Ken Arrow
2009
Arrow's impossibility theorem can be seen as a cohomological obstruction to constructing representative consumers without magical thinking.
There's plenty of beauty in Economics Paul, but that works okay: Coase's Thm, Arrow's Impossibility Thm, Fixed Pt Thms, etc...
VaR -> Kayfabe | Coase -> Economics | Stable Tastes -> Kayfabe | Arrow's Theorem -> Economics | Rep. Consumer -> Kayfabe | B. Scholes-> Econ
Imagine you say to Ken Arrow: "Well you still need a voting system that gets a group to act like an individual." He says: Fuggedaboudit.
2010
Topological Arrow Impossibility theorem for a circle: There is no continuous map from S1xS1 onto its diagonal restricting to the identity.
2017
No economist impressed me one-on-one more than Ken Arrow. He was so generous with his genius helping us with gauge theoretic economics. #rip https://t.co/oeRZ6KWOy4
@disitinerant @tonofbuns @BretWeinstein @primalpoly Iâll take 1 pass at it. Scientists who study optical illusions, cognitive biases, Goedel incompleteness, Arrowâs impossibility theorem etc are tempted to abandon shared objective reality as substrate. Yet these folks cannot be the core. They are the adjustment to shared reality.
2018
@kierhanratty @skdh Arrow? Marshall? Nash? Von Neumann? Black-Scholes-Merton-Bachelier? Modigliani? Coase?
It's about the same to me.
2019
@kmele @FreeSpeechAppar @AndrewYangVFA Damn. That Ken Arrow is really starting to piss-me-off.
Economists: Ken Arrow taught us we canât aggregate rational preferences into the preferences of a mythical super-individual to represent society.
Also Economists: Konus taught us that Inflation is measured relative to agentsâ PERSONAL preferences.
BLS Economists: US CPI is 7.9%
âNone of the usual criteria that **real** experts use says that we are in a recession.â - Prof. @paulkrugman
Have you dealt w/ economics professionally as an academic from another field? If not, itâs exactly like this: âReason, fact, analysis, total bullshit, fact, a lie, fact.â
CNN's @brianstelter: "Can we dispense with the recession debate? Are we in a recession, and does the term matter?
Former Enron adviser @PaulKrugman: "No, we arenât and no, it doesnât."
In fact the truths, insights, facts, analysis, etc. are pretty compelling. And they are the majority of what economists circulate.
And then the conversation turns, and out comes the superior dismissive insufferable gaslighting.
And you think: âWhy ruin analysis with psychosis?â
I was lucky enough as a younger man to get to know Ken Arrow and Paul Samuelson slightly. They didnât have this trait. Talking to Arrow or Samuelson was like talking to a research mathematician, biologist or physicist at the time. It wasnât switching between reality & propoganda.
So my model is that Economics really changed. The old guys who did the most to lay the foundations were a lot less high on their own supply. They welcomed interactions with other disciplines. It feels like the 1970s transformed economics into something less intellectually honest.
Great question. Inflation is SUPPOSED to be a group valued field. In the case of bilateral trade itâs an element of GL(2,R) although the economists havenât gotten there yet. But it is mostly not a field on Geography. Itâs a field on path, Loop, preference and geographic spaces.
I have heard you say inflation looks more like a heat map, than a single number. Would you say a heat map by both geography and product? Good morning
Q1: Why is it a field on Preferences?
A1: Because a true COLA is not an index on baskets (mechanical index) but on welfare derived from baskets (economic index). BLS misrepresents CPI being COLA-driven abusing work of Erwin Diewert on Superlative indices. A COLA prices WELFARE.
Q2: Why is inflation a field on LOOP spaces of preferences?
A2: Tastes are seasonal. In USA âWe never spill Egg Nog on our bikinis.â What you both want & price HAS to be made seasonal to avoid the Cycling Problem (Holonomy) in index number thy. So we have LOOPS of tastes/prices.
A2 Continued: If you donât make loops of tastes and prices, you will show meaningless regular inflation if prices, quantities and tastes Circle back to their initial Jan 1 values. This confuses economic experts (Like Diewert) when it comes to chain/path indicesâŚwhich is up next.
Q3: Why is inflation a field on Path Spaces of Looped Preferences/Prices?
A3: Loosely, Index number theory really died w/ work of Ragnar Frisch (rightly) destroying Irving Fischerâs misguided work on axiomatic tests for bilateral (2 period) mechanical index numbers. Hereâs why.
A3 Cont.: As Ken Arrow challenged us âFrisch showed we canât solve the bilateral index problem because a single agent at multiple points in time is *exactly* dual to multiple agents at a single instant of time. Which is exactly my âImpossibility Theoremâ in Social Choice. QED.â
A3 Cont.: Our response: âAh. That would be true but for 2 differences! First, Indices live in markets with *prices*. Our methods *donât* live in social choice voting paradigms. Second, agents evolve into their future selves via paths. Thereâs no âmorphing pathâ in social choice.â
A3 Cont.: âThis is why index numbers will one day be properly understood as parallel translation in Fiber Bundles wrt Economic Gauge Potentials. But Zoe doesnât become Cam morphing into Fatima when voting. So parallel transport is unavailable. Even in topological social choice.â
Q4: Why do you say indexes are Group-Valued? Isnât inflation just a number?
