Eric Weinstein’s Challenge to Mainstream Mathematical Economics
Summary
Methodology Focus: Discussion centers on Eric Weinstein and Pia Malani’s application of gauge theory to economics, particularly around derivatives and measuring cost-of-living adjustments.
Price Indices: Deep dive into Laspeyres, Paasche, and Divisia indices, highlighting why path dependence in the Divisia index is a feature, not a bug, and how higher-frequency chaining converges to Divisia.
Inflation Measurement: Emphasis on how changing preferences and available goods over time complicate real-wage and purchasing-power comparisons, with a proposed framework to handle these coherently.
Economic Theory Debate: Engages Arrow’s impossibility theorem and distinguishes intertemporal market choice from social choice aggregation, arguing markets enable a non-arbitrary path via prices.
Investment Relevance: No specific tickers, GICS sectors, or subsectors are pitched; insights are conceptual and pertain to interpreting inflation and cost-of-living statistics.
Overall Perspective: A methodological critique of mainstream mathematical economics with potential implications for how investors interpret CPI-like measures, but no direct investment recommendations.
Transcript
[music] This is the Human Action podcast where we debunk the economic, political, and even cultural myths of the days. Here's [music] your host, Dr. Bob Murphy. Hey everybody, welcome back to Human Action Podcast. In this episode, I'm going [music] to play some clips from and then elaborate upon uh a recent interview that I conducted with Eric Weinstein. Now, the podcast where this interview occurred wasn't the human action one. It was a different one. It was called the Infi podcast, which is the podcast uh that I host for my uh fintech day job at the company Infinio. All right. Um let me just explain a little bit on the front end of why I think it's important for fans of Austrian economics to be exposed to some of Eric's ideas. Um so for a long time, Eric has been claiming that if you take what's called gauge theory from mathematics which has had much success for example in physics and that's where where Eric's background is. Eric has a PhD in math from Harvard and he is very well um studied in applying these certain uh the area of math to physics and then he's saying this has great application also to economics and Pia Melany got her PhD from Harvard in economics proper in I think 96 and that's what um you know her her dissertation covers is how would you use gauge theory in economics and Eric claims that it does a lot right that among other things it has implications for how you would do cost of living adjustments and that's what we're going to get to in a minute here on the human action podcast but it's much broader than that so the the big picture the most audacious claim is Eric is saying you back in the 1870s you had the marginal revolution in economics where at least in the the strain of mathematical economic modeling that came out of that, you know, through Bob Ross and then, you know, in the 20th century in the hands of people like Paul Samuelson and so on that at least in that strand of the economics literature, Eric is claiming you economists are stuck with the simplest type of derivative that math has for you and that you need to realize there are other more sophisticated types of derivatives. And so you kind of need the marginal revolution 2.0 and that just like the original marginal revolution was not merely a quibble about calculating some formula but was actually you know broadening the scope of and redefining in a sense how economics operated. Likewise Eric is saying that's what is on the table here if if he's right. And so it can handle things such as um changing ordinal preferences over time. Okay, which in standard mathematical economics you can't deal with. And and then Eric claims because of that vulnerability, the fact that the entire edifice of modern mathematical economics only works if you assume that preferences are static over time. You can build in uncertainty in things but the idea is the basic underlying utility function or even the you know even if you're doing it ordinally the ranking of things that that there is some uh static nature to that over time otherwise nothing works. It's just too open-ended. You can't say anything with the standard tools. And so Eric is saying among other benefits of switching to his framework that he's recommending you can handle stuff like that. Okay. So, um, partly why I wanted to give Eric a platform, I mean, he does Joe Rogan things. It's not that I'm letting the public hear about his name. What I mean is aimed at academic economists specifically, is that I had interacted enough with him to know he wasn't bluffing. Okay. Um, but I could understand why a lot of economists just literally didn't even understand what he was saying. And the more I read his stuff and interacted with him, the more convinced I became that, say what you will about Eric Weinstein, he's not bluffing. All right? He's not just making stuff up. There is substance behind what he's saying. Again, maybe when all is said and done, people are going to say, "Yeah, I don't want to go down this path that he's recommending." Fair enough. But I saw a bunch of academic economists circling the wagons whenever his ideas would pop up and you know just dismissing him like he's a con man or just now this guy's just a charlatan coming along or maybe he's earnest but he doesn't understand our field. He's just some mathematician outsider. He doesn't get economics like we do. And that's what I'm saying. I I know enough to say that's that's not the right way to handle him. That that's not the correct response. um to you uh refer to an analogy that I often make on social media where I'm explaining how a lot of uh big guns like in academia and but also like you know podcast hosts and whatnot and I'll say there's a lot of guys walking around telling the world they have a full house when really they have two pair right that's generally my assessment I think most most men overrate them or at least most popular men o overrate themselves that's partly you know how they get to be popular is they sing their own virtues and so on. Whereas with Eric, to continue with that poker analogy, I would say seeing the way he interacts with others and and the reaction they give to him, I would say, yeah, it's like Eric is going around telling the world that he has the positive root of 16 of people married to monarchs. And I'm like, what are you saying? You have four queens? He's like, yeah, that's that's what I said. I got four queens. And he does. He's not bluffing. He does have four queens. It's just nobody understood. That's even what he was claiming. Okay. [laughter] And so that's the uh the way I'm trying to explain what I think has been partly what's been happening. Now, if you want to say you're, you know, this is the human action podcast. What are you saying, Bob? Is this guy better than Mises? Well, no. If we're going to continue that analogy, Mises has a straight flush in my view. But actually, it's more correct to say Mises is playing chess than Eric is playing poker. that they're literally playing different games and so it doesn't really make sense to say who is better that when it comes to if you want to mathematically model the economy well yeah Eric Weinstein is better than Mises but Mises is going to explain why I don't think that's the right game we should be playing okay but for sure since other economists right now at MIT and Harvard and whatnot are playing that same game of mathematically modeling the economy in that realm I think Eric Weinstein has a much stronger hand than they do. All right, I'll drop the analogy. I'm sure you're sick of it at this point. Okay, let me just mention too, even on paper there this the the breezy dismissal of the work of Pia Milani and Eric on this topic, it doesn't really work. All right. So, Pia Milani, you know, she got her her doctoral dissertation in the economics department at Harvard in I think 96, like I said, and her adviser was Eric Maskin, who would go on to win the Nobel Prize, right? So, and he was a fan of her work, right? So I because I've seen some people refer to there are various papers um like one by this guy Van Ven and then one of the things we'll cover in this episode Kenneth Arrow you know the Nobel prizewinning giant in social choice theory and economics of the 20th century he interacted with Eric at one point and so there are certain what's called impossibility results so Van has it in terms of like trying assess uh the purchasing power in different countries, you know, like if you know using currency exchange rates and how would you adjust for that? And he has these results showing if you listed some attributes of an ideal metric by which you could compare the cost of living in different countries and you and he proves there does not exist, you know, a correction formula that could satisfy all these pretty reasonable criteria simultaneously. And then Kenneth Arrow also has these results saying you can list some attributes about what it would look like to take the various ordinal rankings of individuals in society and aggregate them into a single social ordinal ranking of outcomes and you can't do it in general. There does not exist such a thing. Okay. And so people argued that I, you know, I saw this on Twitter and whatnot that clearly what Eric is claiming that he and Pia Milani have are bringing to the table and this new approach they're recommending, hey economist, look at this cool thing we found, why don't you guys take a look? How come you're not listening to us? At least give it a chance. And these critics are dismissing them and saying, no, we literally can prove that it's mathematically impossible that you found what you think you found. So my push back to that is Pia Milani got her doctoral dissertation approved out of Harvard, right? And her adviser liked it. So clearly it's not that she, you know, claimed she had found some things that didn't exist, right? And also yes, Eric's formal training is in mathematics, but he also had a bunch of posttos in various places of relevance. probably the most relevant for our topic here from 98 to 2001 he was at Harvard where the National Bureau of Economic Research was headquartered and he co-founded the Science and Engineering Workforce Project or SEWP with Richard Freeman