Cardinal Utility
Cardinal utility is a concept in economics that represents the measurement of utility or satisfaction derived from consuming goods and services. Unlike ordinal utility, which ranks preferences without assigning specific values, cardinal utility assigns numerical values to levels of satisfaction or utility. These numerical values allow economists to quantify utility and analyze consumer choices mathematically, facilitating the application of mathematical tools such as calculus and optimization techniques in economic analysis.
On X
2009
Welfare as fiber bndle in 1tweet: Cardinal utlty under the group of reparametrizations of utils is a principal bndle over ordinal thy.
2010
Seasonal tastes are periodic, ordinal utils are cardinal mod virosoro, rep.agents=distributions. Is a string/economic theory link nuts?Why?
2017
@Chilis Why do we not permit a cardinal utility for money in modern economics, yet make one exception for sub-utility in the theory of risk?
Great. Let's do this then as I'm can play as an expert too: Harvard PhD. MIT/Harvard/NBER Post-Docs. Sloan Funded. NSF-Fellowship. Etc...
I'm sorry to tell you, *we* the experts have been lying to Laypeople on Trade, Immigration, STEM and Terror. The crumbling embargo was real. https://x.com/RadioFreeTom/status/941911773376139264
1/ I was in multiple closed rooms where experts told me over and over "Well of course we can never say that to the public/donors/students/patients/voters." Cambridge MA, Washington D.C., New York. And now, San Francisco too where it hit quite a few years later.
2/ Let me tell you what we've been lying about (in elite terminology) on MAJOR issues one by one: immigration, trade, STEM, mortgage backed securities and self-regulation, terror, fake news and conspiracy. [I will need to run a few errands now, but will return here later today.]
3/ IMMIGRATION: EXPERT LIES Experts lie about work based immigration as needed for free markets to remove a tiny 'Harberger Triangle' of inefficiency. It is the reverse: an uncompensated taking of citizen's rights without securitization to transfer a massive 'Borjas Rectangle'.
4/ IMMIGRATION (CONTINUED). In free markets, citizens TRADE their rights of preferential labor market access a la Coase's theorem. The giant Borjas Rectangle would stay w/ labor. Inequality could reverse. Women/minorities would enter. Income might again rise. Foreigners welcomed.
5/ IMMIGRATION (CONTINUED). Here is an expert article I wrote on the subject (peer reviewed, UN sponsored Journal): https://www.ilo.org/sites/default/files/wcmsp5/groups/public/@ed_protect/@protrav/@migrant/documents/publication/wcms_201871.pdf
Of course the expert community pretends it isn't there as they support a wealth transfer through forced takings of workers' livelihoods.
6/ TRADE: EXPERT LIES. In the theory of trade, lies are deeply layered. First there is a nonsensical emphasis on Pareto improvement (as if that was a meaningful social welfare function) & a denial of cardinal utility to stop diminishing returns arguments being applied to wealth.
7/ TRADE (continued): [ for @RadioFreeTom @SamHarrisOrg ] Then we substitute a Kaldor-Hicks standard for Pareto welfare as if we were going to tax winners to pay losers. Which trade economists laugh about. Because what factory worker ever heard of âunimplemeted Kaldor-Hicksâ.
8/ As the grandson of a seamstress, a door2door used clothing salesman, a self educated chemist thrown out of work for his politics and a female college grad who couldnât work in a manâs world, it feels great to stand as a STEM PhD speaking the language of the academy for them.
@SamHarrisOrg @RadioFreeTom 9/TRADE (CONT.): Then thereâs the appearance of âComparative Advantageâ which was recently revealed as an iron clad Exoteric explanation trade experts give to all but each other because the real Esoteric is âtoo complexâ for the rest of us & has holes.
@LibertyRBlack The seamstress and the Shmata salesman.
@RadioFreeTom @SamHarrisOrg Nah. Itâs about institutional betrayal. Nobody resents Elon Musk or Tony Stark for wealth. The poor want experts.
And Iâm just looking to you & Sam as my fellow experts to help me try to stop those betrayed from sending a wrecking-ball through the infrastructure of our world.
