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 Hello, my name is Christian Rudder, and I was one of the founders of OK Cupid. It's now one of the biggest dating sites in the United States. Like almost everyone at the site, I was a math major, and, as you might expect, we're known for the analytic approach we have taken to love. We call it our matching algorithm. Basically OK Cupid's matching algorithm helps us decide whether two people should go on a date. We built our entire business around it. Now, algorithm is a fancy word, and people like to drop it like it's this big thing, but, really, an algorithm is just a systematic, step-by-step way to solve a problem. It doesn't have to be fancy at all. Here, in this lesson, I'm going to explain how we arrived at our particular algorithm so you can see how it's done. Now, why are algorithms even important? Why does this lesson even exist? Well, notice one very significant phrase I used above: they are a "step-by-step" way to solve a problem, and, as you probably know, computers excel at step-by-step processes. A computer without an algorithm is basically an expensive paperweight. And since computers are such a pervasive part of everyday life, algorithms are everywhere. The math behind OK Cupid's matching algorithm is surprisingly simple. It's just some addition, multiplication, a little bit of square roots. The tricky part in designing it, though, was figuring out how to take something mysterious, human attraction, and break it into components that a computer can work with. Well, the first thing we needed to match people up was data, something for the algorithm to work with. The best way to get data quickly from people is to just ask for it. So, we decided that OK Cupid should ask users questions, stuff like, "Do you want to have kids one day?" and "How often do you brush your teeth?", "Do you like scary movies?" and big stuff like "Do you believe in God?" Now, a lot of the questions are good for matching like with like, that is when both people answer the same way. For example, two people who are both into scary movies are probably a better match than one person who is and one person who isn't. But what about a question like, "Do you like to be the center of attention?" If both people in a relationship are saying yes to this, then they are going to have massive problems. We realized this early on, and so we decided we needed a bit more data from each question. We had to ask people to specify not only their own answer, but the answer they wanted from someone else. That worked really well, but we needed one more dimension. Some questions tell you more about a person than others. For example, a question about politics, something like, "Which is worse: book burning or flag burning?" might reveal more about someone than their taste in movies. And it doesn't make sense to weigh all things equally, so we added one final data point. For everything that OK Cupid asks you, you have a chance to tell us the role it plays in your life, and this ranges from irrelevant to mandatory. So now, for every question, we have three things for our algorithm: first, your answer; second, how you want someone else, your potential match, to answer; and three, how important the question is to you at all. With all this information, OK Cupid can figure out how well two people will get along. The algorithm crunches the numbers and gives us a result. As a practical example, let's look at how we'd match you with another person, let's call him, "B". Your match percentage with B is based on questions you've both answered. Let's call that set of common questions, "s". As a very simple example, we use a small set "s" with just two questions in common and compute a match from that. Here are our two example questions. The first one, let's say, is, "How messy are you?" and the answer possibilities are very messy, average, and very organized. And let's say you answered "very organized," and you'd like someone else to answer "very organized," and the question is very important to you. Basically you are a neat freak. You're neat, you want someone else to be neat, and that's it. And let's say B is a little bit different. He answered very organized for himself, but average is OK with him as an answer from someone else, and the question is only a little important to him. Let's look at the second question, it's the one from our previous example: "Do you like to be the center of attention?" The answers are just yes and no. Now you've answered "no," how you want someone else to answer is "no," and the questions is only a little important to you. Now B, he's answered "yes," he wants someone else to answer "no," because he wants the spotlight on him, and the question is somewhat important to him. So, let's try to compute all of this. Our first step is, since we use computers to do this, we need to assign numerical values to ideas like "somewhat important" and "very important" because computers need everything in numbers. We at OK Cupid decided on the following scale: irrelevant is worth 0, a little important is worth 1, somewhat important is worth 10, very important is 50, and absolutely mandatory is 250. Next, the algorithm makes two simple calculations. The first is how much did B's answers satisfy you, that is, how many possible points did B score on your scale? Well, you indicated that B's answer to the first question about messiness was very important to you. It's worth 50 points and B got that right. The second question is worth only 1 because you said it was only a little important, and B got that wrong. So B's answers were 50 out of 51 possible points. That's 98% satisfactory. It's pretty good. And, the second question of the algorithm looks at is how much did you satisfy B. Well, B placed 1 point on your answer to the messiness question and 10 on your answer to the second. Of those, 11, that's 1 plus 10, you earned 10, you guys satisfied each other on the second question. So your answers were 10 out of 11 equals 91% satisfactory to B. That's not bad. The final step is to take these two match percentages and get one number for the both of you. To do this, the algorithm multiplies your scores, then takes the nth root, where n is the number of questions. Because s, which is the number of questions, in this sample, is only 2, we have match percentage equals the square root of 98% times 91%. That equals 94%. That 94% is your match percentage with B. It's a mathematical expression of how happy you'd be with each other based on what we know. Now, why does the algorithm multiply as opposed to, say, average the two match scores together and do the square-root business? In general, this formula is called the geometric mean, which is a great way to combine values that have wide ranges and represent very different properties. In other words, it's perfect for romantic matching. You've got wide ranges and you've got tons of different data points, like I said, about movies, about politics, about religion, about everything. Intuitively, too, this makes sense. Two people satisfying each other 50% should be a better match than two others who satisfy 0 and 100, because affection needs to be mutual. After adding a little correction for margin of error, in the case when we have a very small number of questions, like we do in this example, we're good to go. Any time OK Cupid matches two people, it goes through the steps we just outlined. First it collects data about your answers, then it compares your choices and preferences to other people in simple, mathematical ways. This, the ability to take real world phenomena and make them something a microchip can understand, is, I think, the most important skill anyone can have these days. Like you use sentences to tell a story to a person, you use algorithms to tell a story to a computer. If you learn the language, you can go out and tell your stories. I hope this will help you do that.

# 【TED-Ed】線上約會的數學原理 (Inside OKCupid: The math of online dating - Christian Rudder)

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Why Why 發佈於 2019 年 1 月 11 日

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