while he was there. Okay. So again, it's it's not that Eric is unfamiliar with mainstream economics and just in my discussions with him and you know it it's clear he's very familiar with the literature. All right. So, I don't think you can just dismiss it and say, "Oh, these these are outsiders who don't know the first thing about what we're that's just not that doesn't work." Again, maybe ultimately what they're trying or what they're pushing is a dead end, but not for the reasons that this the you know, the glib critics are advancing. Okay. So, with that preamble, now let me just give a few clips and a teaser. Basically, what I'm doing here in this episode of the human action podcast is to give you enough so that you can understand, oh, do I want to go, you know, watch the full two hourish interview that Eric did with Bob on this other podcast, but more generally just to so you understand when you see him talking elsewhere about this topic, you you understand where he's coming from. Because I it's the kind of thing where the more I would have conversations, I would go back and watch other things I had seen him do and then I was like, "Oh, that now it's crystal clear." Whereas I remember the first time I saw him saying these things, I I thought, "What? This doesn't this can't be right. This guy must not know what he's talking about." Okay, so why don't we go ahead and play this clip from the interviewer talk I'm talking about different price indices. Okay, why don't we hit this right now because this is something I definitely want to make sure we cover is and obviously correct me if I'm not stating this but economists hearing this are going to say yeah there's various indices to correct for changing prices over time like we're trying to say the purchasing power of money between the year 1950 and 1960 how do we there's various ways various types of indices and yeah the divisia is one of them that was yeah proposed in the 1925 or whatever you said sure But each of them have their pros and cons. And one of the problems with that one is it's path dependent. Like just to actually comput it. So it takes more numbers in between. And that seems kind of counterintuitive. Like if I just want to know between 1950 and 60, can I just take a snapshot in various prices and quantities and the Devisia index takes? And so one of the results in Dr. from Melan's dissertation that I found very compelling was to say if we do make the switch that you're saying in terms of like the differential operator swapping out the one that economists conventionally use for this new one that she proposes then all these various indices give the same answer >> that's right but more importantly what I would say is the big shift so Dvisia found sort of an echo of gauge theory >> okay So again to to motivate like why this is neat mathematically is among other results. What Pia Milani, you know, points out in her dissertation and that Eric uh, you know, endorsed in that interview there is that if you take their proposal of using this new fancier uh, differential operator that um, let me let me give a quick example just so you get the context and this is the one that he gave when I asked him can you motivate us? What do you mean the derivative we've been using is wrong? And he said, okay, um, let's say the question we're trying to resolve is, is my employer paying me the same wage month after month? And so he's saying if you want to do that with calculus, what you do, you could do like a function that that gives your salary as a function of the month, right? So, you know, f of January gives the the number that's dollar amount, f of February and so on. And it's just you plug in different things and it's given the the answer. And then what you could say is or you could you know do t t equals 1 t equals 2 t equals 3 like that. It probably makes more sense mathematically right where the t is is indexing the month we're talking about. And so if you say, you know, you do it in terms of continuous time and you're you're taking the derivative and you say, oh, if I take the derivative with respect to t and set it to zero, like the standard calculus derivative that we all learned in high school, then what it would mean to say is it constant, which kind of goes hand inhand with is the derivative zero would just mean that the nominal dollar amount you're getting paid every month stays the same. Right? You got paid whatever, $8,000 the first month. You got paid $8,000 the second month and so on. Yep. The derivative with respect to the time is zero. So you're getting paid the same. But then Eric said, "What if economically though, what you mean is you want your real wages to stay the same over time." Well, then it's not enough to say that the change in the payment is zero monthtomonth. You want to say the change relative to some reference line. That's really what you want to maintain to to be zero to change that to be zero over time. And so, you know, maybe have some index of the, you know, the price of a basket of commodities that this worker cares about. Okay. So, that's just showing, you know, to motivate, it's a real simple example, but what would it mean to say you're replacing the standard derivative with a more sophisticated one? Okay. So in that context now what Melany shows in her dissertation is that if you do make this swap, you know, bringing in these results from gauge theory and applying them in an economic context that the various price indices that economists use to try to measure uh changes in the purchasing power of money or you might say the cost of living between two periods. with this new metric, all the different measures give the same answer. So, that's kind of a neat result. Now, I want to be clear, what I'm going to walk through an example just so you understand better what I'm claiming, what I mean. Um, and I want to be clear, though, it's not that Eric and Pia Melany made this particular discovery. It was known I think like in 1980 that what what the answer is going to be is to show if you um increase the frequency of when you're checking in on the prices that you're using and using these various measures, these indices. And as that frequency gets greater and greater so that you're approaching like instead of discrete snapshots is approaching like a continuous flow of information about the price prices of various goods then all the different price indices converge to what's called the divvisia index. Okay. So that was known in the early 80s. But what's new here is that Eric and Pia are giving the economic intuition like to once you understand their framework you realize oh that's why it makes sense economically that all these different price indices which with discrete measures defined in terms of the initial and final you know baskets and whatnot which which in principle give all kinds of different answers but in they all converge to this one thing called the divvisian index and and so they explain why that makes sense once you see things through their eyes. Okay. So before I get to that part, let me just walk through the mechanics of it. So let's to make this relevant for an Austrian crowd. Ron Paul a lot of times when he was campaigning would talk about how much the dollar had lost its purchasing power since the founding of the Fed. And so if you wanted to do that numerically, like to actually come up with the estimate, what would you do? Well, you'd say, "Okay, well, we want to like figure out what could the dollar buy in 1913 and then what can it buy in 2025?" Okay, so that's what we're trying to somehow quantify to be able to say, you know, how much weaker is the dollar now than it was back then. And so I'll just take two of the most popular indices are the Laspar and the Posh. So the way the Laspar's index works um is say okay well take whatever the the representative bundle of consumer goods is from 1913 and then figure out you know like you have certain quantities like whatever a dozen eggs and a gallon of milk and uh whatever a week's worth of rent you list a bunch of stuff as of 1913 and what the what the prices would be and then you figure out okay what what's the total amount you have to spend to buy that basket, that bundle of household goods and services maybe if you have that in there back in 1913. And then you look ahead to 2025 and you take that same bundle and then you say in 2025 prices, how much would you need to spend? And then you just look at, you know, the number's going to be bigger. And then you just look at that percentage increase and you say that's the cumulative increase in the price index over that time frame. Then, you know, you could annualize it if you wanted to say how much on average per year did prices go up. Okay. So, notice even there it's tricky because what if the bundle, you know, there's some things that you bought back in 1913 that don't exist in 2025. And then what's really tricky, so what the posh index does is the opposite. the posh index to try to figure out you know what happened to the purchasing power of money between 1913 and 2025. It starts at 2025 and says what's the representative bundle of goods and services that the you know the average household that we're trying to you know figure out what happened to them um that they spend their money on figure out what's the dollar amount spent on that and then you look backwards and you say people in 1913 how much would they have spent to get that same bundle. Okay. So, you can see a couple things already at this point. Notice there's no reason that those numbers would be the same, those those two approaches I just told you because they're not doing the same thing. Like the the construction of the bundle is different, right? And then beyond that though, it's tricky because in 2025, you know, the the households like they say, "Oh, well, they got to buy a car." So maybe you're including how much would it cost, you know, what's whatever the monthly payment on a car or something to, you know, to get that in the household's bundle. Well, what do you do for that in 1913, right? And even if you did it to like 1960, a car in 1960 isn't nearly as good as a car in 2025. They might look cooler depending on your taste, but you get the idea. So even if it's a car, it's still that's a vastly different thing. And then certainly, you know, oh well, the average household in 2025 might buy an iPad. What should we do? How much did an iPad cost in 1913? You see, you see the