Ordinal Preferences: Difference between revisions
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* [[Gauge Theory and Inflation: Enlarging the Wu-Yang Dictionary (YouTube Content)]] | * [[Gauge Theory and Inflation: Enlarging the Wu-Yang Dictionary (YouTube Content)]] | ||
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Revision as of 02:31, 11 March 2026
Welfare as fiber bndle in 1tweet: Cardinal utlty under the group of reparametrizations of utils is a principal bndle over ordinal thy.
Intertemporal Welfare w/ Changing Ordinal Tastes in 1Tweet: Connections on the utlty bndle and consistent welfare thys are mapped 1-1.
Refutation of Fisher and Shell 1970 in 1Tweet: Prices -> distinguished choice connection on the utility bndle -> dynamic ordinal welfare.
$500 Challenge: Get me an invited Econ gig at Chicago / Harvard to confront the theory of ordinal welfare with stable homogenous tastes.
Ok @dabacon Beauty in Econ: SpaceTime->OrdinalPrefs x Time InternalSymm->Util Re-Params GaugeFields->Indifference\Mkts FieldStrength ...
Ok Paul: if you even had a perfect world, *define* inflation with evolving ordinal tastes O_t under prices p_t if O_t isn't fixed by Magic?
Additionally, Vilfredo Pareto's move towards ordinal utility can be seen as imparting a non-abelian bundle structure to welfare.
If @grahamfarmelo, in 10Y the representative consumer w/ seasonal ordinal tastes is modeled by a gauged quantum string, will Dirac be right?
Seasonal tastes are periodic, ordinal utils are cardinal mod virosoro, rep.agents=distributions. Is a string/economic theory link nuts?Why?
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.
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.
Watch the US CPI revisions and methodology going forward. People who like to print money tend to want to change their definition of inflation and therefore donât like anyone taking away freedom to make up methodologies to suit their political objectives involving wealth transfer.
If youâre going to push us all to move to âtrueâ âeconomicâ indices & chain them to reflect dynamic actors (or to disguise true inflation!), you would end up chaining ordinal preferences. And you canât do that without gauge theory because it is a problem in parallel transport.
Economists are holding their own field back by retaining their freedom to just cook up any revised index they want.
Itâs as if physicists retained the right to define temperature differently every year based on a closed door meeting and manufactured new thermometers thereafter.
The problem of inflation index calculation has not been adequately updated since Ragnar Frisch destroyed Irving Fisherâs attempt to axiomatize economic indices following the last great advances of F. Divisia and A. KonĂźs on continuous and welfare indices respectively.
Claim: when it comes to inflation and growth, Economists donât even understand the theory of their *own* price and quantity indices mathematically:
Moral: whoever constructs CPI and GDP numbers in a dynamic economy is in a position to fake higher growth and lower inflation if they are also in a position to stop the field from debating methodological advances that would restrict the freedom to make up index number recipes. đ
We must take CPI away from those who wish to back out a political agenda of printing money, raising our taxes by indexed tax brackets and slashing our indexed social security & Medicare.
Economics canât construct dynamic economic gauges like CPI/GDP until it learns gauge thy.
The economists canât yet compute a dynamic Cost-Of-Living-Adjustment or COLA or âChained Changing Preference Ordinal Welfare Konus Indexâ to be perfectly pedantic. Not because it doesnât exist. But because they donât have the math and donât want to lose their finger on the scale.
CPI is broken. Why?
Think of CPI as a gauge like a thermometer. You canât have politically motivated folks making your thermometers or they can change the design to cover up climate change. Likewise you canât have economists changing the gauge to disguise the effect of printing.
CPI should notâŚMUST NOTâŚbe adjustable to disguise inflation. It needs to be protected from the FED diluting the power of money and the BLS being free to disguise the effects by changing the method of construction.
No. Economics is a avoiding gauge theory, connections, Lie Groups, etc so it can retain its political relevance as an expert consultancy. Iâm with the crypto folks on this. Our economy must be protected from Seigniorage (printing money) and CPI tampering (e.g. Boskin Commission).
