 I'm going to open it up then for general discussion. We, through brutal chairing, we have left some time for discussion. Let's take a cluster of questions or inputs. Thank you. Nadia from the University of Pavia. I had a question for Sam. I find the method very interesting. I was wondering which methodological choices you included in the different iterations. Are you only looking at weights? Or are you looking at membership functions, too? Which type of different weight system are you considering? And to how many different methodologies actually do you get? Like, because you talk about 1,000 iterations, I mean, how many different options do you have? I'm asking because I've done similar work and we computed maybe 14 different indexes. So I was wondering to how many different choices do you actually get? Natalie Quinn from Oxford. My question is for Christoph. A very interesting method that you're proposing. I'm struggling a little bit, though, to kind of intuitively work out what it is that this measure will measure. And I'm not fully convinced that it's quite what I intuitively understand by poverty. I'm not sure that I can put this very clearly or concisely. So maybe if I give an example, that's the easiest way of explaining my question. So for example, in the seychelles, I can't remember the exact numbers, but you had quite a small percentage on food, like 8% or something, and then 35% priority on shelter. But what if food really is the most important of the basic needs? And the wonderful thing is that in seychelles, most people are not deprived in food. Hence, think about our angle kind of curves, and most people are not spending that marginal dollar on food. And yet, food could still very well be the most fundamental of the basic needs. And so for the people who are deprived in food, when we're aggregating and assessing their poverty, we want to actually have the highest weighting, the greatest intensity, coming on food. So I think it's interesting the measure. But I'm wondering about the connection between this way of developing the weights and then what is the measure actually measuring? Just a couple of questions. Thank you, Natalie. That was one of my questions. So very good. Also, you only deal with market goods. The whole idea of multidimensional, I thought, was to capture capabilities. Many capabilities cannot be purchased. Therefore, people won't mention them. Therefore, they will not be considered as part of your measure. How do you deal with heterogeneities? You're talking about differences in needs. How is that captured at all in your approach? I see differences in preferences, perhaps, and other types of heterogeneities, but not needs. Why do you keep two priority dimensions? Isn't this kind of like an arbitrary K cutoff? And therefore, aren't we returning back to arbitrariness throughout? What questions did you ask? And don't your questions frame the answer in terms of dimensions and so forth of interest? How do you know? Yeah, that's what I said before, needs or basic needs. Finally, in terms of the second one, in terms of robustness, the idea of the HDI, of course, I mean, you know already what the answer is if you want to know full robustness of weights, right? In terms of dominance, and that's that. My question to that is, don't you have degrees of robustness and wouldn't that be important, particularly aren't there particular weights, such as equal weights with the human development index that have higher a priori weight, if you will? And therefore, since you treat them all the same, you reject even if something that's highly irrelevant, extreme full weight on one of the three, you treat it as the same thing as if you found it something right next to one third, one third, one third. And I bring to mind, of course, my paper with Suman Seth that addresses exactly that question, so. Two more, and then we'll stop this round. Mario Negre from German Development Institute, following on this discussion on Christoph presentation. My impression is that instead of determining priorities, this methodology is determining the opportunity cost of this extra cash, which is not necessarily the same than priorities. Yeah, I believe my question is addressed to Christopher Simat-Muller. And that is that when ascertaining the priorities, did you make a gender separation? Or was it just asking the household, basically? So who in the household would determine what their priorities would be, the woman or the man? That's one aspect. And the other aspect probably was covered by a previous speaker, which is, shouldn't one compare those priorities as you determined empirically with what might be the best priorities in that social economic society or situation? Because sometimes a parent might not realize that their children are malnourished, and so they'll build shelter rather than concentrate on feeding the children. This sort of thing happens. The out of ignorance or out of social preference and things like that, social status and so on. So from our scientific knowledge, we might know what is the best priority for a family, but we measure and find that actually that's not what they think are the priorities. So that kind of comparison is rather important, I would assume. Thank you. Let's take some answers to that. Do you want to start? Yeah, do I do this? Great. So there was, I think two questions