problem. Okay. So, a different index though is called the Devisia index that was devised by this guy um I think it came out like in 1925ish is when he first proposed this. And there you know it uses calculus and what it does is like from moment to moment it will take like if you're trying to isolate a household and and you know what happens to the cost of living that it faces and you'd say okay at every snapshot in time you look at you know the price of the various goods that we're talking about and then the the quantities but you um but but you wait it based on the share of that item in the household's overall budget or its overall expenditure. Okay. So that's why the you know so if the idea is if something goes up by you know of the things that the household buys if if one thing doubles in price and something else goes up 2% it's not that you just average those together like if the thing that goes up that doubled in price if that's a small part of your budget anyway that's not going to have as big an impact. Okay. Whereas if it's already if it's something that was already 40% of your budget and then it doubles in price, that's going to be devastating. Okay? So that's why the Devisia index in the actual formula weights things in terms of their overall share in the household's budget. Okay? So that's how it like from instant to instant sort of accounts for the change in the aggregate price structure. you I want to say level um price array that the household is facing but again the things are the impact of each thing is weighted by you know what share was it of the household's expenditures in the prior moment okay and so it does that like instant to instant and then integrates that change over the whole time period that we're talking about and then it's that cumulative rise over the whole stretch that is the change in the divisia index from you know the starting time to the end time Okay. So, you know that that had some interesting features, but historically the reason economists tended not to talk about that like I don't even think I knew what that was. Like I had heard of the Laspar and the Posh just you know through my studies and getting an undergrad and then eventually a PhD in economics. I those those are common place. I don't know that I even heard of the Devisia index until I was you know doing the research for Weinstein stuff. Maybe I had and I forgot about it. But my point is that's not nearly as popular. And so two there's two objections at least. So one is you need a lot more data to do the the Devisia approach right whereas with the Laspares of the posh for the question of hey what's happened the purchasing power of money from 1913 to 2025 all you need are you know a few data points from 1913 and then a few from 2025 and you just do the arithmetic right so it's pretty straightforward. Um whereas with the Devvisia in principle you need a continuous flow of you know like an infinite series of of price and quantity data throughout the whole time span. So there's that. The other weird thing about the Devisia index is it's what's called path dependent. All right. So just um it depends going along with the fact that you can't just look at the starting and ending snapshots of the prices and quantities purchased of the various goods and the two end points but you need to know all the intermediate steps along the way. That's kind of related to the fact that the path by which that household goes from the starting point to the end point affects the final answer, right? That because because you're integrating over that whole interval, what happens in between matters. And so again, that one way of describing that is to say, oh, with the divisia index, it's path dependent. It's not it doesn't matter. It's not enough information just to know what happens at the start and the end. the way with the Laspar and posh. I don't care what happened in the year 1950 and 1970, 1980. All I need to know is what did this? What's the snapshot in 1913? What's the snapshot 2025? That's all you need to pop out the answer and say, "Ah, the dollar's lost such and such of its purchasing power." Okay? And so economists thought that was a a bug of the um the Vizia index. Okay? But with this new approach now we understand why that's fine. So very quickly the economic intuition that Eric is giving is he wants to say what it would mean and and notice this approach is going to handle the problem of there's different goods that are available in 2025. Another issue is the people themselves could be different. I mean literally the people who were alive in 1913 a lot of them aren't going to be alive in 2025. There's that problem as well. All right. But even if you just do it on an individual level, like you want to say, "Oh, there's some guy who he's 20 years old and he lives in Phoenix and you know what what would he do with $100?" And then you want to say, "Okay, now 20 years later, the guy is now 40. He's married. He's got two kids. And he doesn't live in Phoenix anymore. Now he moved to Miami." And you want to say what is how has the purchasing power of money changed in the interim? And so really what you're kind of asking is how much money how many dollars would I have to give this guy now so that he would kind of be the same as the $100 gave him back when he was a 20-year-old and was single and living in Phoenix. And so you see how it's not just that, oh the types of goods available and in a different g geographical location are different, but the guy himself is different. He's not the same person. And so you see when you start getting into this, like it's a really complex problem. Like there's some, you know, deep philosophical issues going on, right? And so I think intuitively what Eric is recommending is the way at least in principle you could handle that problem. The only sensible way besides just throwing your hands up and saying it's impossible is you would say okay in principle if you could do something like this. You go to the guy who's when he's 20 in Phoenix and you give him $100 and then he buys the bundle of goods and services at that moment in time. Of course that you know maximizes his utility given where he was. Then you give him the $100. He does the thing that, you know, on the margin increases his satisfaction the most with that extra $100. And then you let whatever 10 minutes pass and you say to him, um, take that bundle that you purchased. So forget the $100 is gone. He spent it on the bundle. and now barter that bundle for other goods and services if you want that have the same market value. Right? So he he can't kick in more money and he's and he's not going to trade it for stuff that's cheaper and then siphon some of the money out of it. He's just now going to keep rolling over his bundle of goods and services for things of equal total market value. Okay? And then he just keeps doing that every 10 minutes. And then you check in 20 years later, you know, he's moved along the way, you know, so you take that into account. You know, wherever he finds himself, every 10 minutes, he transfers the bundle and rolls it over. So he he's doing it in a way that maximizes his utility at every moment, right? It's not just that he's rolling it over because he thinks, "Oh, I'm just holding this because this econometrician is asking me to do it." No, he's at every moment given the option to reallocate, but maintaining his budget constraint. you know, that he's not kicking in more income or, you know, like I say, pulling some out if he if he has a cost savings. No, he keeps rolling it over into things that have the same market value, but yet give him more utility or if he has the best bundle at that moment, he [snorts] just keeps it, right? If that's the case, right? So, all along the way through that history of that 20 years, he keeps doing that process until finally he ends up in Miami. And then you can check at that point and you say, "Okay, now this bundle that you're getting if you sold this bundle now for money, how much would you raise? And he would probably get more than $100 for it and then that's the way you would say the cumulative change in prices from 20 years ago to now is this. Okay. So I think that is capturing the spirit at least of what Eric is suggesting. And so what's interesting now is so you understand why path dependency is a virtue. Okay. Um, but then also, and I'll play a clip to underscore that in a second, but also now that sheds more light on that early result that I talked about that that was known at least as of in the early 1980s that in practice with the Laspair and the Posh and there's other indices too. if you increase the frequency of the data. So instead of just looking between 1913 and 2025, what if instead you did that every 10 years, you know, for all the, you know, jumps in between and then you just chained it. So you looked at between 1913 to 1923 and you did the Laspar's approach and you got your number and then you did from 2023 to or sorry uh 1923 to 1933 and you did it and then you just linked all those 10-year increments but you know by multiplying them together. You could do that way and then do the same thing with the posh. And the point is if doing that and and also if the um if the representative bundle of goods household goods that you use at each checkpoint happen to coincide with what the you know the the Devisia guys bundle was at all those checkpoints. Well then all these different measures all converge to the same answer as you let the number of those checkpoints increase. Right? Right? So instead of doing it every 10 years, what if it do it every if you do it annually, then you do it quarterly, then you do it monthly, weekly, daily, right? And so they all kind of converge to the same thing. So long as again the bundles you're using at each checkpoint coincide with what that representative household would choose to do using Eric's method. Okay, so you sort of see the elegance there, I hope, and why Eric thinks this is neat. Okay. So, let me go ahead and play the the path dependence clip where you can see where he's saying once you get what's going on and you see it like I'm seeing it. The path dependence element in the Devvisia index isn't a bug, it's a feature. And if you don't have path dependence, you're not doing economics. >> That's right. But more importantly, what I would say is the big shift. So, Devisia found sort of an echo of gauge theory and it had the mysterious property of being