1 00:00:02,360 --> 00:00:07,754 In the previous lecture, we saw that if you're going to bet, then you ought to 2 00:00:07,754 --> 00:00:13,659 pick a favorable bet over an unfavorable bet, and even over a neutral or fair bet. 3 00:00:13,659 --> 00:00:17,377 But the next question is, do you want to bet at all? 4 00:00:17,377 --> 00:00:21,460 And there we have to look at other values besides money. 5 00:00:21,460 --> 00:00:27,470 Let's consider this case. Suppose that you can't just bet a dollar. 6 00:00:27,470 --> 00:00:32,494 This game's not for fun. These are serious gamblers. 7 00:00:32,494 --> 00:00:38,800 Your minimum bet is $100,000. And now, if you draw a spade, you win 8 00:00:38,800 --> 00:00:40,972 $1,000,000 net. Cool. 9 00:00:40,972 --> 00:00:47,803 Well what's the expected financial value? One chance in four of picking a spade, 10 00:00:47,803 --> 00:00:54,549 the amount you win net is a $1,000,000. You have to subtract the probability of 11 00:00:54,549 --> 00:01:01,980 losing three out of four because you lose if you pick a heart a diamond or a club 12 00:01:01,980 --> 00:01:06,860 times the amount you bet which is 100,000. 13 00:01:06,860 --> 00:01:14,474 Pretty neat, this bet's got an expected financial value of a $175,000. 14 00:01:14,474 --> 00:01:22,080 Now that sounds like a great bet, but is it really a great bet? 15 00:01:22,080 --> 00:01:27,080 It is favorable and it's only favorable financially. 16 00:01:28,100 --> 00:01:34,740 Imagine that a $100,000 is all the money you've got in the world. 17 00:01:34,740 --> 00:01:41,344 It's what you use to pay your rent with it's all your retirement money and if you 18 00:01:41,344 --> 00:01:45,773 lose it you're going to be out on the street with nothing. 19 00:01:45,773 --> 00:01:49,720 Then should you bet this money? No, absolutely not. 20 00:01:49,720 --> 00:01:54,593 It just doesn't make sense to take that kind of risk with this money if you're 21 00:01:54,593 --> 00:01:59,528 going to be out on the street if you lose because you've got three chances in four 22 00:01:59,528 --> 00:02:02,550 of losing. Sure you might win you might be better 23 00:02:02,550 --> 00:02:07,423 off but you've got an awful lot to lose and that's why you shouldn't make this 24 00:02:07,423 --> 00:02:10,014 bet because there's just too much to lose. 25 00:02:10,014 --> 00:02:13,900 And what does that mean? Think about what it means that there's 26 00:02:13,900 --> 00:02:17,417 too much to lose. It's not that there's too much money to 27 00:02:17,417 --> 00:02:21,550 lose, because you've just calculated the financial value of the bet. 28 00:02:21,550 --> 00:02:26,717 What really is the loss, is security. You're not going to have a place to live. 29 00:02:26,717 --> 00:02:30,976 You're not going to know. How to make ends meet, or buy your next 30 00:02:30,976 --> 00:02:34,049 meal. That's the problem, is there're lots of 31 00:02:34,049 --> 00:02:38,517 other values besides money. And, in these situations where we say 32 00:02:38,517 --> 00:02:42,917 you've got too much to lose. It's those other considerations in 33 00:02:42,917 --> 00:02:46,160 addition to money. That make it, a bad bet. 34 00:02:46,160 --> 00:02:51,977 Now let's look at the other side. In some cases, you don't have too much to 35 00:02:51,977 --> 00:02:57,166 lose, you got too much to win. That is, the amount that you win just 36 00:02:57,166 --> 00:03:01,411 might not add up in the way that you thought it would. 37 00:03:01,411 --> 00:03:07,857 This is the phenomenon called diminishing marginal utility and what that means is 38 00:03:07,857 --> 00:03:13,596 that each increment decreases as you get more and more and more of those 39 00:03:13,596 --> 00:03:17,360 increments. You just don't need that much. 40 00:03:17,360 --> 00:03:21,417 One example is hamburgers. If you're really hungry and you don't 41 00:03:21,417 --> 00:03:24,460 have anything to eat you might want a hamburger. 42 00:03:25,480 --> 00:03:29,583 But what about two hamburgers? Is two hamburgers twice as good as one 43 00:03:29,583 --> 00:03:32,378 hamburger? Not really, I mean, maybe you want two 44 00:03:32,378 --> 00:03:35,768 hamburgers, that would be nice but it's not twice as good. 45 00:03:35,768 --> 00:03:39,515 What about three hamburgers? Is that three times as good as one 46 00:03:39,515 --> 00:03:42,369 hamburger? And what about four or five or six or 47 00:03:42,369 --> 00:03:45,700 seven or eight or nine or ten? What about ten hamburgers? 48 00:03:45,700 --> 00:03:50,371 Are ten hamburgers ten times as valuable to a hungry person as one hamburger? 