addressed to me. The first one was, which choices? So in the two applications that I showed, the, what I was varying in each draw, are simply essentially the weighting parameters and the cutoff threshold in the case of the Alkia fosta measure. But there's no, the kappa, the, yeah, yeah. So both the weights and the cutoff were simultaneously being varied. There's no a priori, there's no reason to stop that. One could extend to even the functional form. For example, in the case of the HDI, one could extend to the normalization methods they use. So there's no reason in any form of uncertainty analysis to stop, one could extend further. But for pragmatic reasons one always has to stop somewhere on what's analytically perhaps most interesting, at least with a multi-dimensional poverty, is the variation with the weights and the cutoff, I would say. But one could extend the method theoretically to other aspects as well. With respect to the, I mean, the question, which is in a sense on some weights more, a priori more important than others. I mean, certainly one might want to argue that. What I was using in the stochastic simulations is a flat priori. So every draw has equal weight. But there's no reason if we have x anti some prior view of the distribution. For example, we could say, well, I believe that the distribution of the weights should be normally distributed around an equal weight vector. That's fine. So one could introduce alternative parameterizations of the underlying parameter draws in a sense. Or we can use alternative distributions for the stochastic draws. Another alternative approach is to bound the draws. So one could say, well, I'm not interested in draws for which one dimension has 50 times the weight of any other dimension. So it's very easy using a simulation-based approach to make a priori bounding on what we believe is a reasonable parameter space. I didn't do that, but that's an easy extension to do. Alternatively, x post, one can look at those areas of the parameter space that are yielding interesting outcomes. One can then see, well, is this being driven by a certain weight or a particular vector? So x post, you can start looking at that. I don't know if that addresses completely your views, but that's some alternatives. Thanks for all these comments. Well, what is it this measure? Will measure, la, la, la? Well, it says multi-dimensional poverty. This is the name. What in measure is what you put in it? What are the properties that you put in it? But your question was worrying about food. First, some people are deprived of food. To be deprived of food at this level of development is not to be undernourished. It is to feel that they would like to spend more on food because the quality of their food, perhaps, or the quantity is not up to their standards. So there are actually a few percentages of people when you look at these data, which are actually deprived of food. But this is not your point. Your point is perhaps you would like to have a higher weight on food because it's really a serious issue. They may be undernourished people. And on the household, on the hold, the household you look at, even if you focus on some lower classes, they may not put food on the first place. So this is about, that's why I say there is a lot of work on axiomatic switches still needed. There are deep issues on how you aggregate data on priorities in this type of problem. And it is what you are great. You have data which is ordered, which is ranked, and you want to aggregate this data with the other household characteristics to produce weights. On the way you do it is not revealed. It's not exactly, it's not judgment aggregation. It's not preference aggregation. It's another kind of mathematical problem. On the way, but there are ways to propose some axiomatics which would account, for example, for the relative position of people. You may weight priority answer of the poor in a different way. You weight the priority answer of the rich. But I agree there is quite a lot of work. Interesting to work to do to account for these subtleties. The question on gender. Gender is not significant in the regression for the number of priorities that people state. But when you look at the kind of priorities, it has an effect that I don't remember it, but I've done some estimates of this quite short. It's a primary estimate to see. And there are things that we know well about the fact that women, they give more weight on health issues, for example, than men, et cetera. So that's true when you use some data and opinions. The kind of people you interview is influencing the answer. But not usually. Not usually. That would not change the outcome of this very simple exercise at the moment, which is that shelter on food are really dominating, but it has a smaller influence. Your question is more about are people really, should we trust what people answer? Are the household really aware of their priorities? If you don't want to use this priority data, you can use some other priority data. You can use priority designed by experts. You have some experts that choose some priority and there is in the development literature. There is a literature saying that in the development, you have a rank of priorities on democracy would come gradually in the ranks, for example. Now you can use also the implicit state priority. You look at