path dependent and that was thought to be a negative and that's bedeled the field ever since. What gauge theory shows you is why it is path dependent. Why that is a positive thing. It is something that you should not try to rid the world of. Effectively, what this is is curvature. And curvature is what generates path dependence. And so what you're seeing when people try to say we don't want a path dependent measure is that they are effectively the flat earth society of economics. They're the flat market society. And so you're trying to have a conversation saying the economy is round with a bunch of people saying no it isn't. It's flat. We just can't get this thing to go away. Because if you take any mechanical index that is anything that takes in let's say dual period prices and quantities and you chain it and you you say well okay originally I have a year between readings now I'm going to do it every half a year then quarterly then every month then every week so now I have 52 readings as you increase that frequency you approximate usually one index the divisi doesn't matter whether you begin with a fiser a torancquist posh pairs they all become the divisian and the reason for that has to do with the fact that it is the correct way of thinking the path dependence is a feature it's not a bug you can't get rid of it and if you don't have path dependence it's a sign that you're not actually doing economics >> okay okay let me now another great part of my discussion with Eric that I think should interest fans of the Austrian school. Again, not that you're gonna go out and throw away human action and man economy and state and instead just devote your life to studying uh fiber bundles, but where you I think you will see that Eric is perhaps not the uh the heretic that you think he is that actually oh no his problem with the main mathematical mainstream is not the same as what Amises or Rothberg would say but it's it's coming from a valid point or place. So here uh I'm going to play a clip where Eric is explaining what he told Kenneth Arrow. So let me just set the clip up first. So Kenneth Arrow has this very famous result in social choice theory. Um very quickly what what he does is he's showing the limits of the ability even in principle to aggregate individual preferences into a single uh you know social preference. Okay. He doesn't use anything with cardinal utility nothing like that. He just says suppose various individuals have ordinal you know meaning like first second third rankings of whatever it is that we care about. It could be political candidates but it could be very general. It could be like states of the world, right? So, this isn't tied to some particular social setting. This is a pretty general abstract result and it's it's breathtaking when you understand what it what it's claiming. Like it it's amazing that this is true, but it is. It's it's surprising. Okay. Um and so what Arrow showed is in general if you have you know if people are allowed to have any kind of ordinal rankings they want on whatever the space of possible outcomes is. Um and then you want to say do we have some way of mapping from all the individual rankings of the individuals of society into a single social ranking? And you want to say okay well yes this mapping should obey some uh axioms. And so one thing is if every single person thinks that outcome A is preferred to outcome B, then it better be the case that the social ranking also thinks outcome A is preferred to outcome B. Okay, does everyone get that? Like it would be weird if it were the other way around. Now if different people have different views, if some people think A is better than B and some people think B is better than A, then it's fine. Then you know the arrows axioms aren't pinning down what needs to be said, but it's it's just making the very modest claim requirement that if literally every single person in society thinks A is better than B, then if we're going to have a social ranking that in some sense aggregates all of the individual rankings into one for society, clearly the social ranking has to agree with the unanimous opinion held by every single individual. Okay, there's another one that says nobody can be a dictator and this is a very weak requirement. It's fine in any particular distribution of rank individual rankings and whatever if there's some guy Jim in his ordinal ranking of A versus B C D you know all the it could be you know a huge number of quadrillion different of outcomes and if Jim's ordinal ranking of all of them from best to worst is identical to the social ranking that's fine. That doesn't make Jim a dictator. What makes Jim a dictator is if no matter what, no matter what the possible ordinal rankings of all the individuals are, if the social ranking is always identical to Jim's, then Jim is a dictator. And so Arrow's theorem says we're going to rule out rules that work like that. Okay? And then there's some other ones that aren't as intuitive as the two I just listed, but when you understand what the axioms are claiming, they're not unreasonable. Okay? And so what er arrow proved is that there does not exist a mapping from the individual rankings to a social one that satisfies all of his criteria. Okay, so it's a very general powerful result. And so now um let me explain. So when Eric and Pia Milani are going around telling people, hey, she, you know, her dissertation shows how the application of gauge theory to math uh to economics. We've done things like we've come up with a way to non-arbit solve the problem of, you know, correcting for changing, you know, changing preferences and uh the composition of of goods that are available and things like that to to isolate the purchasing power of money over time. we've solved this in a way that, you know, other theories can't deal with without handwaving. This is clearly the objectively correct way as economists to approach these problems. And so Arrow has him out to breakfast or something and says, "This is interesting, but what you're claiming to have found is impossible." And Eric says, "Why?" And he said, "Well, because you know, mathematically, here I'm paraphrasing, but this is I think what Arrow was saying. what what you're doing is you're saying, "Oh, I found a way to like handle objectively the fact that an individual's ordinal rankings might change over time." So, the fact that the individual ranks various things a certain way at time t, but then at time t2, he might rank them differently and then at time three, he might rank them differently again and so on. And you're saying you've come up with this framework by which you can rationally handle all that and put it into a coherent framework. And I'm saying no, you can't because if you could do that, well then my theorem would be wrong, right? Because in my theorem, I can handle Jim at time one, Jim at time two, Jim at time three. I can just say that's the same as like Alice at time one, Bob at time one, and Charlie at time one. Right? In other words, arrows theorem, you typically think of it as a bunch of individuals at the same time, but mathematically it's the same thing as thinking of the same individual at future points in time if his preferences can change. It's like he's a different guy in the future in various snapshots, right? And so Arrow is saying this doesn't work. So now here, once Eric understood what Arrow's deal was, this is how Eric responded. >> So what I didn't understand was is that he saw that as equivalent. And I said, "No, no, no. I hadn't understood that this is how you were seeing it. There are two pivotal differences between the two situations. This is a false duality. He said, "What do you mean?" I said, "The first thing is your result is a result in social choice theory. There is no market. You're voting on let's say three different candidates or as you say three different outcomes of the world. And what you're saying is that you cannot aggregate a heterogeneous group as if it was a single consistent super individual. So that if everybody agrees on a choice, that choice has to hold. There isn't one person who has dictatorial rights and small changes don't result in violent changes, you know, whatever this list of aims is. And he said, 'And the second, and I said, 'Well, the second is that there is no morphing of Bob into Sally into Arjun into Leticia. That just doesn't exist. And you do morph into your future selves over time. So, you're also not in possession of a path which connects all of the individuals who are being aggregated. And those two things break the apparent duality that you're appealing to. And I'm not going to disagree with you that in their absence you'd be right. You'd be correct. >> But that's why the intertemporal market situation and the intra aagent social choice situation are not in duality. There was like a long silence and he said, "Oh, >> okay." So I think that should be very interesting to Austro libertarian viewers because you see how Eric is responding that on the one hand he's saying oh no your system Dr. Arrow or Professor Arrow isn't relying on the you know the benefits of market prices that there's a sense in which you know to go back to my guy who starts in what Phoenix and ends up in Miami him rolling over the bundle for equivalent market value there he's relying on market prices so that's sort of like a non-object or a non-arbitrary path to in a sense rely on the wisdom of crowds you know if you will I'm speaking intuitively but I hope you guys get the idea and he and and so Eric is claiming the arrow in your theorem people can't rely on the market price system to help with this issue. And then the other element he's saying is you know arrow in your framework these really are distinct people. it's Alice and Bob and Charlie at a given snapshot in time and you show that yeah in general we can't aggregate their preferences and I agree with that and he's saying but there's that's different from saying Jim at time zero gym at time one Jim at time two if if the time increment shrinks to you know using calculus to be into you know infiniteesimal it's like you evolve into your future self and that doesn't seem nearly as big of a jump as just saying you can't compare the preferences between Alice and that you can you can imagine your future self. So even though your preferences might change radically over a 20-year stretch when you get married and move to Miami, your preferences between right now in a minute in the future aren't going to change nearly as much. And so or at least that's the assumption that underlies the math that Eric and Pia Milani are doing. Okay. So I think people might appreciate that element and how Eric responded to Arrow. Okay. Well, I hope I've given you enough of a teaser to get you to go watch the full interview. Thanks for your attention, everybody. See you next time. [music] >> Check back next week for a new episode of the Human Action podcast. In the meantime, you can find [music] more content like this on mises.org. [music] >> [music]