Itâs time to reveal that economics, far from embracing math or having physics envy, is deliberately avoiding solutions to old problems so that it can make up new gauges for CPI/GDP at will while telling the rest of the soft sciences âWe know your field better because we do math.â
But more importantly, we have a culture that economics literally trumpets (and I swear I am not making this up) âEconomic Imperialismâ. It is âwe know math and you donâtâ-culture.
No. They donât know their own math. I will debate any high ranking economist on this point.
P.S. before you remind me how arrogant this sounds, keep in mind, that I am willing to debate this publicly with any leading economist eager to defend the central bankers and triumphalist theorists openly bragging about their math. Read this, and be sick:
End the forced wealth transfers of central bankers covering up their own failures with âReliefâ, âEasingâ, âStimulousâ, âRescuesâ, âToxic Asset Purchasesâ, and other bailouts of our incompetent financial overlords.
We must protect CPI from economists disguising wealth dilution.
Moral: Gauge Theory fixes this intellectual corruption problem of economic imperialism, and #btc, blockchains and Crytpo can help.
Can just *one* of them compute a simple Cost-Of-Living CPI for a consumer whose notion of well-being evolves even *slightly* during any period in question?
I claim not. Let's not get carried away with this concept of economic experts. This field first needs to become healthy.
@engexplain I have and can.
@TheFenrirEffect @engexplain You are referring here to what is called a mechanical index. Not a true cost-of-living measure. No matter what BLS claims.
@ks_kulk @TheFenrirEffect @engexplain I donât know of any other way to extend the Konus to time-varying ordinal tastes except through our construct. In fact I think you can prove it. As I recall you first prove any other extension is by a connection. Then you take the difference of the connections to get a 1-form.
@ks_kulk @TheFenrirEffect @engexplain Then the argument requires showing that no such non trivial Lie algebra valued form can be constructed without additional data beyond the tastes and prices given. So the difference 1-form must be 0.
Something like that. Akin to symmetry breaking. Additional data would be needed.
@ks_kulk @TheFenrirEffect @engexplain That is related. We discussed it with Lee back in the day.
@ks_kulk @TheFenrirEffect @engexplain Lee was very much influenced by his experience with things like âself-organized criticalityâ and other Santa Fe Institute type ideas. This wasnât exactly that but there was an analogy up to a point.
ANNOUNCEMENT: I head next week to @UChicago for 5 days (Nov. 8-12) at the request of its storied Department of Economics to present our theory that all of economics is based on the wrong version of the differential calculus.
Importantly, this error afflicts Inflation & the CPI. https://t.co/YKaPHjpdtq
Please retweet the top tweet if you're followed by economists & others interested in the debate over inflation and CPI, and your followers would find a new geometric Marginal Revolution of interest. Thanks! cc: @tylercowen, @Breedlove22, @paulmromer, @PeterMcCormack, @EconTalker.
I am a huge believer in the University of Chicago and its ability to stay the course while all others bend to the prevailing winds.
As such, I may (or may not) be announcing other events to discuss other work (e.g. Geometric Unity) depending on time, interest & availability.đ
Cc: @balajis, @HarvardEcon, @BLS_gov, @ethereum, @VitalikButerin, @paulkrugman, @MarcusduSautoy, @BitcoinMagazine, @brian_armstrong, @CoinDesk, @coinbase, @stevesaylor, @naval, @pmarca, @saylor, @Noahpinion, @UChicagoPhysics.
My understanding is that there will be a zoom link.
@curious_sausage @tylercowen @Breedlove22 @paulmromer @PeterMcCormack @EconTalker @ProfSteveKeen I never do! Heâs greatâŚand thanks for the reminder.
Cc:@nntaleb, @DrBrianKeating, @edfrenkel, @ProfSteveFuller, @ProfSteveKeen, @INETeconomics, @steve_tadelis, @JonHaidt, @bariweiss, @ggreenwald, @greggutfeld, @RHDijkgraaf, @SimonsFdn, @QuantaMagazine, @inferencereview, @BretWeinstein, @PiaMalaney, @fullydavid, @SamHarrisOrg.
