse of her at all for having made a sex tape. So even if you think there can be harm done to someone without the person ever knowing about it, still, the ‘harm’ is not in people watching the tape but in them thinking worse of her. Which I didn’t, so — no harm done.”

Of course, it’s hard to speculate about someone’s mental state. Maybe the woman would’ve been embarrassed even if she knew people weren’t judging her poorly for the tape. After all, a lot of people don’t like the idea of someone accidentally seeing them naked. And there’s no danger of someone thinking worse of you if he’s the one who accidentally walked in on you — obviously you didn’t do anything wrong — so the embarrassment people feel in cases like that is clearly just from the fact of being seen naked.

So I suppose I didn’t entirely buy my friend’s argument (I’m not sure he did either, honestly), and I’m still left a bit torn about how to evaluate situations like this. But even if you don’t think you’re causing any harm by watching leaked sex tapes like this one, you’ll have to admit that you are ceding your “right” to complain if something like this ever happens to you. So if I find out that you help yourself to celebrity sex tapes, be warned: if a private sex tape of yours ever finds its way onto the Internet, I’ll have no qualms about watching it.

Filed under Ethics

Video Short: Sentient Meat

August 5, 2011 by 1 Comment

One of my earlier posts quoted the Terry Bisson “Sentient Meat” short story – well, it turns out that there’s a film short based on the story!

Great exchange:

And the ones who have been aboard our vessels, the ones you have probed? You’re sure they won’t remember?

They’ll be considered crackpots if they do. We went into their heads and smoothed out their meat so that we’re just a dream to them.

A dream to meat! How strangely appropriate, that we should be meat’s dream.

I liked the feeling of surrealism surrounding something we take for granted every day: we are thinking, loving, dreaming meat.

And yes, that IS Ben Baily of Cash Cab.

Filed under Humor, Video

RS#40: Q&A with Massimo and Julia

August 1, 2011 by Leave a comment

The latest episode of the Rationally Speaking podcast is a special one-hour Q&A, in which Massimo and I answer selected questions from our listeners. In this installment the topics include: What would we teach in a class on critical thinking? What are our views on on analytic vs. continental philosophy? Is it ethical to take advantage of a drought to sell water at marked-up prices? How do we compartmentalize our rationality? How does modern technology affect the way we think about things? What is, or should be, the primary purpose of our species? And is there really a rational argument to prove the divine origin of the Bible?

http://www.rationallyspeakingpodcast.org/show/rs40-qa-with-massimo-and-julia.html

Filed under Uncategorized

The Ethics of Paranormal Investigation, Part 2 of 2

July 30, 2011 by 2 Comments

A continuation of my discussion about the panel I moderated at The Amazing Meeting, on the ethics of paranormal investigation:

Filed under Uncategorized

The Ethics of Paranormal Investigation, Part 1 of 2

July 26, 2011 by 3 Comments

Today we end our first hiatus (which turned out to by much longer than we’d planned — apologies, dear readers!) with the first of a two-part video blog. It’s a discussion of the panel I moderated at TAM9 this year, titled “The Ethics of Paranormal Investigation.” Topics include: Is it acceptable to use deception in the course of unmasking someone else’s deception? What do you do when the person claiming paranormal powers is a child? How much do you feel obligated to ensure the confidentiality of the people you’re investigating? And do you have any responsibility, as a mentalist or magician, to make sure your audience understands what you’re doing isn’t real?

Filed under Uncategorized

Happy Tau Day!

June 28, 2011 by 11 Comments

I almost missed the chance to promote Tau Day! Many of you probably know about Pi Day, held on March 14th. At my high school we used to bring in pies to the math room and eat them at 1:59PM in a glorious (and delicious) celebration of mathematics. But the inimitable Vi Hart lobs an objection: using Pi often doesn’t make as much sense as using Tau, the ratio of the circumference of a circle over its RADIUS.

Thus, we need a new day in celebration of the more-useful Tau:

Seeing as Tau is approximately 6.28 and today is June 28th, have yourself a great Tau Day and enjoy two pi(e)s! While you’re eating, you can go check out more of Vi Hart’s work – she does a fantastic job showing how much fun math can be. We need more voices like hers, and I’ll be sure to post more of her videos!