Eric Weinstein’s Challenge to Mainstream Mathematical Economics
Summary
Transcript
[music] This is the Human Action podcast where we debunk the economic, political, and even cultural myths of the days. Here's [music] your host, Dr. Bob Murphy. Hey everybody, welcome back to Human Action Podcast. In this episode, I'm going [music] to play some clips from and then elaborate upon uh a recent interview that I conducted with Eric Weinstein. Now, the podcast where this interview occurred wasn't the human action one. It was a different one. It was called the Infi podcast, which is the podcast uh that I host for my uh fintech day job at the company Infinio. All right. Um let me just explain a little bit on the front end of why I think it's important for fans of Austrian economics to be exposed to some of Eric's ideas. Um so for a long time, Eric has been claiming that if you take what's called gauge theory from mathematics which has had much success for example in physics and that's where where Eric's background is. Eric has a PhD in math from Harvard and he is very well um studied in applying these certain uh the area of math to physics and then he's saying this has great application also to economics and Pia Melany got her PhD from Harvard in economics proper in I think 96 and that's what um you know her her dissertation covers is how would you use gauge theory in economics and Eric claims that it does a lot right that among other things it has implications for how you would do cost of living adjustments and that's what we're going to get to in a minute here on the human action podcast but it's much broader than that so the the big picture the most audacious claim is Eric is saying you back in the 1870s you had the marginal revolution in economics where at least in the the strain of mathematical economic modeling that came out of that, you know, through Bob Ross and then, you know, in the 20th century in the hands of people like Paul Samuelson and so on that at least in that strand of the economics literature, Eric is claiming you economists are stuck with the simplest type of derivative that math has for you and that you need to realize there are other more sophisticated types of derivatives. And so you kind of need the marginal revolution 2.0 and that just like the original marginal revolution was not merely a quibble about calculating some formula but was actually you know broadening the scope of and redefining in a sense how economics operated. Likewise Eric is saying that's what is on the table here if if he's right. And so it can handle things such as um changing ordinal preferences over time. Okay, which in standard mathematical economics you can't deal with. And and then Eric claims because of that vulnerability, the fact that the entire edifice of modern mathematical economics only works if you assume that preferences are static over time. You can build in uncertainty in things but the idea is the basic underlying utility function or even the you know even if you're doing it ordinally the ranking of things that that there is some uh static nature to that over time otherwise nothing works. It's just too open-ended. You can't say anything with the standard tools. And so Eric is saying among other benefits of switching to his framework that he's recommending you can handle stuff like that. Okay. So, um, partly why I wanted to give Eric a platform, I mean, he does Joe Rogan things. It's not that I'm letting the public hear about his name. What I mean is aimed at academic economists specifically, is that I had interacted enough with him to know he wasn't bluffing. Okay. Um, but I could understand why a lot of economists just literally didn't even understand what he was saying. And the more I read his stuff and interacted with him, the more convinced I became that, say what you will about Eric Weinstein, he's not bluffing. All right? He's not just making stuff up. There is substance behind what he's saying. Again, maybe when all is said and done, people are going to say, "Yeah, I don't want to go down this path that he's recommending." Fair enough. But I saw a bunch of academic economists circling the wagons whenever his ideas would pop up and you know just dismissing him like he's a con man or just now this guy's just a charlatan coming along or maybe he's earnest but he doesn't understand our field. He's just some mathematician outsider. He doesn't get economics like we do. And that's what I'm saying. I I know enough to say that's that's not the right way to handle him. That that's not the correct response. um to you uh refer to an analogy that I often make on social media where I'm explaining how a lot of uh big guns like in academia and but also like you know podcast hosts and whatnot and I'll say there's a lot of guys walking around telling the world they have a full house when really they have two pair right that's generally my assessment I think most most men overrate them or at least most popular men o overrate themselves that's partly you know how they get to be popular is they sing their own virtues and so on. Whereas with Eric, to continue with that poker analogy, I would say seeing the way he interacts with others and and the reaction they give to him, I would say, yeah, it's like Eric is going around telling the world that he has the positive root of 16 of people married to monarchs. And I'm like, what are you saying? You have four queens? He's like, yeah, that's that's what I said. I got four queens. And he does. He's not bluffing. He does have four queens. It's just nobody understood. That's even what he was claiming. Okay. [laughter] And so that's the uh the way I'm trying to explain what I think has been partly what's been happening. Now, if you want to say you're, you know, this is the human action podcast. What are you saying, Bob? Is this guy better than Mises? Well, no. If we're going to continue that analogy, Mises has a straight flush in my view. But actually, it's more correct to say Mises is playing chess than Eric is playing poker. that they're literally playing different games and so it doesn't really make sense to say who is better that when it comes to if you want to mathematically model the economy well yeah Eric Weinstein is better than Mises but Mises is going to explain why I don't think that's the right game we should be playing okay but for sure since other economists right now at MIT and Harvard and whatnot are playing that same game of mathematically modeling the economy in that realm I think Eric Weinstein has a much stronger hand than they do. All right, I'll drop the analogy. I'm sure you're sick of it at this point. Okay, let me just mention too, even on paper there this the the breezy dismissal of the work of Pia Milani and Eric on this topic, it doesn't really work. All right. So, Pia Milani, you know, she got her her doctoral dissertation in the economics department at Harvard in I think 96, like I said, and her adviser was Eric Maskin, who would go on to win the Nobel Prize, right? So, and he was a fan of her work, right? So I because I've seen some people refer to there are various papers um like one by this guy Van Ven and then one of the things we'll cover in this episode Kenneth Arrow you know the Nobel prizewinning giant in social choice theory and economics of the 20th century he interacted with Eric at one point and so there are certain what's called impossibility results so Van has it in terms of like trying assess uh the purchasing power in different countries, you know, like if you know using currency exchange rates and how would you adjust for that? And he has these results showing if you listed some attributes of an ideal metric by which you could compare the cost of living in different countries and you and he proves there does not exist, you know, a correction formula that could satisfy all these pretty reasonable criteria simultaneously. And then Kenneth Arrow also has these results saying you can list some attributes about what it would look like to take the various ordinal rankings of individuals in society and aggregate them into a single social ordinal ranking of outcomes and you can't do it in general. There does not exist such a thing. Okay. And so people argued that I, you know, I saw this on Twitter and whatnot that clearly what Eric is claiming that he and Pia Milani have are bringing to the table and this new approach they're recommending, hey economist, look at this cool thing we found, why don't you guys take a look? How come you're not listening to us? At least give it a chance. And these critics are dismissing them and saying, no, we literally can prove that it's mathematically impossible that you found what you think you found. So my push back to that is Pia Milani got her doctoral dissertation approved out of Harvard, right? And her adviser liked it. So clearly it's not that she, you know, claimed she had found some things that didn't exist, right? And also yes, Eric's formal training is in mathematics, but he also had a bunch of posttos in various places of relevance. probably the most relevant for our topic here from 98 to 2001 he was at Harvard where the National Bureau of Economic Research was headquartered and he co-founded the Science and Engineering Workforce Project or SEWP with Richard Freeman while he was there. Okay. So again, it's it's not that Eric is unfamiliar with mainstream economics and just in my discussions with him and you know it it's clear he's very familiar with the literature. All right. So, I don't think you can just dismiss it and say, "Oh, these these are outsiders who don't know the first thing about what we're that's just not that doesn't work." Again, maybe ultimately what they're trying or what they're pushing is a dead end, but not for the reasons that this the you know, the glib critics are advancing. Okay. So, with that preamble, now let me