1 00:00:00,000 --> 00:00:03,751 All right, in the previous lecture we talked about multi-criterion decision 2 00:00:03,751 --> 00:00:07,702 making, right? We had lots of different dimensions and you weighted alternatives 3 00:00:07,702 --> 00:00:11,704 according to those dimensions. In this lecture we're going to move in a slightly 4 00:00:11,704 --> 00:00:15,755 different direction. We're still going to consider multi-criteria, what we want to 5 00:00:15,755 --> 00:00:19,756 do, is we want to have a spatial model. So the difference here is that instead of 6 00:00:19,756 --> 00:00:23,808 just wanting sort of more square footage or a larger lot, you're going to have an 7 00:00:23,808 --> 00:00:27,809 ideal point. So there's going to be sort of perfect amount that lies between too 8 00:00:27,809 --> 00:00:32,123 much and too little. So these are known as sort of spatial choice models. Now spatial 9 00:00:32,123 --> 00:00:36,109 choice models originally started by thinking about geographic choice. There's 10 00:00:36,109 --> 00:00:39,888 a guy named Harold Hoteling who's an economist who thought about, imagine 11 00:00:39,888 --> 00:00:44,236 you're on a beach and there's an ice cream vendor, you know, 50 feet to your left and 12 00:00:44,236 --> 00:00:48,378 there's another ice cream vendor 40 feet to your right. You made decide well, you 13 00:00:48,378 --> 00:00:52,623 know, since the one to my right is closer what I'll do is I'll go and, you know, buy 14 00:00:52,623 --> 00:00:56,816 my ice cream from the one that's closer and I don't have to walk as far. Well you 15 00:00:56,816 --> 00:01:01,009 can take that idea and you can apply it to attributes of a good. So for example, I 16 00:01:01,009 --> 00:01:04,909 love Indian food. Right? And I like my Indian food to be reasonably hot. We can 17 00:01:04,909 --> 00:01:08,684 imagine one of the dimensions, then, in Indian food, is whether it's, you know, 18 00:01:08,684 --> 00:01:12,508 cold, right? In terms of, you know, cold in terms of how spicy it is. Or you can 19 00:01:12,508 --> 00:01:16,283 imagine [inaudible] means it's really, really hot. So I could all the Indian 20 00:01:16,283 --> 00:01:20,208 restaurants. I could put, you know, one Indian restaurant here, Indian restaurant 21 00:01:20,208 --> 00:01:26,324 one. Indian restaurant two. Ending in restaurant three and this is how hot their 22 00:01:26,324 --> 00:01:30,386 food is. And so, there's me as a consumer and I'm trying to decide. Okay. Where do I 23 00:01:30,386 --> 00:01:34,111 go buy. Do I go buy from Indian restaurant one, Indian restaurant two, Indian 24 00:01:34,111 --> 00:01:38,035 restaurant three. What could be that if since I like my food really hot. This is 25 00:01:38,035 --> 00:01:41,562 my ideal point right here. I'm go to Indian restaurant one because it's 26 00:01:41,562 --> 00:01:45,287 closest. So, this is the idea that there's, what each person has is sort of a 27 00:01:45,287 --> 00:01:49,062 preference, an ideal point and then buy right the thing, they purchase a firm 28 00:01:49,062 --> 00:01:53,534 right, that offers the product that is closest to their ideal point. So this is 29 00:01:53,534 --> 00:01:58,738 hi, Hoteling's idea. It was Anthony Downs, who was also an economist that, so, sort 30 00:01:58,738 --> 00:02:02,935 of moved into political science. And what Anthony Downs did, he said, now we can 31 00:02:02,935 --> 00:02:06,916 apply this to how people vote what we can do, we can put politicians, right, 32 00:02:06,916 --> 00:02:10,629 somewhere between left and right. So, maybe, you know, this might be the 33 00:02:10,629 --> 00:02:14,987 Democratic candidate for president, let's say, and this might be the Republican, so, 34 00:02:14,987 --> 00:02:19,237 both are, you know, Democratic sorted to the left, Republican sorted to the right, 35 00:02:19,237 --> 00:02:23,228 but their not really completely extreme. And then you've got a voter who perhaps 36 00:02:23,228 --> 00:02:26,950 sits right here and the voter's got to decide okay to I vote for the democrat or 37 00:02:26,950 --> 00:02:30,672 vote for the republican. And what they do is they look at this distance. How far am 38 00:02:30,672 --> 00:02:34,027 I from the democrat? This would be distance one. And how far am I from the 39 00:02:34,027 --> 00:02:37,749 republican. This is distance two. Remember I talked about this sort of in an earlier 40 00:02:37,749 --> 00:02:41,517 lecture about why we construct models and using this model the voter can say well 41 00:02:41,517 --> 00:02:45,193 you know what since I'm closer to the democrat, I'm gonna vote for the democrat. 