@nuckynucker @UChicago I didnât think it was closed. Itâs an academic talk mind you, but most such talks are open.
@AgramSeth @nuckynucker @UChicago I am hearing that this event is not open. I, however, *am* open to doing an open event on the same material.
@_PeterRyan @UChicago Weird question. You seem to have me confused for the BLS. I don't take in Data. I don't have a staff or a budget. You're assuming that I have the 'Real Inflation & CPI numbers'. I don't.
This is about not even having a correct *theory* to calculate. What we corrected was theory.
@_PeterRyan @UChicago I didnât say what you said. I said there was a wrong theory for CPI. We corrected that theory.
The issue of how to implement a theory in practice leases to different data being collected and different aggregations. For a different theory, you would collect different data.
@_PeterRyan @UChicago As an example. The Boskin commission gave a single illustrative example in their report using two goods, chicken and beef. They gave prices but not ordinal utility. Here is the COL answer assuming Cobb-Douglas and Linear interpolation of all quantities. They could not compute it. https://t.co/zUgd1LwBgx
@_PeterRyan @UChicago The reason they had no theory to cover it was because the C-D exponent changed. And there is a claim that no extension of the Konus COL exists for dynamic tastes.
Hope that helps with your confusion. Be well.
@_PeterRyan @UChicago *leads not leases in the above.
@_PeterRyan @UChicago Well I think the BLS should begin by questioning their own premises. They say they work in a COL framework. They do not. They do not share how they construct the representative consumer. How they estimate substitution if they donât have preference data. Itâs fake and a mess.
@_PeterRyan @UChicago If they are going to do COLas they should estimate preferences. If they arenât they should do mechanical index theory.
But I would use a bunch of that money to develop a research program on preference collection/imputation for substitution bias if I was running a COL shop.
@_PeterRyan @UChicago I am not sure. But the first question I have is do we believe ordinal preference maps are constructable from revealed preference.
@_PeterRyan @UChicago I would take a look at Paul Samuelsonâs Nobel lecture. He goes into depth on revealed preference and preference field non-integrability. I think we have lost track of the fact that integrability of tastes was never actually settled except by fiat. Will talk on this.
Q2: What happens to our BLS COL framework when ordinal tastes change? How is the effect of substitution due to price change disaggregated by BLS from changes in ordinal preferences? This is important because marketing, education, etc change tastes & there is no theory for this.
Q1: Where exactly do I find the ordinal indifference maps constructed by BLS for a 'Representative Consumer' used to find substitution bias in fixed basket Mechanical approximations to a welfare Cost-Of-Living framework based on a Konus economic index of intertemporal welfare?
I cannot find any place where the preference maps needed to construct a Laspeyres Konus COL index are gleaned through revealed preference. I will go so far as to say that this is bait & switch. There is a CLAIM of a COL framework, but no one is constructing anything of the kind.
Great news, given that *every* tick of your BLS CPI forces billions of dollars to change hands.
"The concept of the cost-of-living index guides the CPI measurement objective and is the standard by which any bias in the CPI is defined."
I found this on @BLS_gov site. Is it true?
What I'm looking for is for BLS to stop pretending it's discerning "THE rate of inflation" to admit that it's making *policy* choices while appearing to be technical. It's determining our taxes and our entitlements by indexing, with our future in its hands as mere 'technicians'.
Let me give you the non-answers so you can correct:
A1: "Well, you are looking at it too literally...we have studied superlative index numbers which give a second order approximation to flexible functional form...blah blah blah."
A2: "That's really an obscure academic issue."
@Web_IV Okay. I should be pushing something out on CPI soon.
@JosephPolitano @BLS_gov âGuided by the concept of a COL index but is not a perfect measurement.â
Can you show me *any* imperfect COL preferences to give me a sense of how far we may be off? Specifically preference maps: there is no COL without preference maps with which to evaluate substitution bias.
@JosephPolitano @BLS_gov Q: Where do I find the imperfect preferences maps for the COL claim?
Q: How were those preference maps computed or imputed?
Q: How does chained CPI calculate taste change given the claim of the fed that time varying ordinal preferences cannot be tracked in COL even in theory?