just give a few clips and a teaser. Basically, what I'm doing here in this episode of the human action podcast is to give you enough so that you can understand, oh, do I want to go, you know, watch the full two hourish interview that Eric did with Bob on this other podcast, but more generally just to so you understand when you see him talking elsewhere about this topic, you you understand where he's coming from. Because I it's the kind of thing where the more I would have conversations, I would go back and watch other things I had seen him do and then I was like, "Oh, that now it's crystal clear." Whereas I remember the first time I saw him saying these things, I I thought, "What? This doesn't this can't be right. This guy must not know what he's talking about." Okay, so why don't we go ahead and play this clip from the interviewer talk I'm talking about different price indices. Okay, why don't we hit this right now because this is something I definitely want to make sure we cover is and obviously correct me if I'm not stating this but economists hearing this are going to say yeah there's various indices to correct for changing prices over time like we're trying to say the purchasing power of money between the year 1950 and 1960 how do we there's various ways various types of indices and yeah the divisia is one of them that was yeah proposed in the 1925 or whatever you said sure But each of them have their pros and cons. And one of the problems with that one is it's path dependent. Like just to actually comput it. So it takes more numbers in between. And that seems kind of counterintuitive. Like if I just want to know between 1950 and 60, can I just take a snapshot in various prices and quantities and the Devisia index takes? And so one of the results in Dr. from Melan's dissertation that I found very compelling was to say if we do make the switch that you're saying in terms of like the differential operator swapping out the one that economists conventionally use for this new one that she proposes then all these various indices give the same answer >> that's right but more importantly what I would say is the big shift so Dvisia found sort of an echo of gauge theory >> okay So again to to motivate like why this is neat mathematically is among other results. What Pia Milani, you know, points out in her dissertation and that Eric uh, you know, endorsed in that interview there is that if you take their proposal of using this new fancier uh, differential operator that um, let me let me give a quick example just so you get the context and this is the one that he gave when I asked him can you motivate us? What do you mean the derivative we've been using is wrong? And he said, okay, um, let's say the question we're trying to resolve is, is my employer paying me the same wage month after month? And so he's saying if you want to do that with calculus, what you do, you could do like a function that that gives your salary as a function of the month, right? So, you know, f of January gives the the number that's dollar amount, f of February and so on. And it's just you plug in different things and it's given the the answer. And then what you could say is or you could you know do t t equals 1 t equals 2 t equals 3 like that. It probably makes more sense mathematically right where the t is is indexing the month we're talking about. And so if you say, you know, you do it in terms of continuous time and you're you're taking the derivative and you say, oh, if I take the derivative with respect to t and set it to zero, like the standard calculus derivative that we all learned in high school, then what it would mean to say is it constant, which kind of goes hand inhand with is the derivative zero would just mean that the nominal dollar amount you're getting paid every month stays the same. Right? You got paid whatever, $8,000 the first month. You got paid $8,000 the second month and so on. Yep. The derivative with respect to the time is zero. So you're getting paid the same. But then Eric said, "What if economically though, what you mean is you want your real wages to stay the same over time." Well, then it's not enough to say that the change in the payment is zero monthtomonth. You want to say the change relative to some reference line. That's really what you want to maintain to to be zero to change that to be zero over time. And so, you know, maybe have some index of the, you know, the price of a basket of commodities that this worker cares about. Okay. So, that's just showing, you know, to motivate, it's a real simple example, but what would it mean to say you're replacing the standard derivative with a more sophisticated one? Okay. So in that context now what Melany shows in her dissertation is that if you do make this swap, you know, bringing in these results from gauge theory and applying them in an economic context that the various price indices that economists use to try to measure uh changes in the purchasing power of money or you might say the cost of living between two periods. with this new metric, all the different measures give the same answer. So, that's kind of a neat result. Now, I want to be clear, what I'm going to walk through an example just so you understand better what I'm claiming, what I mean. Um, and I want to be clear, though, it's not that Eric and Pia Melany made this particular discovery. It was known I think like in 1980 that what what the answer is going to be is to show if you um increase the frequency of when you're checking in on the prices that you're using and using these various measures, these indices. And as that frequency gets greater and greater so that you're approaching like instead of discrete snapshots is approaching like a continuous flow of information about the price prices of various goods then all the different price indices converge to what's called the divvisia index. Okay. So that was known in the early 80s. But what's new here is that Eric and Pia are giving the economic intuition like to once you understand their framework you realize oh that's why it makes sense economically that all these different price indices which with discrete measures defined in terms of the initial and final you know baskets and whatnot which which in principle give all kinds of different answers but in they all converge to this one thing called the divvisian index and and so they explain why that makes sense once you see things through their eyes. Okay. So before I get to that part, let me just walk through the mechanics of it. So let's to make this relevant for an Austrian crowd. Ron Paul a lot of times when he was campaigning would talk about how much the dollar had lost its purchasing power since the founding of the Fed. And so if you wanted to do that numerically, like to actually come up with the estimate, what would you do? Well, you'd say, "Okay, well, we want to like figure out what could the dollar buy in 1913 and then what can it buy in 2025?" Okay, so that's what we're trying to somehow quantify to be able to say, you know, how much weaker is the dollar now than it was back then. And so I'll just take two of the most popular indices are the Laspar and the Posh. So the way the Laspar's index works um is say okay well take whatever the the representative bundle of consumer goods is from 1913 and then figure out you know like you have certain quantities like whatever a dozen eggs and a gallon of milk and uh whatever a week's worth of rent you list a bunch of stuff as of 1913 and what the what the prices would be and then you figure out okay what what's the total amount you have to spend to buy that basket, that bundle of household goods and services maybe if you have that in there back in 1913. And then you look ahead to 2025 and you take that same bundle and then you say in 2025 prices, how much would you need to spend? And then you just look at, you know, the number's going to be bigger. And then you just look at that percentage increase and you say that's the cumulative increase in the price index over that time frame. Then, you know, you could annualize it if you wanted to say how much on average per year did prices go up. Okay. So, notice even there it's tricky because what if the bundle, you know, there's some things that you bought back in 1913 that don't exist in 2025. And then what's really tricky, so what the posh index does is the opposite. the posh index to try to figure out you know what happened to the purchasing power of money between 1913 and 2025. It starts at 2025 and says what's the representative bundle of goods and services that the you know the average household that we're trying to you know figure out what happened to them um that they spend their money on figure out what's the dollar amount spent on that and then you look backwards and you say people in 1913 how much would they have spent to get that same bundle. Okay. So, you can see a couple things already at this point. Notice there's no reason that those numbers would be the same, those those two approaches I just told you because they're not doing the same thing. Like the the construction of the bundle is different, right? And then beyond that though, it's tricky because in 2025, you know, the the households like they say, "Oh, well, they got to buy a car." So maybe you're including how much would it cost, you know, what's whatever the monthly payment on a car or something to, you know, to get that in the household's bundle. Well, what do you do for that in 1913, right? And even if you did it to like 1960, a car in 1960 isn't nearly as good as a car in 2025. They might look cooler depending on your taste, but you get the idea. So even if it's a car, it's still that's a vastly different thing. And then certainly, you know, oh well, the average household in 2025 might buy an iPad. What should we do? How much did an iPad cost in 1913? You see, you see the problem. Okay. So, a different index though is called the Devisia index that was devised by this guy um I think it came out like in 1925ish is when he first proposed this. And there you know it uses calculus and what it does is like from moment to moment it will take like if you're trying to isolate a household and and you know what happens to the cost of living that it faces and you'd say okay at every snapshot in time you look at you know the price of the various goods that we're talking about and then the the quantities but you um but but you wait it based on the share of that