49 00:03:50,371 --> 00:03:52,569 No. because you're going to get full, before 50 00:03:52,569 --> 00:03:57,025 you ever eat that tenth hamburger. So the marginal utility of a hamburger 51 00:03:57,025 --> 00:04:00,200 goes down. The first one might be very valuable to a 52 00:04:00,200 --> 00:04:04,047 hungry person with nothing to eat. The second 1's a little less. 53 00:04:04,047 --> 00:04:07,527 The third 1's a little less. The fourth one's a little less, 54 00:04:07,527 --> 00:04:11,923 and the difference between nine and ten might be totally negligible, because 55 00:04:11,923 --> 00:04:15,342 they're all going to go bad before you eat all ten of them. 56 00:04:15,342 --> 00:04:20,628 The same thing happens in lotteries. Let's compare two lotteries. 57 00:04:20,628 --> 00:04:29,009 In the first lottery, if you buy one ticket for $100, then you have one chance 58 00:04:29,009 --> 00:04:36,353 in a million of winning $300,000,000. That sounds like a pretty good bet. 59 00:04:36,353 --> 00:04:41,330 I'll let you calculate the actual expected financial value of that bet in 60 00:04:41,330 --> 00:04:46,577 one of the exercises after this lecture. But I bet you can do it in your head 61 00:04:46,577 --> 00:04:49,680 pretty quickly and compare it to this lottery. 62 00:04:49,680 --> 00:04:56,532 If you buy one ticket for $200, then you have a one in 2,000,000 chance of winning 63 00:04:56,532 --> 00:05:01,100 billion dollars. Which of these lotteries has a higher 64 00:05:01,100 --> 00:05:06,683 expected financial value? Well, we'll leave the actual calculations 65 00:05:06,683 --> 00:05:13,112 of the expected financial values to the exercises, but you can probably tell, 66 00:05:13,112 --> 00:05:19,380 that the one with the larger expected financial value is lottery B. 67 00:05:19,380 --> 00:05:24,378 Does that mean that you ought to spend the extra money to play in lottery b 68 00:05:24,378 --> 00:05:28,748 instead of lottery A? Well, that depends, I suppose. 69 00:05:28,748 --> 00:05:33,383 How much more valuable is a billion dollars to you than 300 million? 70 00:05:33,383 --> 00:05:38,154 300 million is a lot of money. I could buy pretty much anything I ever 71 00:05:38,154 --> 00:05:43,266 wanted if I had 300 million dollars. I'm not sure why I would want all that 72 00:05:43,266 --> 00:05:46,333 extra money. It's like that tenth hamburger, I 73 00:05:46,333 --> 00:05:50,627 wouldn't really need it. So, which of these lotteries should you 74 00:05:50,627 --> 00:05:55,330 pick if that's the way you see the relationship between the winnings. 75 00:05:55,330 --> 00:06:01,793 Well even though the expected financial value is greater in lottery b you might 76 00:06:01,793 --> 00:06:07,610 reasonably pick lottery a cause you have a bigger chance of getting the 77 00:06:07,610 --> 00:06:11,282 $300,000,000. And the difference between 300 million 78 00:06:11,282 --> 00:06:15,080 and a billion doesn't matter that much to you. 79 00:06:15,080 --> 00:06:18,199 Not everybody's going to share that value judgement. 80 00:06:18,199 --> 00:06:23,164 But if it doesn't really matter much to you whether you have 300 million or a 81 00:06:23,164 --> 00:06:26,220 billion, then it makes sense to go for lottery A. 82 00:06:26,220 --> 00:06:31,887 And this shows, yet again, that there's more to life than expected financial 83 00:06:31,887 --> 00:06:35,438 value. The other values in life are captured in 84 00:06:35,438 --> 00:06:40,425 the notion of overall value. The actual overall value or sometimes 85 00:06:40,425 --> 00:06:46,470 called utility of an act is simply all of the good and bad effects that the act 86 00:06:46,470 --> 00:06:51,759 actually has, the values of those effects, positive values and negative 87 00:06:51,759 --> 00:06:57,065 values calculated together. And the, expected overall value. 88 00:06:57,065 --> 00:07:02,540 Of the bet, or of an action. Sometimes called the expected utility of 89 00:07:02,540 --> 00:07:07,736 the act is all the good and bad effects of the act multiplied by the probability 90 00:07:07,736 --> 00:07:12,977 of each of those effects. So you bring not just the values into 91 00:07:12,977 --> 00:07:16,540 play, but also. The probabilities. 92 00:07:16,540 --> 00:07:21,138 And if you're really going to decide what you ought to do, you shouldn't be looking 93 00:07:21,138 --> 00:07:23,839 just at money. You should be looking at all the 94 00:07:23,839 --> 00:07:26,828 different values, including security as we mentioned. 95 00:07:26,828 --> 00:07:30,851 Or how much good the money's really going to do you if you've going to have 96 00:07:30,851 --> 00:07:34,300 $300,000,000 anyway. There's lots of other things to consider. 