42 00:02:45,193 --> 00:02:48,702 So this is a, a fairly simple spatial model. You know what we want to do is we 43 00:02:48,702 --> 00:02:52,553 want to ramp this up a little bit, so. Let me ramp this up just in two ways. One is 44 00:02:52,553 --> 00:02:56,275 you can take this model to data, so this is work by Andrew Gellman, Columbia 45 00:02:56,275 --> 00:03:00,245 University. Anyway what Andrew does is he looks at Supreme Court Justices and so 46 00:03:00,245 --> 00:03:03,868 here's a whole list of Supreme Court Justices, I realize this is a little 47 00:03:03,868 --> 00:03:07,689 blurry but here's people like Justice Blackman, right? And here's Judge Scalia 48 00:03:07,689 --> 00:03:11,362 and here's Judge Ginsberg, Justice Ginsberg. And what you can do is you can 49 00:03:11,362 --> 00:03:15,382 chart. Ideologically, where they are in t-, over time. Where this, here, is to the 50 00:03:15,382 --> 00:03:19,471 left, and this here is to the right. So you notice that Scalia's up here on the 51 00:03:19,471 --> 00:03:23,560 right, and Blackman's down here to the left. So what you can do is you can sort 52 00:03:23,560 --> 00:03:27,860 of use this model to keep track of where the different Supreme Court Justices are. 53 00:03:27,860 --> 00:03:31,505 What's interesting about this, is, then when you think about, where does a 54 00:03:31,505 --> 00:03:35,506 president, who does the president appoint? Well, the president may also have some 55 00:03:35,506 --> 00:03:39,253 ideal points. If they're a liberal president, their ideal point may be down 56 00:03:39,253 --> 00:03:42,798 here. If you have a conservative president, their ideal point may be up 57 00:03:42,798 --> 00:03:47,051 here. And they're gonna want to appoint a judge that has the same sort of ideologies 58 00:03:47,051 --> 00:03:51,153 that they have. So, it's really nice, very simple model. But you can take it to data, 59 00:03:51,153 --> 00:03:54,748 and then you can use that data to understand how people, how presidents 60 00:03:54,748 --> 00:03:58,495 appoint judges. And also, how the [inaudible], how the ideology of the court 61 00:03:58,495 --> 00:04:02,698 has changed over time. Okay, we want to do this, we want to sort of take this model 62 00:04:02,698 --> 00:04:06,728 and show how we can expand it to more dimensions. So before, that was just one 63 00:04:06,728 --> 00:04:10,810 dimension, hot, cold, left, right but we can do the same thing in more dimensions. 64 00:04:10,810 --> 00:04:14,474 So let's go back, right, to the car example, remember? I'm just trying to 65 00:04:14,474 --> 00:04:18,713 decide between the Ford and the Chevy and I said there might be two things. There 66 00:04:18,713 --> 00:04:22,794 might be sort of the speed of the car, right, and there might be comfort. Right, 67 00:04:22,794 --> 00:04:27,831 once again [inaudible] and what I do is I decide which of these two cars is closer? 68 00:04:27,831 --> 00:04:32,625 Okay, so lets do this in a, a sort of a fun example, in terms of getting a burger. 69 00:04:32,625 --> 00:04:37,237 So, you know I like burgers, a lot of people like burgers and we can think of 70 00:04:37,237 --> 00:04:42,092 what's my ideal burger? Well, my ideal burger might have two pieces of cheese and 71 00:04:42,092 --> 00:04:46,149 it might have two patties. And two tomatoes. And also some ketchup, let's 72 00:04:46,149 --> 00:04:50,447 say, four tablespoons of ketchup, four tablespoons of mayo. And I'm a pickle guy, 73 00:04:50,447 --> 00:04:54,855 four pickles. So, this is my ideal burger, right? And so we can write that down. And 74 00:04:54,855 --> 00:04:59,043 so, more carefully, [inaudible] is a better font. [inaudible], this is my ideal 75 00:04:59,043 --> 00:05:03,176 point. And this would be, if I do this out, it's not in two dimensional space, 76 00:05:03,176 --> 00:05:07,143 like it's in multidimensional space. I can't draw it, because this is six 77 00:05:07,143 --> 00:05:10,781 dimensions. Right? But this is where computers are nice because I can code this 78 00:05:10,781 --> 00:05:14,594 into a computer and it's just a vector of length six. We're not gonna decide, where 79 00:05:14,594 --> 00:05:18,057 do I go for lunch? Should I go to McDonald's and get a big Mac, or go to 80 00:05:18,057 --> 00:05:22,057 Burger King and get a Whopper? What we can do is we could say, okay, let's look at my 81 00:05:22,057 --> 00:05:25,861 ideal point, which is right here, and let's look at the Big Mac. The Big Mac has 82 00:05:25,861 --> 00:05:29,715 two pieces of cheese, which is great, two patties, which is great. No tomatoes, not 83 00:05:29,715 --> 00:05:33,470 so good. Not enough ketchup, not enough mayo for me. And a few too many pickles. 