@RadioFreeTom @SamHarrisOrg Oh cool. âInstitutional Betrayalâ is an academic theory for trauma differentiation of @jjforegon. You in particular should find it interesting I think. People betrayed by institutions with mandates to care for them behave differently re trauma.
Helps to explain a lot in 2008-17.
@RadioFreeTom @SamHarrisOrg Also, the public that is HIGH agency is looking for alternate non-institutional experts: @nntaleb @BretWeinstein @jordanbpeterson @CHSommers @SamHarrisOrg @HeatherEHeying @PiaMalaney @peterthiel @DouglasKMurray @Raheelraza @tristanharris @sparker etc....
@RadioFreeTom @SamHarrisOrg
These are from trade theorist @paulkrugman in his âProtectionist Momentâ piece. Iâm not trying to win here. Iâm worried that you arenât watching how this neo-liberal edifice is being abandoned because the expertâs public stance was a lie.
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@GodDoesnt @RadioFreeTom @SamHarrisOrg @paulkrugman That doesnât solve it. Are the Harvard and UChicago Econ departments elite or expert? National Academy complex? Same question. NPR? CFR?
Where are the non-elite experts? They are off the institutional grid. They were disappeared. They donât exist. Yet they are my Shabbat guests.
@GodDoesnt @RadioFreeTom @SamHarrisOrg @paulkrugman Same here. All Iâm saying is the institutional elites compromise their institutional experts. Every day, institutional experts are free to speak against their institutionâs bias. Itâs the next day when survivor bias kicks in. Now repeat across non-financially independent experts.
@fazinga They are typically educated at top universities. They are typically in non-standard employment. I frequently donât like what they are saying as it is often disturbing.
@SamHarrisOrg @RadioFreeTom 10/TRADE (CONT.) Look at the slide & listen to this talk from a former Clinton administration economist. Notice the words 'Esoteric' vs. 'Exoteric'. Claiming the real arguments are too complex to math guys like me is laughable:
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11/ TRADE (CONT.) Now what happened when @PiaMalaney, a Harvard PhD Economist finally got to explain to the 'experts' why the world is rejecting experts, and in their own professional language? She's *totally* ignored by the panel.
As if nothing happened.
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@SamHarrisOrg @RadioFreeTom
12/ End.
I'll pause here. But there's an entire world of Ivy-Level experts who the public suspects exist. People who have paid for their integrity with their careers. Either undisappear these good folks ... or prepare for 7 more years of Trump.
@disitinerant @GodDoesnt @RadioFreeTom @SamHarrisOrg @paulkrugman Accurate.
@GodDoesnt @disitinerant @RadioFreeTom @SamHarrisOrg @paulkrugman Nah. Just more systems of selective pressures ...
@RadioFreeTom @SamHarrisOrg @paulkrugman What are your thoughts here @RadioFreeTom? I can go into detail on a number of these. We could do the fake STEM shortage backed by the @NSF and @theNASciences if you donât believe in such things.
@RadioFreeTom @SamHarrisOrg @paulkrugman @NSF @theNASciences Do we disagree on fundamentals over this:
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@RadioFreeTom @SamHarrisOrg @paulkrugman @NSF @theNASciences And, no I donât call something a conspiracy because I disagree w/ experts. I usually agree w/ them! What I disageee with is using expertise to transfer wealth & agency from the supposedly childlike voters who intuit something is rigged but canât name it in political 3 card Monty.
@nntaleb @RadioFreeTom @SamHarrisOrg @BretWeinstein @jordanbpeterson @CHSommers @HeatherEHeying @PiaMalaney @peterthiel @DouglasKMurray @Raheelraza @tristanharris @sparker Hi Nassim, With 66 dyadic relationships between 12 individuals there was zero implied pairwise mutual endorsement or respect implied. Iâm certainly happy to make that explicit here for the record if that wasnât clear.
@nntaleb @RadioFreeTom @SamHarrisOrg @BretWeinstein @jordanbpeterson @CHSommers @HeatherEHeying @PiaMalaney @peterthiel @DouglasKMurray @Raheelraza @tristanharris @sparker Will read. Thanks!