Filed under Math, Video

Loaded words

June 24, 2011 by 24 Comments

It’s striking how much more unreasonable you can make someone sound, simply by quoting them in a certain tone of voice. I’ve noticed this when I’m listening to someone describe a fight or other incident in which he felt that someone was being rude to him — he’ll relate a comment that the person made (e.g, “And then she was like, ‘Sure, whatever…'”) And when he quotes the person, he uses a sarcastic or cutting tone of voice, so of course I think, “Wow, that person was being obnoxious!”

But then I wonder: Can I really be confident that he’s accurately representing the tone of her comment? It’s pretty easy for someone to, intentionally or not, distort the tone of a comment they’re recounting, while still accurately quoting the person’s official words. Especially if they’re already annoyed at that person. So to be fair, I try to replay the comment in my head in a more neutral tone to see if that makes it seem less obnoxious. (“Sure, whatever” could be said in a detached, I-don’t-have-a-strong-opinion-about-this way, just as easily as it could be said in a sarcastic or dismissive way.)

And there’s an analogy to this phenomenon in print. Journalists and bloggers can cast a totally different light on someone’s quote just through the word choice they use when they refer to the quote. Compare, for example, “Hillary objected that…” to “Hillary complained that…” The former makes her sound controlled and rational; the latter makes her sound whiny. The writer can exert an impressive amount of influence over your reaction to the quote, without ever being accused of misrepresenting what Hillary said.

One insidious example of a loaded word that I’ve found to be quite common is “admitted.” It’s loaded because it implies that whatever content follows reflects poorly on the speaker, and that he would have preferred to conceal it if he could. Take these recent examples:

“In his blog, Volokh admitted that his argument ‘was a joke’” (Wikipedia)
“Bill O’Reilly Admits That His TV Persona Is Just An Act” (Inquisitr)
“Paul Krugman admitted that the zero bound was not actually a bound” (Free Exchange)
Kennedy admitted that ‘the end result’ under his standard ‘may be the same as that suggested by the dissent…’” (Basman Rose Law)

I investigated the original quotes from the people whom these sentences allude to, and as far as I can tell, they gave no sense that they thought what they were saying was shameful or unflattering. The word “admitted” could just as easily have been replaced by something else. For example:

“In his blog, Volokh clarified that his argument ‘was a joke.’”
“Bill O’Reilly Says That His TV Persona Is Just An Act”
“Paul Krugman explained that the zero bound was not actually a bound”
“Kennedy acknowledged that ‘the end result’ under his standard ‘may be the same as that suggested by the dissent…’”

Suddenly all the speakers sound stronger and more confident, right? This isn’t to say that the word “admitted” is never appropriate. Sometimes it clearly fits, such as when someone is agreeing that some particular point does, in fact, weaken the argument she is trying to advance. But in most cases, reading that someone “admitted” some point can subtly make you think more poorly of him without reason. That’s why I advise being on the lookout for this and other loaded words, and when you notice them, try mentally replacing them with something more neutral so that you can focus on the point itself without your judgment being inadvertently skewed.

Filed under Language, Rationality

Why being vegetarian can kill more animals than eating meat

June 22, 2011 by 173 Comments

The most common justification I hear for vegetarianism is “It’s wrong to kill an animal for food.” Of course there are other motivations, such as health, religion, environmentalism, preventing suffering, and trying to score with liberal chicks — but the moral wrongness of killing an animal for food is the probably the most common, at least in my experience.

Consequently, I’ve found it surprising that people so rarely acknowledge that vegetarians do kill millions of animals for food.  If you buy eggs or milk or cheese, it’s true in theory that the dairy cows and laying hens don’t have to be killed in order to supply you with those products, but in practice, they are. A modern factory farm isn’t just going to let their animals die of old age; they kill them at whatever point the farm considers to be the most profit-maximizing. For dairy cows, that’s usually at age 3-5, out of a natural 20-25 year lifespan. For egg-laying hens, it’s usually after one or two laying cycles. And since the males of the laying species are useless to the egg farmer, they’re killed right after they hatch.