the budget, this is something that I'm doing at the moment with this data, comparing what comes out from the household answer from what is in state budget, how much money is spent on education, health, et cetera. So the idea of using priority is not completely dependent on the kind of data you want to use. It's a more general issue, but I agree. This is data you have to be careful about. It's credibility. On James' turn of questions. So, yeah, capabilities, yeah, this is one of the, in this research project, there are a lot of effort in trying to go around some difficulties. We know that, we think, we don't know, but we think that there are dimensions of welfare which don't go through the market. But what is used here is not the amount spanned on a dimension of welfare, but it's the fact that for almost any dimension of welfare, it's possible for us to improve marginary their situation in this dimension. For example, in Seychelles, roughly, education is free. Education is free. If you look at education spending, you are going to say why people don't care about education. It's free, but if people think they are restricted in their education need, they are going to ask people to give them further courses, extra teaching and so on. And that's how you can try to detect and include the dimension of capabilities which don't go through market goods. But I agree, if there were no connection at all of the capability with the market, in that case, you cannot use that trick. And it remains to see if, in practice, this trick is going to be very efficient on what is the, a very cool performance of it. Atherogenity needs, yeah, atherogenity needs, it's always by using answer about deprivation. So people state their own deprivation. So in practice, you put together the welfare indicators on the needs indicators and you just concentrate on deprivation information which group on control for the needs. Again, if you believe that people know better the needs than analysis, preferences, I have to think about it, I don't know. And I'll say a few words in connection with the question on opportunity course about preferences. Two dimension, no, the cutoff, it's estimated. It's estimated, we look at the distribution, we have asked in fact what is your first, second, third priorities and we know how many priorities people have. So we can look at the distribution, do some econometrics and estimate some conditional central tendency and we find something close to two. So this is an objective return which can be discussed. You perhaps this criterion is not the right one to use, but it's not arbitrary, it comes from the data. Question framing, yes, of course, it's always conditional on the questioner you use. Last point, on the opportunity cost and also on the preferences. How do you consider priority data when you have in mind that these guys have preferences and you want to relate to the preferences? It's not completely clear that you want to relate to preferences, it's not utility consistent stuff, it's multi-dimensional poverty, that's something else. But think about the standard consumption model. If you adjust the measurement unit, there is no reason why people would have preferences. The marginal utilities, if you adjust for measurement unit would be all the same for all the goods. So the reason why people answer something and they all answer and they have no difficulty to answer about their priorities is an objective investigation in itself and it's likely that part of the reason why they have priorities is that the basic consumer model where there is only a budget constraint is not necessary for it. These people are partly constrained and they're constrained in their capabilities because the market is not going to provide there anything, you know. So that's right, it looks a little bit like opportunity cost, but if you want to call it opportunity cost, that's fine, you just use it in the same way. I'm going to allow, any questions for James? I'm going to... Yeah, yeah, I have one. Eric. The, any question? I, okay, my question. Just for you. And I'll be extremely brief. But on the issue of priorities and the choice of weights, essentially what was done was an attempt to endogenize it by essentially asking people what their priorities were. But after all, this session is on inclusive growth and it's quite conceivable that consumer sovereignty might be in conflict with some of the goals of inclusive growth. For instance, it is conceivable that from the standpoint of promoting inclusive growth, households should spend more on health or maybe education. So this brings up a very difficult problem. I mean, we as economists firmly believe in consumer sovereignty. And yet we would like in order to achieve inclusive growth to change their values in a way that is more consistent with inclusive growth. I'm going to take that as an excellent closing comment for the session. If you can ask Tee if I may. I need to close the session. So thank you all very much. I think we should give a round of applause to our presenters. Please note, notice from the organizers that after Tee, there's a poster session. The presentation's on the program. There's seven groups who will be presenting at the same time, okay? And each presentation will be seven minutes long. So it's quite a complicated story going on. After Tee, poster session. Thank you.