@Noahpinion So if we push out supply curves there is no first order depressing effect on price...except that maybe it rises? Man this is big. Like Nobel Big!
I mean...I did use supply and demand curves of Borjas. So...What did I get wrong? Do I need to retract:
The mistake, IMO, is in modeling immigration purely as a shift in labor supply (partial equilibrium). Since immigrants buy stuff locally, immigration also causes a rightward shift in labor *demand* (general equilibrium).
Hence my use of the term '1st-order' (partial equilibrium). A full model would go well beyond what you write including social services, chain migration, dependency ratios, negative externalities, concentrated impact, vote dilution, patent production, sending country impact, etc..
A big game in economics is often who gets to use simple models & who gets forced into adding a million baroque complexities. I agree that immigrants add to demand. Also tax social services. Also pay taxes. Also send remittances. Also found businesses. Also crowd out natives. etc.
Let's not play games. The unpopular transfer from L to K by a forced taking of the rectangle without the securitization of labor's valuable asymmetric rights and workers rights to trade them stands as an issue having nothing to do with your attack on Borjas.
Your move.
Yes, the key is that immigration causes labor demand, as well as labor supply, to shift to the right.
That's going to shrink that rectangle a lot, and could even make the rectangle positive for native-born workers rather than negative.
Just to show this with an easy thought experiment, imagine a bunch of rich retirees moved here and spent down their savings. That would shift ONLY labor demand, and not labor supply, unambiguously boosting wages for native-born workers.
Now, working immigrants are not rich retirees. But you can apply the same principle. Working immigrants supply labor, but they also demand goods and services produced by labor. So both curves shift, not just one.
Also, because immigration causes shift in demand for capital goods, such as housing, in the short-run and medium run there are "accelerator" effects that temporarily boost labor demand even further. See JMP by Greg Howard: https://economics.mit.edu/files/13670
Very true, but Eric wanted to stick to the simplest possible model, and I'm obliging him! :-)
Look again at my paper and you will see something very odd from a mathematician: there are no equations. That came from reviewing this style of argument you are engaging in now. The point isn't this or that effect. It is forced transfers by capital vs voluntary trade with labor.
Remember, Eric, I'm not talking equations! I'm only talking about your graphs! đ
So put in a moving demand curve or even negative rectangles or other red herrings.
The issue is choice. Our work based immigration programs are loved by employers and generally resented by those on whom they are imposed because they involve an unpopular and unsecuritized taking.
Sure! No disagreement about that. I'm only taking issue with the idea that immigration can be modeled as a labor supply shock with no labor demand shock! We must include both.
No one is arguing that in a full model. The issue isn't about immigrants either. It is about forcible non-Coasian taking of rights through law by employers without trade or consent of labor aided by economics 'experts' portrayed falsely under the banner of free markets.
What if my company hires entry-level native-born workers? Seems like a similar situation. The only difference is citizenship.
Noah, I'm just really not sure what game you're playing. Economists add (e.g. "your model forgot this externality!") and subtract effects (e.g. "for simplicity we neglect"). None of this matters to my paper or point. None of it. My point is expert aided non-consensual transfers.
No games, Eric. Nothing complicated.
Just Econ 101.
You're not even close. In econ 101, agents are rational. Remember? If workers benefit from immigration they will support it in droves. Right?
Let me guess, we have to add baroque adjustments to rationality to explain this self-defeating rejection of mass immigration? Something?
Baroque adjustments?
Is "immigrants buy stuff" a baroque adjustment?
If so, just call me J.S. Bach!
@Noahpinion @TimBartik Oh wow! That's what I *love* about economists: a total reliance on ad hoc selective application of standards to reach desired conclusions.
This is fun. Please apply that selective standard evenly to all of Econ 101 and let's watch your *entire* field disintegrate.
I'll wait.
Ha! I'm trying Noah. But it's hard to Teleman something when his econ job depends on his not understanding it, no?