item in the household's overall budget or its overall expenditure. Okay. So that's why the you know so if the idea is if something goes up by you know of the things that the household buys if if one thing doubles in price and something else goes up 2% it's not that you just average those together like if the thing that goes up that doubled in price if that's a small part of your budget anyway that's not going to have as big an impact. Okay. Whereas if it's already if it's something that was already 40% of your budget and then it doubles in price, that's going to be devastating. Okay? So that's why the Devisia index in the actual formula weights things in terms of their overall share in the household's budget. Okay? So that's how it like from instant to instant sort of accounts for the change in the aggregate price structure. you I want to say level um price array that the household is facing but again the things are the impact of each thing is weighted by you know what share was it of the household's expenditures in the prior moment okay and so it does that like instant to instant and then integrates that change over the whole time period that we're talking about and then it's that cumulative rise over the whole stretch that is the change in the divisia index from you know the starting time to the end time Okay. So, you know that that had some interesting features, but historically the reason economists tended not to talk about that like I don't even think I knew what that was. Like I had heard of the Laspar and the Posh just you know through my studies and getting an undergrad and then eventually a PhD in economics. I those those are common place. I don't know that I even heard of the Devisia index until I was you know doing the research for Weinstein stuff. Maybe I had and I forgot about it. But my point is that's not nearly as popular. And so two there's two objections at least. So one is you need a lot more data to do the the Devisia approach right whereas with the Laspares of the posh for the question of hey what's happened the purchasing power of money from 1913 to 2025 all you need are you know a few data points from 1913 and then a few from 2025 and you just do the arithmetic right so it's pretty straightforward. Um whereas with the Devvisia in principle you need a continuous flow of you know like an infinite series of of price and quantity data throughout the whole time span. So there's that. The other weird thing about the Devisia index is it's what's called path dependent. All right. So just um it depends going along with the fact that you can't just look at the starting and ending snapshots of the prices and quantities purchased of the various goods and the two end points but you need to know all the intermediate steps along the way. That's kind of related to the fact that the path by which that household goes from the starting point to the end point affects the final answer, right? That because because you're integrating over that whole interval, what happens in between matters. And so again, that one way of describing that is to say, oh, with the divisia index, it's path dependent. It's not it doesn't matter. It's not enough information just to know what happens at the start and the end. the way with the Laspar and posh. I don't care what happened in the year 1950 and 1970, 1980. All I need to know is what did this? What's the snapshot in 1913? What's the snapshot 2025? That's all you need to pop out the answer and say, "Ah, the dollar's lost such and such of its purchasing power." Okay? And so economists thought that was a a bug of the um the Vizia index. Okay? But with this new approach now we understand why that's fine. So very quickly the economic intuition that Eric is giving is he wants to say what it would mean and and notice this approach is going to handle the problem of there's different goods that are available in 2025. Another issue is the people themselves could be different. I mean literally the people who were alive in 1913 a lot of them aren't going to be alive in 2025. There's that problem as well. All right. But even if you just do it on an individual level, like you want to say, "Oh, there's some guy who he's 20 years old and he lives in Phoenix and you know what what would he do with $100?" And then you want to say, "Okay, now 20 years later, the guy is now 40. He's married. He's got two kids. And he doesn't live in Phoenix anymore. Now he moved to Miami." And you want to say what is how has the purchasing power of money changed in the interim? And so really what you're kind of asking is how much money how many dollars would I have to give this guy now so that he would kind of be the same as the $100 gave him back when he was a 20-year-old and was single and living in Phoenix. And so you see how it's not just that, oh the types of goods available and in a different g geographical location are different, but the guy himself is different. He's not the same person. And so you see when you start getting into this, like it's a really complex problem. Like there's some, you know, deep philosophical issues going on, right? And so I think intuitively what Eric is recommending is the way at least in principle you could handle that problem. The only sensible way besides just throwing your hands up and saying it's impossible is you would say okay in principle if you could do something like this. You go to the guy who's when he's 20 in Phoenix and you give him $100 and then he buys the bundle of goods and services at that moment in time. Of course that you know maximizes his utility given where he was. Then you give him the $100. He does the thing that, you know, on the margin increases his satisfaction the most with that extra $100. And then you let whatever 10 minutes pass and you say to him, um, take that bundle that you purchased. So forget the $100 is gone. He spent it on the bundle. and now barter that bundle for other goods and services if you want that have the same market value. Right? So he he can't kick in more money and he's and he's not going to trade it for stuff that's cheaper and then siphon some of the money out of it. He's just now going to keep rolling over his bundle of goods and services for things of equal total market value. Okay? And then he just keeps doing that every 10 minutes. And then you check in 20 years later, you know, he's moved along the way, you know, so you take that into account. You know, wherever he finds himself, every 10 minutes, he transfers the bundle and rolls it over. So he he's doing it in a way that maximizes his utility at every moment, right? It's not just that he's rolling it over because he thinks, "Oh, I'm just holding this because this econometrician is asking me to do it." No, he's at every moment given the option to reallocate, but maintaining his budget constraint. you know, that he's not kicking in more income or, you know, like I say, pulling some out if he if he has a cost savings. No, he keeps rolling it over into things that have the same market value, but yet give him more utility or if he has the best bundle at that moment, he [snorts] just keeps it, right? If that's the case, right? So, all along the way through that history of that 20 years, he keeps doing that process until finally he ends up in Miami. And then you can check at that point and you say, "Okay, now this bundle that you're getting if you sold this bundle now for money, how much would you raise? And he would probably get more than $100 for it and then that's the way you would say the cumulative change in prices from 20 years ago to now is this. Okay. So I think that is capturing the spirit at least of what Eric is suggesting. And so what's interesting now is so you understand why path dependency is a virtue. Okay. Um, but then also, and I'll play a clip to underscore that in a second, but also now that sheds more light on that early result that I talked about that that was known at least as of in the early 1980s that in practice with the Laspair and the Posh and there's other indices too. if you increase the frequency of the data. So instead of just looking between 1913 and 2025, what if instead you did that every 10 years, you know, for all the, you know, jumps in between and then you just chained it. So you looked at between 1913 to 1923 and you did the Laspar's approach and you got your number and then you did from 2023 to or sorry uh 1923 to 1933 and you did it and then you just linked all those 10-year increments but you know by multiplying them together. You could do that way and then do the same thing with the posh. And the point is if doing that and and also if the um if the representative bundle of goods household goods that you use at each checkpoint happen to coincide with what the you know the the Devisia guys bundle was at all those checkpoints. Well then all these different measures all converge to the same answer as you let the number of those checkpoints increase. Right? Right? So instead of doing it every 10 years, what if it do it every if you do it annually, then you do it quarterly, then you do it monthly, weekly, daily, right? And so they all kind of converge to the same thing. So long as again the bundles you're using at each checkpoint coincide with what that representative household would choose to do using Eric's method. Okay, so you sort of see the elegance there, I hope, and why Eric thinks this is neat. Okay. So, let me go ahead and play the the path dependence clip where you can see where he's saying once you get what's going on and you see it like I'm seeing it. The path dependence element in the Devvisia index isn't a bug, it's a feature. And if you don't have path dependence, you're not doing economics. >> That's right. But more importantly, what I would say is the big shift. So, Devisia found sort of an echo of gauge theory and it had the mysterious property of being path dependent and that was thought to be a negative and that's bedeled the field ever since. What gauge theory shows you is why it is path dependent. Why that is a positive thing. It is something that you should not try to rid the world of. Effectively, what this is is curvature. And curvature is what generates path dependence. And so what you're seeing when people try to say we don't want a path dependent measure is that they are effectively the flat earth society of economics. They're the flat market society. And so you're trying to have a conversation saying the economy is