A4: Here goes. In the most famous case you *can* get away with a number. But that 8.9% style CPI nonsense is actually secretly a 1x1 matrix in GL(1,R). And that actually matters! Why? B/c Non-linearity.
A4 Cont.: Only 1x1 matrices commute. NxN matrices do not! And if A.B isnât B.A, the system goes non-linear. So if you have 2 countries with 2 currencies, the commutative case doesnât work at all. You need to use Freeman Dysonâs system of Time Ordered Products to save inflation.
A4 Cont.: But even in the case of one Currency like the Dollar, economists donât get the group issue. True COLAs are valued in an *infinite* dimensional non-commutative group called DIFF_0(R^+) equivalent to increasing differentiable functions from 0â>âž reparameterizing âUtilsâ.
Q5: So letâs see. Inflation is a field like temperature. But a field in a fiber bundle over âž-dimensional path spaces of loops of preferences/prices valued in non-commuting groups leading to non linearities not addressed by economists? What about actual geography!â
A5: Fair. đ
A5 Continued: Prices vary by zip code. So throw in a geographical map as a reward for getting to the end!
Just try to understand my bewilderment when @BLS_gov says 7.9% and everyone pretends that they arenât really raising taxes & slashing social security. Youâre being screwed.
Your life savings are being stolen through seignorage as you are being taxed into oblivion with your social Security beaten to a pulp. Meanwhile @paulkrugman and Robert Reich are playing with finger paints.
If you want help, do let me know. But I canât watch this massacre again.
Either do something to save yourselves or continue to sit & wait to be eaten by the Fed and @BLS_govâs fakely precise single number CPI.
Iâll debate ANYONE on this high enough up for you. But I canât watch & Iâm done w economist abuse & yelling at clouds.
Thanks for asking.đ
Note Added After Posting:
I responded to a question about proper index construction here. Would love to have Prof @RBReich thoughts. Maybe even a debate on CPI and measurement?
Great question. Inflation is SUPPOSED to be a group valued field. In the case of bilateral trade itâs an element of GL(2,R) although the economists havenât gotten there yet. But it is mostly not a field on Geography. Itâs a field on path, Loop, preference and geographic spaces.
who's your favourite economist?
François Divisia or Ken Arrow or Paul Samuelson or Satoshi or Ronald Coase etc.... would be easy to defend.
But Graciela Chichilnisky or Bert Balk would be more interesting offbeat choices I could defend. I don't think they got their due for what is coming in mathematical econ.
He was very supportive of me. If I had to make a single choice it might be him or Samuelson.
Yes, but when I said âbrightest mindsâ I meant it.
2025
Unlike Paul Samuelson & Ken Arrow, Gary Becker was cut from different cloth. He reminded me of my dealings w/ Lenny Susskind, Larry Summers, Brad Delong, Jagdish Bhagwati, Ed Witten, Mildred Dresselhaus & others, so possessed by ideology that academic reason could just vanish.
In my recent interview of @EricRWeinstein, he referred to "stable preferences" as Achilles' heel of neoclassical econ. Exhibit A is this famous quote from Becker. At face value, Becker is saying a model w/dynamic preferences wouldn't even be economics anymore. Do others agree?
Gary wasnât stupid. He was just on a failed dead end mission of intellectual suicide. He was shrewd, creative and wildly wrong about human beings at levels that are difficult to convey.
And so it fell to him to tell the ultimate academic lie on behalf of his profession of economics: all humans have stable unchanging tastes.
So dumb. So unethical. Such an intellectually pathetic move. But then he was refereeing the same game within which he was flagrantly cheating.
He was easy to beat in any argument not judged by ideologues. But in Chicago and elsewhere they pretended this was genius rather than a flagrant attempt at patching the vulnerabilities that will sink Neo Classixal economic imperialism.
He lived, and died, in a protected world, not unlike an academic Hermit Kingdom. An intellectual North Korea where people were always bowing before him if they wanted to survive and needed his favor.
But the vulnerability is real. And believe me, he and I both knew it. It was tense as hell dealing with him for a reason:
The fiction of Stable Tastes is THE analog of rhe exhaust vent on the Death Star of NeoClassical Economjc Imperialism. His lifeâs work.
I look forward to showing you just how that little exhaust vent works.
Related Pages
- Arrow's Impossibility Theorem
- Borjas Rectangle Theory
- Boskin Commission
- CPI
- François Divisia
- Gauge Theory
- Immigration
- Paul Samuelson
- Ronald Coase
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