84 00:05:33,470 --> 00:05:37,324 You know, like, pickles seems to have, you know, a few too many pickles. So I could 85 00:05:37,324 --> 00:05:41,841 ask, how much do I like that Big Mac? What we can do is we can take my ideal point 86 00:05:41,841 --> 00:05:46,750 and the Big Mac and take the difference. So here the difference is zero. Here the 87 00:05:46,750 --> 00:05:51,690 difference is zero. Here the difference is two. Here the difference is one. Here the 88 00:05:51,690 --> 00:05:55,935 difference is zero and here the difference is two. Now notice I've got these little 89 00:05:55,935 --> 00:05:59,669 lines on the, on the, on this side of difference. That means I'm taking the 90 00:05:59,669 --> 00:06:03,403 absolute value of the difference. Otherwise, because there's, you know, it's 91 00:06:03,403 --> 00:06:07,495 got two to few tomatoes. If you put a minus two here and a plus two here the two 92 00:06:07,495 --> 00:06:11,689 few tomatoes and the to many peoples would cancel out, right? So what I can do is I 93 00:06:11,689 --> 00:06:15,730 can add all these things up and say my total distance from the Big Mac is five. 94 00:06:15,730 --> 00:06:20,616 Let's suppose I walk across the street and now I decide, let's see how the, the 95 00:06:20,616 --> 00:06:25,680 whopper stacks up. Well, the whopper has. Two pieces of cheese, that's great. It's 96 00:06:25,680 --> 00:06:30,359 got one patty, so it's off by one. Two tomatoes, that's great. Little long, not 97 00:06:30,359 --> 00:06:35,474 quite enough ketchup but perfect amount of mayo, perfect amount of pickles. So it's 98 00:06:35,474 --> 00:06:40,705 only off by two. So my distance from the. Big Mac, right? That, if we go back, was 99 00:06:40,705 --> 00:06:46,028 five. And my distance from the Whopper was only two. So, we could, you know, 100 00:06:46,028 --> 00:06:51,572 represent that by, here's the Whopper and here's the Big Mac. This is only a 101 00:06:51,572 --> 00:06:57,348 distance of two for me, and the Big Mac is a distance of five for me. So what I could 102 00:06:57,348 --> 00:07:01,091 do is, I could, if they're writing down my ideal burger, I can look at the Big Mac, 103 00:07:01,091 --> 00:07:04,694 look at the Whopper, and say, you know what? I'd rather buy the Whopper, because 104 00:07:04,694 --> 00:07:08,303 it's closer to me, it's closer to my ideal point. Now this is really good, 'cause 105 00:07:08,303 --> 00:07:11,803 this is a way, this is a thing I can use to figure out, you know, what should I 106 00:07:11,803 --> 00:07:15,166 choose? What burger should I buy? And also, I can use this to figure out, who 107 00:07:15,166 --> 00:07:18,393 should I vote for? Because instead of thinking of these as Big Macs and 108 00:07:18,393 --> 00:07:21,893 Whoppers, I could think of their, maybe there's two dimensions to policy, right? 109 00:07:21,893 --> 00:07:25,241 So one dimension could be some sort of social policy between liberal. And 110 00:07:25,241 --> 00:07:29,517 conservative and there could be some sort of fiscal policy, right, between liberal 111 00:07:29,517 --> 00:07:33,582 and conservative. So this would say I'm sort of socially liberal but on fiscal 112 00:07:33,582 --> 00:07:37,382 dimensions I sort of lie in-between liberal and conservative. And so this 113 00:07:37,382 --> 00:07:41,500 would be my ideal point, not in sort of big mac whopper space, but in political 114 00:07:41,500 --> 00:07:45,882 space. And then what I could do is I could vote for the party or the candidate that 115 00:07:45,882 --> 00:07:50,105 is close to me. Another thing we can do with this model, and this is sort of cool, 116 00:07:50,105 --> 00:07:54,292 is, remember we talked about how we can use this positively. So suppose I watch 117 00:07:54,292 --> 00:07:58,582 one of my friends, right, what do I mean by positively, right is to figure out 118 00:07:58,582 --> 00:08:03,268 explain why we see what we see. So suppose I watch one of my friends and I, and I go 119 00:08:03,268 --> 00:08:07,897 in and I see that my friend doesn't go to Burger King. My friend goes to McDonalds 120 00:08:07,897 --> 00:08:12,300 and gets the big mac, but I don't know anything about my friend's ideal points, 121 00:08:12,300 --> 00:08:16,919 but I do know about the big mac and the whopper. Well notice the big mac and the 122 00:08:16,919 --> 00:08:21,335 whopper are the same on this