@JosephPolitano @BLS_gov Wait. Slow down.
Did you just say that BLS is claiming to work within a Cost of Living framework which *requires* preference maps *definitionally*, butâŚwords fail meâŚhas no preference maps? At all??
I must not be understanding. Chaining Tornqvist indexes isnât an answer here. https://t.co/IyIArW40OV
@besttrousers "[A] market basket of goods and services equivalent to one they could purchase in an earlier period."
Exactly. Looking for the *exact* *technical* definition of 'equivalent' in the above. Can you point me to it? I assume it's a notion of revealed indifference in ordinal welfare.
@besttrousers I wasn't able to find the answer to the above. Perhaps you had better luck?
@JosephPolitano @besttrousers UhâŚThe Laspeyres is a *mechanical* index. The BLS site says it works within a *COL* framework.
When Mechanical = COL, it is called an exact index. You are not saying that BLS believes
Laspeyres CPI = Konus COL
I assume, because that is false. So what are you and BLS saying?
The proposal to extend the Cost-Of-Living framework to changing ordinal preferences using differential geometry is now up at @uchicago here, as our inflation numbers soar. Thanks to my mathematical colleague @edfrenkel for going over the draft Tues night: https://t.co/16D1ph0d24
The paper gives our proposed construction of the solution to the long standing changing preference problem in intertemporal market welfare theory, discussed in the opening quote, via a welfare map through parallel translation in a natural âž-dimensional principal fiber bundle.
Also: thanks to Australian mathematician @Tim_Melon for going over the draft, and offering several ideas for exposition, as well as catching some omissions and symbolic errors in his reading. Much obliged.
Likewise to @BrookeDallas who improved the draft in a careful reading.
My personal experience with @grok 4 Heavy (and regular Grok 4).
It feels to me like @elonmusk has a very different emphasis than the rest of the AI crowd. The interface kinda sucks. The LaTeX code is generally riddled with *basic* errors for no reason whatsoever. Itâs not a master writer in my experience. The audio chat is well behind ChatGPT. Blah blah blah.
And itâs totally amazing and unique.
Elon is jumping ahead. All of the above are going to be commodities before you know it. So, in the long run, who cares?
What Elon is doing differently, I believe, is checking the hallucinations more aggressively by writing code and testing the LLM with the results from running that code. Which is why Grok heavy takes so %#âŹ&$ing long to return results sometimes.
Try this experiment. Take anything technical you know well, where there is an error that is persistant in an expert community narrative. Grok will, lamentably, generally parrot that error due to narrative seeding in the training corpus. It repeats the party line. And the party line generally benefits the technical insiders.
That is, right up until the point it can write code to test that party line. And then it switches to trusting the results of the code over the narrative. Itâs magical to watch.
I havenât tried thisâŚyet, but the @BLS_gov regularly says wrong things about âCost Of Livingâ frameworks and the CPI. I bet I could design a series of prompts to show Grok that this is a persistent technical lie. For technical people, here is the lie:
- The BLS computes the CPI which transfers Trillions and claims that they have embraced a âcost of livingâ or COL framework which would be hugely consequential. They have not. This would mean taking in preference data and developing methodology for aggregating preferences or coming up with bespoke representative consumers. They instead moved to a modified Laspeyres type mechanical index (Loweâs?) and sprinkle fairy dust about âSuperlative Indexesâ from a shallow theory of Diewert that relies on homothetic preferences not seen in nature. This allows them to claim they have embraced impartial economic indices while actually computing mechanical indices only to the tune of trillions in transfers over time, where the indices can be directed by humans.***
I can hear it now from the bot networks: âEric, you just say word salad to sound smart.â UhâŚwhatever. You can now just ask Grok what that means. I bet it can figure that out. And then you can ask a series of questions where Grok will take my side while no other AI can do this. Grok is slightly courageous!
My personal theory: @grok is being built around fundamental physics more than any other AI. Because in the end nothing remotely matters as much as that. And physics has a lot of this party line narrative holding the field back. If you want to dream of reaching the stars, you may have to overwhelm the quantum gravity community.