round with a bunch of people saying no it isn't. It's flat. We just can't get this thing to go away. Because if you take any mechanical index that is anything that takes in let's say dual period prices and quantities and you chain it and you you say well okay originally I have a year between readings now I'm going to do it every half a year then quarterly then every month then every week so now I have 52 readings as you increase that frequency you approximate usually one index the divisi doesn't matter whether you begin with a fiser a torancquist posh pairs they all become the divisian and the reason for that has to do with the fact that it is the correct way of thinking the path dependence is a feature it's not a bug you can't get rid of it and if you don't have path dependence it's a sign that you're not actually doing economics >> okay okay let me now another great part of my discussion with Eric that I think should interest fans of the Austrian school. Again, not that you're gonna go out and throw away human action and man economy and state and instead just devote your life to studying uh fiber bundles, but where you I think you will see that Eric is perhaps not the uh the heretic that you think he is that actually oh no his problem with the main mathematical mainstream is not the same as what Amises or Rothberg would say but it's it's coming from a valid point or place. So here uh I'm going to play a clip where Eric is explaining what he told Kenneth Arrow. So let me just set the clip up first. So Kenneth Arrow has this very famous result in social choice theory. Um very quickly what what he does is he's showing the limits of the ability even in principle to aggregate individual preferences into a single uh you know social preference. Okay. He doesn't use anything with cardinal utility nothing like that. He just says suppose various individuals have ordinal you know meaning like first second third rankings of whatever it is that we care about. It could be political candidates but it could be very general. It could be like states of the world, right? So, this isn't tied to some particular social setting. This is a pretty general abstract result and it's it's breathtaking when you understand what it what it's claiming. Like it it's amazing that this is true, but it is. It's it's surprising. Okay. Um and so what Arrow showed is in general if you have you know if people are allowed to have any kind of ordinal rankings they want on whatever the space of possible outcomes is. Um and then you want to say do we have some way of mapping from all the individual rankings of the individuals of society into a single social ranking? And you want to say okay well yes this mapping should obey some uh axioms. And so one thing is if every single person thinks that outcome A is preferred to outcome B, then it better be the case that the social ranking also thinks outcome A is preferred to outcome B. Okay, does everyone get that? Like it would be weird if it were the other way around. Now if different people have different views, if some people think A is better than B and some people think B is better than A, then it's fine. Then you know the arrows axioms aren't pinning down what needs to be said, but it's it's just making the very modest claim requirement that if literally every single person in society thinks A is better than B, then if we're going to have a social ranking that in some sense aggregates all of the individual rankings into one for society, clearly the social ranking has to agree with the unanimous opinion held by every single individual. Okay, there's another one that says nobody can be a dictator and this is a very weak requirement. It's fine in any particular distribution of rank individual rankings and whatever if there's some guy Jim in his ordinal ranking of A versus B C D you know all the it could be you know a huge number of quadrillion different of outcomes and if Jim's ordinal ranking of all of them from best to worst is identical to the social ranking that's fine. That doesn't make Jim a dictator. What makes Jim a dictator is if no matter what, no matter what the possible ordinal rankings of all the individuals are, if the social ranking is always identical to Jim's, then Jim is a dictator. And so Arrow's theorem says we're going to rule out rules that work like that. Okay? And then there's some other ones that aren't as intuitive as the two I just listed, but when you understand what the axioms are claiming, they're not unreasonable. Okay? And so what er arrow proved is that there does not exist a mapping from the individual rankings to a social one that satisfies all of his criteria. Okay, so it's a very general powerful result. And so now um let me explain. So when Eric and Pia Milani are going around telling people, hey, she, you know, her dissertation shows how the application of gauge theory to math uh to economics. We've done things like we've come up with a way to non-arbit solve the problem of, you know, correcting for changing, you know, changing preferences and uh the composition of of goods that are available and things like that to to isolate the purchasing power of money over time. we've solved this in a way that, you know, other theories can't deal with without handwaving. This is clearly the objectively correct way as economists to approach these problems. And so Arrow has him out to breakfast or something and says, "This is interesting, but what you're claiming to have found is impossible." And Eric says, "Why?" And he said, "Well, because you know, mathematically, here I'm paraphrasing, but this is I think what Arrow was saying. what what you're doing is you're saying, "Oh, I found a way to like handle objectively the fact that an individual's ordinal rankings might change over time." So, the fact that the individual ranks various things a certain way at time t, but then at time t2, he might rank them differently and then at time three, he might rank them differently again and so on. And you're saying you've come up with this framework by which you can rationally handle all that and put it into a coherent framework. And I'm saying no, you can't because if you could do that, well then my theorem would be wrong, right? Because in my theorem, I can handle Jim at time one, Jim at time two, Jim at time three. I can just say that's the same as like Alice at time one, Bob at time one, and Charlie at time one. Right? In other words, arrows theorem, you typically think of it as a bunch of individuals at the same time, but mathematically it's the same thing as thinking of the same individual at future points in time if his preferences can change. It's like he's a different guy in the future in various snapshots, right? And so Arrow is saying this doesn't work. So now here, once Eric understood what Arrow's deal was, this is how Eric responded. >> So what I didn't understand was is that he saw that as equivalent. And I said, "No, no, no. I hadn't understood that this is how you were seeing it. There are two pivotal differences between the two situations. This is a false duality. He said, "What do you mean?" I said, "The first thing is your result is a result in social choice theory. There is no market. You're voting on let's say three different candidates or as you say three different outcomes of the world. And what you're saying is that you cannot aggregate a heterogeneous group as if it was a single consistent super individual. So that if everybody agrees on a choice, that choice has to hold. There isn't one person who has dictatorial rights and small changes don't result in violent changes, you know, whatever this list of aims is. And he said, 'And the second, and I said, 'Well, the second is that there is no morphing of Bob into Sally into Arjun into Leticia. That just doesn't exist. And you do morph into your future selves over time. So, you're also not in possession of a path which connects all of the individuals who are being aggregated. And those two things break the apparent duality that you're appealing to. And I'm not going to disagree with you that in their absence you'd be right. You'd be correct. >> But that's why the intertemporal market situation and the intra aagent social choice situation are not in duality. There was like a long silence and he said, "Oh, >> okay." So I think that should be very interesting to Austro libertarian viewers because you see how Eric is responding that on the one hand he's saying oh no your system Dr. Arrow or Professor Arrow isn't relying on the you know the benefits of market prices that there's a sense in which you know to go back to my guy who starts in what Phoenix and ends up in Miami him rolling over the bundle for equivalent market value there he's relying on market prices so that's sort of like a non-object or a non-arbitrary path to in a sense rely on the wisdom of crowds you know if you will I'm speaking intuitively but I hope you guys get the idea and he and and so Eric is claiming the arrow in your theorem people can't rely on the market price system to help with this issue. And then the other element he's saying is you know arrow in your framework these really are distinct people. it's Alice and Bob and Charlie at a given snapshot in time and you show that yeah in general we can't aggregate their preferences and I agree with that and he's saying but there's that's different from saying Jim at time zero gym at time one Jim at time two if if the time increment shrinks to you know using calculus to be into you know infiniteesimal it's like you evolve into your future self and that doesn't seem nearly as big of a jump as just saying you can't compare the preferences between Alice and that you can you can imagine your future self. So even though your preferences might change radically over a 20-year stretch when you get married and move to Miami, your preferences between right now in a minute in the future aren't going to change nearly as much. And so or at least that's the assumption that underlies the math that Eric and Pia Milani are doing. Okay. So I think people might appreciate that element and how Eric responded to Arrow. Okay. Well, I hope I've given you enough of a teaser to get you to go watch the full interview. Thanks for your attention, everybody. See you next time. [music] >> Check back next week for a new episode of the Human Action podcast. In the meantime, you can find [music] more content like this on mises.org. [music] >> [music]