dimension, this dimension, this dimension. Same 123 00:08:21,335 --> 00:08:26,228 amount of cheese, same amount of ketchup, same amount of mayo. So what I could do is 124 00:08:26,228 --> 00:08:30,942 I could just wipe out those categories, right because they're the same, and then 125 00:08:30,942 --> 00:08:35,418 it comes down to number of patties, tomatoes, and pickles. So now if I see my 126 00:08:35,418 --> 00:08:40,367 friend buying the big mac. What can I infer? I can infer either that they like, 127 00:08:40,367 --> 00:08:45,563 sort of, two patties, or that they don't like tomatoes. Or that they really like 128 00:08:45,563 --> 00:08:50,626 pickles, or some combination of those things. And so what I can do, by looking 129 00:08:50,626 --> 00:08:55,334 at choices, I can understand what someone's ideal point is. And again, once 130 00:08:55,334 --> 00:08:59,892 we've got this idea in our head, we can go to data, and we can figure stuff out. So 131 00:08:59,892 --> 00:09:04,225 for example, let's look at political parties. So what you can do, and this is a 132 00:09:04,225 --> 00:09:08,896 map by Michael [inaudible], using some data from Poole and Rosenthal, to nominate 133 00:09:08,896 --> 00:09:12,583 scores. And what this does is it takes every single member of congress, and it 134 00:09:12,583 --> 00:09:16,301 looks at all their different votes. Now, based on their votes, you can figure out, 135 00:09:16,301 --> 00:09:20,159 how conservative are they and how liberal are they? Now, nominate breaks thing down 136 00:09:20,159 --> 00:09:23,924 into two dimensions. You think of this being one dimension and another dimension. 137 00:09:23,924 --> 00:09:27,535 So, just for our purposes, let's suppose this is a social dimension. Right. And 138 00:09:27,535 --> 00:09:31,682 this is a fiscal dimension, right. So this is money up and down here, right, and this 139 00:09:31,682 --> 00:09:35,474 is more policies on this dimension. So what you see is you see, look, all the 140 00:09:35,474 --> 00:09:39,823 Republicans lie to the right on the social dimension and the Democrats all lie to the 141 00:09:39,823 --> 00:09:43,413 left. And if you look, this is a particular map looking at the Tea Party 142 00:09:43,413 --> 00:09:47,509 which is a movement within the Republican Party, and if you look at the Tea Party, 143 00:09:47,509 --> 00:09:51,636 people are pretty well evenly mixed. So, what you can do is by taking this modeled 144 00:09:51,636 --> 00:09:55,481 data, what you can figure out by looking at the choices people made, this is 145 00:09:55,481 --> 00:09:59,632 sometimes called revealed preference, you look at the choices people make, in this 146 00:09:59,632 --> 00:10:03,836 case, you know, politicians voting and you can map out where they are ideologically. 147 00:10:03,836 --> 00:10:07,834 And see you notice the Democrats are all to the left of Republicans on social 148 00:10:07,834 --> 00:10:11,730 issues, but on the fiscal dimension, it's a little bit more complicated, right? 149 00:10:11,730 --> 00:10:17,583 Okay, so, that spatial model is really cool. We can use spatial models to figure 150 00:10:17,583 --> 00:10:22,253 out sort of, what we should, where we should. Buy Indian food. Who we should 151 00:10:22,253 --> 00:10:25,959 vote for. Which car to buy. Whether to go to Burger King or McDonalds, right, by 152 00:10:25,959 --> 00:10:30,002 looking at these dimensions and seeing how close something is to ideal point. Now we 153 00:10:30,002 --> 00:10:34,045 can also take these models to data and do more serious things. We can figure out you 154 00:10:34,045 --> 00:10:37,510 know, where Supreme Court justices are and where members of Congress are 155 00:10:37,510 --> 00:10:41,361 ideologically, and whether it's on one dimension or two dimensions. We can do the 156 00:10:41,361 --> 00:10:45,355 same thing for products, right so we could do that same sort of matching, and look at 157 00:10:45,355 --> 00:10:48,917 different products, in space, whether it types, whether it's types of coffee, 158 00:10:48,917 --> 00:10:52,714 right, whether it types of automobiles, and we could look at people's. Decisions 159 00:10:52,714 --> 00:10:56,592 on which to buy and we could figure out sort of are people, where people's 160 00:10:56,592 --> 00:11:00,890 preferences really lie based on the cars they buy or based on the coffee they buy. 161 00:11:00,890 --> 00:11:06,073 So spatial model is really powerful, helps explain what people do and helps us make 162 00:11:06,073 --> 00:11:08,260 better choices ourselves. Thank you.