But surely eating a vegetarian diet must kill far fewer animals than an omnivore diet, right? Well… sort of. I’m sure that a typical vegetarian kills fewer animals than a typical omnivore. But it’s certainly possible to be a vegetarian and kill more animals than an omnivore, and in fact, I’m confident that many vegetarians fall into that category.

The culprit is eggs. While you only need to kill one single steer to get about 450 pounds (405,000 calories) worth of meat, you’d need to kill about 20 chickens to get enough eggs to match that number of calories. So if you’re a vegetarian who eats a lot of omelets, you’re likely responsible for more animal deaths than someone who chows down on burgers and steaks but doesn’t like eggs.

I’ve scrounged up data on the typical amount of meat, eggs, and dairy that we get out of a modern farm animal, and combined it with data on the calorie counts of those foods. That allowed me to calculate the number of calories of food that we get out of each type of animal, or more to the point, the “lives-per-calorie” statistic for each food. The results are below, with the foods ordered from “kills the fewest animals per calorie” to “kills the most animals per calorie.” (All numbers are approximate, of course, but they’re from as recent and reliable sources as I could find. Detailed citations are at the end of this post.)


*The yield for a laying hen over its lifetime is actually about 550 eggs, but I’ve divided it by two because approximately one male chick is killed for each laying hen.

The lives-per-calories cost of eggs is so many times higher than that of beef that even a small amount of eggs outweighs the life cost of a larger amount of beef. So let’s say you’re a vegetarian and you go out to lunch with your omnivorous friend, where he orders a burger and you order an egg-salad sandwich. The two eggs in your sandwich are only 150 calories, compared to the 300 calories in his beef patty, but the eggs cost almost 9 times as much life as the beef.

Of course, as I said earlier, these calculations are only concerned with the question of taking animals’ lives. They don’t take into account the amount of suffering the animal experiences. That would change the calculations somewhat, but I suspect the overall verdict would remain similar if you were looking at suffering-per-calorie – or, if anything, things would look even grimmer for egg-lovers. Laying hens arguably lead some of the most miserable lives out of all livestock, spending all their time crammed into cages with less space than half a piece of paper, having their beaks cut off, and being starved to induce molting. (Although the male chicks would count less if you’re looking at suffering-per-calorie, since their lives are so short.)

These calculations also don’t take into account impact on the environment. Raising beef is pretty clearly the worst industry in terms of things like producing greenhouse gases, breeding antibiotic-resistant bacteria, and requiring huge amounts of farmland just to feed the cattle. So there’s still a good case for choosing eggs over beef in the sense of minimizing your environmental impact, but that doesn’t change the fact that you’d be making a tradeoff: killing more animals to hurt the environment less.

Citations:

According to the USDA, the average dairy cow produced 21,000 lbs of milk last year, and according to several sources, the average dairy cow is culled from the herd after about 3 years, so I multiplied 21,000*3 to get the average amount of milk produced over the lifetime of a dairy cow. It takes about 1 gallon of milk to produce 1 lb of cheese, and there are about 8.5 lbs of milk per gallon, so I divided 63,000 lbs by 8.5 to get the 7,400 lbs of cheese figure.

The figures on beef and pork come from the Oklahoma Department of Agriculture.

The average number of eggs per laying hen per year comes from the USDA, and I multiplied by two because that’s the most common figure I found for the number of laying cycles. The average weight of a broiler chicken I got from the USDA’s annual Poultry Slaughter publication.

Filed under Ethics

RS#37: The science and philosophy of happiness

June 19, 2011 by 2 Comments

On Episode #37 of the Rationally Speaking podcast, Massimo and I talk about the science and philosophy of happiness:

“Debates over what’s important to happiness — Money? Children? Love? Achievement? — are ancient and universal, but attempts to study the subject empirically are much newer. What have psychologists learned about which factors have a strong effect on people’s happiness and which don’t? Are parents really less happy than non-parents, and do people return to their happiness “set point” even after extreme events like winning the lottery or becoming paralyzed? We also tackle some of the philosophical questions regarding happiness, such as whether some kinds of happiness are “better” than others, and whether people can be mistaken about their own happiness. But, perhaps the hardest question is: can happiness really be measured?”

Filed under Maximizing utility, Philosophy, Psychology

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