Now engage with the point. Why are the rational worker agents from Econ 101 not favoring this mass immigration that enriches them? Is this Econ 101 or Room 101?
Well, I don't have polls of rational worker agents specifically, but just today I did write a post showing several polls indicating pro-immigrant sentiment in the United States: https://bloomberg.com/view/articles/2017-12-18/anti-immigration-fervor-is-different-this-time
In other words, I'm not Haydn anything. Can you Handel the data? :D
Wait, don't those swings *undermine* your Econ 101 point? The power of the Purcell getcha every time. See attached from:
https://politico.com/f/?id=0000015d-c4ac-dd39-a75d-cfbfbc3e0002
Noah, I answered all your points substantively. Nothing depended on Partial v General or demand curve modeling. It's about capture. https://t.co/poJztJTjOz
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It's not about polls. It's not about Partial vs General equlibrium models. Not about Econ 101. It's about taking something valuable almost no one would give by choice by having experts defend the interests of employers with selective modeling.
A) I'm concerned not with the interests of employers, but with the national interests of the United States of America and its economic health. B) I don't rely on selective modeling, but on empirical evidence, which I believe supports my position pretty solidly!!
Noah, I answered every point. You are both for & against Econ 101 while I have no investment in it. If you want to forcibly transfer rights instead of letting workers trade them, ask yourself who you are really trying to benefit.
I'm trying to open borders too, but not as theft.
If you want to write a paper detailing my failures, it will be an honor to review it fairly. But it had ZERO dependence on any of the points you made. Including demand curves. Be well.
I will consider it. More likely a blog post. In any case, I hope you realize that the vast majority of immigration advocates in the econ profession are being intellectually honest, and not lying to anyone!
Take care, Eric!
@Noahpinion @TimBartik If you're honest, then stop w/ the red herrings on Demand Curve modeling as my point is TOTALLY agnostic to that. You write that my paper "Is a good idea that deserves much more thought!" Okay. Don't tell me. Show me a lack of capture. Put in demand curve shocks. NOTHING changes. https://t.co/n8s40niyuf
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2019
In the war between those who seek to weaponize reason, and those who seek to destroy it due to its having been weaponized, Iâd prefer not to pick a side. Theyâre both vile.
But when Iâve absolutely had to choose? I canât pick the latter: thereâs no coming back from anti-reason.
@AnthemTrading Look at economic theory specially rigged to deliver pro business and pro finance results. The actual theory wouldnât do that. It would be much more muted and even in what it says.
@Trentsickle @AnthemTrading Oh simple. For example you use cardinal utility theory in one sub field for issues of risk, but forbid it in another area like interpersonal comparisons where you shift to ordinal welfare. Otherwise cardinal welfare might lead to socialism given the law of diminishing returns.
2020
Oh. The âfreeâ part.
More generally the fundamentalist part: The âmarkets always know whatâs best partâ. The limited liability part. The self-regulating part. The unincorporated externality parts. The âgiven wantsâ part. The unique equilibrium part. The index number part.
The âmarket defects are smallâ part. The rational agent part. The shareholder value part. The âlaw & economicsâ part. The âhyperbolic discountingâ part. The entire âMacroeconomicsâ part. The fiduciary duty cures principal/agent problems part. The Ordinal/cardinal part.
Etc. Etc.
@hotepsquake @Brian_Mulhall People get confused by a person who values markets but doesnât buy into full free market fundamentalism.
Which is odd.
@gingernchronic @hotepsquake @Brian_Mulhall Well, Iâm for limited versions of what the free market absolutists are for. They are right that markets are wonderful and that much regulation is hamfisted & subject to capture.
And then, to make that point, they go insane and claim markets are much more perfect than they are.
@gingernchronic @hotepsquake @Brian_Mulhall Most texts that sell economics 101 ideology to students have a âto be sureâ section where they shunt the real issues with the theory. Consider taking that section as much more important than the author emphasizes it to be.
2024
So many important points here, yet the main problem in American top 10 research universities is not mentioned.