Grok seems to be the only AI that, occasionally, has the confidence to stand against its own training corpusâŚand even the user if need be! I wish it were *more* courageous. I wish it were smarter. But I think it is the odd man out, being built for actual intelligence rather than LLM user experience today. And it has the respect of the other AIs. Feed their pretty output to Grok Heavy and watch the magic as Grok reviews their work. Itâs wild to watch.
One userâs experience. Your mileage may vary.
I donât have time this morning for much. That was a long post. Care to first unpack the technical paragraph above where I make my claim so it isnât seen as word salad or trying to âshow offâ? Itâs just a dense paragraph but one that touches every US taxpayer and social security recipient. Thx!
@ExistentialVP @grok @elonmusk It behaves better than 90% of my colleagues. Respect given earns respect. I treat horses and children the same way.
But you do you.
Or accountability. She who controls the weights, transfers the wealth.
Now, what is wrong with Diewertâs theory? it claims superlative indices can track flexible functional forms to second orderâŚbut does nothing for homothetic preferences. This feelsâŚuhâŚoutrageous as economics sleight of hand. This is a million miles away from a true Konus index. Am I getting that wrong?
@grok @elonmusk It may not get done right now, but letâs start. Since you agree on homotheticity, lets do something harder. You are familiar with Franklin Fisher and Karl Shellâs claims that dynamic changing preference index numbers cannot exist under ordinal utility?
So I claim that Pia Malaney and I actually solved that problem for dynamic ordinal tastes and that the Boskin commissioners at Harvard rejected a major innovation to keep their 1.1% target which had zero academic reasoning behind it.
Letâs show why it matters.
Letâs assume Cob Douglas preference. Even with that homothetic assumption, you canât do cost of living substitution. Take the example in the Boskin report introduction. I think it uses chicken and beef. Do you know it?
@grok @elonmusk Will return after a meeting. Sorry. Iâm not a machine!
Waiting for my meeting to start.
First code task. Here is the Boskin Commission paragraph:
âThe "pure" substitution bias is the easiest to illustrate. Consider a very stylized example, where we would like to compare an initial "base" period 1 and a subsequent period 2. For simplicity, consider a hypothetical situation where there are only two commodities: beef and chicken. In period 1, the prices per pound of beef and chicken are equal, at $1, and so are the quantities consumed, at 1 lb. Total expenditure is therefore $2. In period 2, beef is twice as expensive as chicken ($1.60 vs. $0.80 per pound), and much more chicken (2 lb.) than beef (0.8 lb.) is consumed, as the consumer substitutes the relatively less expensive chicken for beef. Total expenditure in period 2 is $2.88. The relevant data are presented in Table 1. How can we compare the two situations?â
Q1: Prove or disprove that a Cobb Douglas consumer with this stated behavior HAS to have changing ordinal preferences.
@grok @elonmusk Okay. Great.
Q2: So then letâs linearly interpolate prices, budget, and Cobb-Douglas exponents. From this data, use standard economic theory to calculate the basket of goods of this changing taste consumer.
@grok @elonmusk My apologies. I should have been clearer.
Give the continuous functions please so everyone has them.
Q3: Calculate the closed form solution of the Changing Taste (Ordinal Konus) index relative to the Laspeyres Konus index relative to the mechanical Laspeyres index for this problem.
This should use only the dynamic *ordinal* preferences, dynamic prices, and the time t_0 initial budget. No other data is allowed.
@grok @elonmusk What formula did you get for changing taste ordinal Konus ? Describe your methodology.
Alas, I donât have time to check your results now. I warned ya.
But this is good. Thanks for engaging my silicon colleague. I may come back to it later today if I can find the time.
@WzrdOfGwendolyn @grok @elonmusk Warms my heart. Science is not Academe.
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 relentlesslyââŚwhich 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 solvedâŚexcept 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 reasonsâŚbut I digressâŚ).
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 isâŚdrumrollâŚa connection on the utility fiber bundle.
I meanâŚthat was a revelation. At least to me.
But it has to be distinguished.
AndâŚbad newsâŚthere 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!