97 00:07:34,300 --> 00:07:37,908 The problem is, how do you calculate that? 98 00:07:37,908 --> 00:07:44,765 How are you going to actually calculate overall value or expected overall value? 99 00:07:44,765 --> 00:07:52,072 Here's an example to show how hard it is, imagine that you have a friend that you 100 00:07:52,072 --> 00:07:57,515 love playin with after school and. You then get an offer, of a job. 101 00:07:57,515 --> 00:08:01,757 And you can make a bunch of money. By doing the job after school. 102 00:08:01,757 --> 00:08:05,220 But then you won't get to play with your friend. 103 00:08:05,220 --> 00:08:08,330 Well, how are we going to figure this out? 104 00:08:08,330 --> 00:08:11,850 Let's calculate the expected overall value. 105 00:08:11,850 --> 00:08:16,223 What's the probability that if you take the job you won't be such good friends 106 00:08:16,223 --> 00:08:20,652 with him anymore, because you won't be playing as much and then you'll lose your 107 00:08:20,652 --> 00:08:23,033 friend? And what's the value of that friend? 108 00:08:23,033 --> 00:08:27,573 You've got to multiply the probability of losing your friend by the value of that 109 00:08:27,573 --> 00:08:29,843 friend. Well, how are you going to do that? 110 00:08:29,843 --> 00:08:32,556 How do you put a dollar value on that friendship? 111 00:08:32,556 --> 00:08:36,985 How do you figure out the probability that your friend's going to leave you and 112 00:08:36,985 --> 00:08:40,979 not be as close anyway as he was before? Well, you just can't do that. 113 00:08:40,979 --> 00:08:43,965 You can't really put it into numbers like that. 114 00:08:43,965 --> 00:08:48,541 There are some economists have very sophisticated techniques for taking 115 00:08:48,541 --> 00:08:53,306 preferences and attaching values to those preferences and then multiplying 116 00:08:53,306 --> 00:08:58,390 probabilities and so I don't want to say it can not be done, but the point here is 117 00:08:58,390 --> 00:09:03,283 just it's a lot more difficult than figuring out whether you ought to make a 118 00:09:03,283 --> 00:09:08,557 bet in a simple little poker game or even whether you ought to put your money into 119 00:09:08,557 --> 00:09:11,974 the lottery. When we start talking about real 120 00:09:11,974 --> 00:09:17,398 decisions about friends and about other values in life, some of them cannot be 121 00:09:17,398 --> 00:09:21,222 reduced to money. And then it's hard to put a number on 122 00:09:21,222 --> 00:09:24,630 them, and it's hard to do the actual calculations. 123 00:09:24,630 --> 00:09:30,123 So I don't want to suggest that any of this decision theory regarding expected 124 00:09:30,123 --> 00:09:34,080 utility is going to actually be applied in real life. 125 00:09:34,080 --> 00:09:38,674 Another reason that's worth mentioning is that third kind of decision that I 126 00:09:38,674 --> 00:09:43,090 mentioned at the beginning of the lecture, namely decisions with ignorance. 127 00:09:43,090 --> 00:09:47,505 Sometimes you don't even know the probabilities and if you don't know the 128 00:09:47,505 --> 00:09:52,040 probabilities, you can't enter the probabilities in the formula for expected 129 00:09:52,040 --> 00:09:55,740 utility or expected financial value or expected overall value. 130 00:09:55,740 --> 00:10:00,236 If you don't know the probabilities, how you going to calculate? 131 00:10:00,236 --> 00:10:03,682 You can't. Now there lots of tricky rules that 132 00:10:03,682 --> 00:10:09,752 people have proposed, for decisions under uncertainty, or decisions with ignorance, 133 00:10:09,752 --> 00:10:13,873 as I call them, but none of those are really conclusive, 134 00:10:13,873 --> 00:10:18,220 and there's big dispute about which one is the right rule. 135 00:10:18,220 --> 00:10:21,615 So a lot of this discussion is going to be inconclusive. 136 00:10:21,615 --> 00:10:26,844 You might have wished that I would come in here and tell you, here's how you 137 00:10:26,844 --> 00:10:30,715 figure out exactly what to do in every area of your life. 138 00:10:30,715 --> 00:10:35,130 Well, I'm sorry, but I just can't do it, and nobody else can either. 139 00:10:35,130 --> 00:10:40,039 Nonetheless, if you think in terms of the various factors that we've been 140 00:10:40,039 --> 00:10:45,418 discussing, Financial value, other kinds of values, probabilities of the different 141 00:10:45,418 --> 00:10:48,646 outcomes. Maybe at least you'll be able to avoid 142 00:10:48,646 --> 00:10:52,480 some of the worst mistakes that people make in decisions.