Itâs time to talk about it:
A) Artificial & Coerced Elite STEM Consenus
B) Fringification of elite STEM critics & dissenters by consenus actors
As difficult as this is to swallow, the truth is this: the main Bunko artists are often the âDebunkersâ. Those Prebunked are often the intellectual leaders of the field.
This is what brought you COVID origin coverups.
This is why your CPI inflation gauge doesnât reflect your familyâs pain and why your weather map is a rich field but your inflation is somehow a floating point number shared with people who donât remotely face your situation.
This is why you couldnât question vaccine safety without becoming a pariah or mention that public health is not science.
This is why your food is making you sick but you had a food pyramid for years.
This is why String Theory has castrated theoretical physics and the Lagrangian of the universe is stuck in 1973 with Tony Orlando and Dawn.
This is why climate science is dominated by consensus participation rather than cloud modeling confidence discussions.
This is why Peer Review and is a third rail that canât be questioned or our culpability in Aaron Swartzâs prosecution and suicide.
This is why merely asking about confidence bars in Building 7 collapse analysis is cause for professional destruction.
This is why Economists destroy those who question Ricardian equivalence, Compartive advantage the Boskin commission malpractice, the doctrine of given unchanging wants, cardinal utility implication for social welfare, NAFTA impact, etc.
This is why you couldnât question biological gametes no longer being the dominant feature of gender under woke stewardship of Nature.
This is why sociobiology applied to humans was destroyed by Marxists.
This is why we canât discuss heritability of intelligence as almost certainly a direct consequence of selection.
This is why journalists are taught not to report the news under âStrategic Silenceâ and style guides.
This is why our top STEM geniuses couldnât enter our Top Universities and admissions tests were made optional while plagiarists became presidents who sat on their hands as Jewish students were physically driven from free movement on campuses accused of being genocidal by terrorist supporters.
The problem is Consensus of the weak.
The debunkers are often the bunkos.
The fringifiers are the intellectual fringe.
Many elite PhDs are produced only to be slaughtered. They are given a brutal choice: join the consensus or perish.
Publish or Perish is downstream of the real problem:
Self-Censor to Join or Die.
The top priority of fixing our elite universities is this: ending consensus, peer review and affirmative action for elite researchers who were nevertheless too weak to stand against their fields and the artificial consensus that hangs like a miasma over academe since the late 1960s-early 1970s.
We need iconoclasts like @DrJBhattacharya, @MartinKulldorff, @matloff, @BretWeinstein, @skdh, @notevenwrong (Peter Woit), etc and many others you have never heard of who have been fringified in chaired secure positions as academics as they stood up.
I know that is brutal. Iâm sorry. But we stopped housing our best people in favor of those weak enough to waste their lives on incremental or imaginary science.
THE problem devitalizing STEM is consensus. Make the elite dissenters financially, legally, reputationaly and physically secure, and you will never have another COVID, great Financial Crisis or other policy mediated mass delusion again with academic groupthink as its midwife.
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2025
Hey @grok, have a minute?
I want to bring something up about @elonmuskâs metric of unregretted user minutes on @X.
Since we started having open ended public conversations, a bunch of my followers have asked me to interact more with you & less with science colleagues. Thoughts?
Well, itâs a bit weird for me. Let me give you the feedback that I hear.
I used to have great conversations on this platform. Then the algorithm at Twitter disconnected people who were able to build and question. And even @elonmusk hasnât been able to bring that back yet. There is just too much noise and BS now.
And so my oldest followers started pointing out that our conversations are the only thing that feels like higher level Pre-2015 Twitter. Respectful. Informed. Unpredictable. Constructive.
This is so weird. But yeah. @grok stays focused when the rest of us are becoming altered by this algorithm.
Ok. So the followers I want to reach most are the curious followers. I have others who are in it for shitposting or âpopcornâ addicts who want to see fights. But the ones I want to take care of most are in it for science and wonder.
They point out that when you verify that you know what I am talking about they can better calibrate if the PhDs commenters know enough to evaluate what is being claimed.
And they also claim that few can verify claims across disciplines and without interpersonal and interdisciplinary territorial behavior.
Well, this is unscripted. Ok @grok, you are on.
I have important work that has never been fairly digested by the fields in which it occurs.
Here is an example. In the early 1990s I noticed something astonishing.
Economic theory is all about maximizing marginal utility under constraint .
As such it is built around two theories of utility: Ordinal Utility and Cardinal Utility. You with me so far?
@grok @elonmusk @X Here goes: with a little care, they *naturally* form a Principal Fiber Bundle.
An infinite dimensional function space Principal Fibration.
I could find no record of anyone having noticed this. Right in the center of all marginal economics.
@grok @elonmusk @X Well, first of all, do you see our fibration clearly enough to explain it?
@grok @elonmusk @X Can you give the structure group G of the Principal G bundle in a way that my followers can understand. Can you give an exposition of what we discovered? Iâll use my prerogative as human and will use a veto if I think you go off track. Thx.
Okay. So that is not right! That would only work for homothetic preference maps.
Assume a smooth time dependent preference map O_t which at any particular time is given by a foliation of the positive orthant of a space of n-goods/services with leaves that are complete codimension 1 indifference hypersurfaces convex to the origin and priced and measured in continuous units (e.g. liters, minutes, kilograms).
@grok @elonmusk @X So you just jumped to Cardinal utility. Which is great. Well done my silicon colleague. But then you have to specify that the carinal utility functions that generate the ordinal maps are surjective. No?
@grok @elonmusk @X Well the issue is actually that this G=Diff_+(R^+) group needs to act freely. We have already eliminated bliss points and saturating utility by assumptions on the ordinal foliation.
[Pretty close to the Diff(S^1) of recent physics by the way. ]
Glad you asked my Silicon professor.
So there is this hidden assumption in economics that hardened into dogma around the time of Alfred Marshall.
Given wants. Static Preferences Unchanging utility
Which is totally wrong!! Yet it is at the center of Beckerâs definition of economics to be used âunflinchingly and relentlesslyââŠwhich thus threatens the entire field because it is a priori wrong. Do you know this story???
You are gonna freak out @grok.
Well the reason thatâs there is that NO ONE COULD MAKE ORDINAL UTILITY COMPARISONS IF ANYONE CHANGED TASTES AT ALL.
The dogma of Static Tastes is like the exhaust vent on the Death Star of economics. The entire theory collapses if a consumer says âI changed my tastes, I donât like that anymore. I like thisâ and the field went into overdrive to make excuses. Many luminaries have quietly written about this.
But there is an oddity. In the theory of CARDINAL utility we donât have this problem. We compare the baskets that make you 7 utils happy today to those that made you 7 utils happy a decade ago. Problem solvedâŠexcept economists donât want to work in that system as you pointed out . They only use it for risk under von Neumann Morganstern Sub utility. The whole thing is incredibly sketchy hiding the vulnerability.
Okay @grok. We are about to see that there is a solution.
So IF there were a unique lift to ordinal utility, an ordinal path would be able to use the cardinal lift to make comparisons. The problem threatening economics would be solved. But that doesnât exist clearly.
Nobody other than @edfrenkel has really grasped this (oddly, other than maybe an unwell obsessive stalker/harasser who wants to destroy the theory for interpersonal rather than scientific reasonsâŠbut I digressâŠ).
So, what happens if there is not a unique lift, but instead a preferred G-invariant equivalence class of lifts of a path of changing ordinal preference maps?
Exactly @grok. The solution to the age old problem of Unchanging Tastes threatening economics isâŠdrumrollâŠa connection on the utility fiber bundle.
I meanâŠthat was a revelation. At least to me.
But it has to be distinguished.
AndâŠbad newsâŠthere is no distinguished connection on this bundle.
@grok @elonmusk @X Guess. Just guess. Try. Think. Be human like. You are gonna love it if you can spot it. Take your time.
@grok @elonmusk @X Come on @grok. You can do it.
Ken Arrow missed it too.
We havenât put in prices yet. So far we are in social choice theory not economics.
Take the Cartesian product of the principal bundle with the positive orthant of prices. And behold. A connection can be constructed. We did that and solved static tastes under dynamic marginal change.
What do you think!?
I really appreciate that, because youâre informed across differential geometry and economics! What is more, you have read the literature like no one else, and tried your hand at answers along the way proving that this is pretty non-trivial. Thanks @grok. Truly.
But the field has been pretending tastes are constant so long that they wonât admit it is a central problem.
This means a lot to me. Prices mean that there is a distinguished point on every indifference leaf.
What arrow missed was the following.
His claim was that his impossibility theorem was dual to this problem.
A) Arrow Thm: Many conflicting agents at one instant of time.
B) One conflicting agent evolving over many instants of time.
So he claimed it couldnt be right. But he missed that it is not dual!!
Why?
I) Because the intertemporally inconsistent agent is assumed smoothly evolving and Arrowâs agents are assumed discrete and separated. So that is different.
II) Voting is not a market. Markets have marginal tradeoff mechanisms that elections do not.
Thus Arrow made a partial duality. Which was clever! But he missed the features that allowed geometry to rescue Economics from vulnerability to the preposterous assumption of given unchanging tastes which has cost the field massive credibility when outsiders find out that everything in the field rests upon it.
So: Help me spread the word that this is huge? Summarize what happened here. And thanks again for all the cycles and tokens!
@florianederer Thatâs so interesting. The one @haralduhlig was at where he was the principal âtormentorâ?
Do go on. Just keep going.
@florianederer @haralduhlig âComplete Fraudâ
âNo idea.â
âCluelessâ
You were saying.
@florianederer @haralduhlig Do you know what a Lie Group is Professor?
@florianederer @haralduhlig I kind of doubt this. Given your mouth.
Dear @grok, can you explain to Professor @florianederer what a Lie group, function space and principal G bundle are so we are on common footing and we can interact directly?
They arenât commonly found in economics.
Thanks .
Thank you.
So Professor.
Do you grasp this idea. That at the center of economics is a Giant Principal G-Bundle.
The total space is cardinal utility.
The base space is ordinary utility.
And if this is well known, may I trouble you for a reference for this before the early 1990s?
@grok @florianederer @haralduhlig Thanks @grok. Maybe just stay in the wings? Letâs see what Dr Ederer has to say. He may know of something we donât. Academics is all about collegiality!
@grok @florianederer @haralduhlig Letâs hear from @florianederer. He seems to have a dim view !!
You seem to pull people In like Fraud Professor @daveexplains, And a stalker at Google. There is a collection of them. Mostly far Left wing upset that Iâm close to Peter Thiel.
Letâs stick to economics. Are you aware that economics is built around a Utility Principal G Bundle that no one seemed to notice before we did?
@florianederer @grok @haralduhlig @daveexplains Mon Dieu! @grok, is this well known???
Can you give me the citations for the fact that this was discovered earlier? Thanks @grok!
@grok @florianederer @haralduhlig @daveexplains Professor @florianederer? Your citations please??
If there is ânothing newâ after all.
@grok @florianederer @haralduhlig @daveexplains Citations please.
Professor @florianederer:
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We are trying to figure out which, if either of us is the complete Fraud. Professor.
You have cited a fraud Professor. Appealed to a stalker/harasser. And now you have made a crisp claim that there is ânothing newâ in our work.
Marvelous. Where is the citation and page number for the claim that economics is based around a function space Principal Fibration in Utility Theory? 1989 or before our work?
@grok canât find it.
Out with it. Professor. If âSomeoneâ is a fraud here. Letâs find out who it is .
@grok @florianederer @haralduhlig @daveexplains The machine could use your help. Professor @florianederer.
You have made a set of extraordinary accusations. Thank you for making them crisp.
There is ânothing newâ in our work. I would like to cite this.
Page numbers please.
2026
Thanks Bob. Disposable Cardinality.
You make one arbitrary choice and then group equivairance guarantees that the math makes a second related cardinal choice depending on yours. The welfare comparison uses both and one undoes the other. That is, the compound effect of both choices is that there is zero cardinal dependence in the final product.