Posts tagged with daniel ellsberg

I loved being a rifle company commander. Having the responsibility for 211 men. Being totally in charge of their welfare and their training. That was the happiest period of my life, professionally, looking back on things.




lembarrasduchoix asked:

thank you for the introduction to Newcomb’s paradox! Could you do a post on your favorite paradoxes? 

 
The decision theory paradoxes I’m familiar with are:
Ellsberg Paradox— Theorists encode bothsituations with unknown probabilities, such as the chance of extraterrestrial intelligence in the Drake Equation or the chance of someone randomly coming up and killing you, and
situations that are known to have a “completely random” outcome, like fair dice or the runif function in R,
the same way. However the two differ materially and so do behavioural responses to the types of situations. 
Allais Paradox — The difference between 100% chance and 99% chance in people’s minds is not the same as the difference between 56% chance and 55% chance in people’s minds. (In other words, the difference is nonlinear.) At least when those numbers are written on paper.Prospect theory proposes the following [0,1]→[0,1] function describing how "we" perceive probabilities(Remember that it shouldn’t be taken for granted that everybody thinks the same, or that it’s possible to simnply re-map a person’s probability judgment onto another probability. Perhaps the codomain needs to change to something other than [0,1], for example a poset or a von Neumann algebra.)
Newcomb’s Paradox — This one has a self-referential feel to it. At least as of today, the story is well told on Wikipedia. The Newcomb paradox seems to undercut the notion that “more is always preferred to less” — a central tenet of microeconomics. However, I believe it’s really undercutting the way we reason about counterfactuals. I actually don’t like this one as much as the Ellsberg and Allais paradoxes, which teach an unambiguous lesson.
 
Despite the name, they’re notreally paradoxes. They are just evidence that probability + utility theory ≠ what’s going on inside our 10^10 neurons. I don’t think Herb Simon would be surprised at that. (Simon is famous for arguing to economists that “economic agents” — both people and firms — have a finite computational capacity, so we shouldn’t put too much faith in the optimisation paradigm.)
You can find out a lot more about each of these paradoxes by googling. As is my way, I’ve tried to provide the shortest-possible intro on the subject. Twenty-two slides opening the door for you.
I also think it’s interesting how the calculus disproves Zeno’s paradox and how a proper measure-theory-conscious theory of martingales disproves the St. Petersburg paradox. I also think Vitali sets and the Banach-Tarski paradox are compelling arguments against the real numbers. Particularly since everything practical is accomplished with (finite) floats, I’m not sure why people hold on to ℝ in the face of those results.
But personally, I’m more interested in decision theory / choice theory than those pure-maths clarifications.
 
I know I am forgetting several interesting paradoxes which have revolutionised the way people think. (Zeno thought his reasoning was so revolutionary that he concluded, via modus tollens, that the world didn’t actually exist. One of many religions that has come to such a belief, not to mention Neo and Morpheus thought so.)If I’ve neglected one of your favourite paradoxes, please leave a comment below telling us about it.

lembarrasduchoix asked:

thank you for the introduction to Newcomb’s paradox! Could you do a post on your favorite paradoxes? 
 

The decision theory paradoxes I’m familiar with are:

  • Ellsberg Paradox— Theorists encode both
    1. situations with unknown probabilities, such as the chance of extraterrestrial intelligence in the Drake Equation or the chance of someone randomly coming up and killing you, and
    2. situations that are known to have a “completely random” outcome, like fair dice or the runif function in R,
    the same way. However the two differ materially and so do behavioural responses to the types of situations. 
  • Allais Paradox — The difference between 100% chance and 99% chance in people’s minds is not the same as the difference between 56% chance and 55% chance in people’s minds. (In other words, the difference is nonlinear.) At least when those numbers are written on paper.
    image
    Prospect theory proposes the following [0,1]→[0,1] function describing how "we" perceive probabilities
    I tried to edit this to make it more readable, really I should just redo it in R myself.(Remember that it shouldn’t be taken for granted that everybody thinks the same, or that it’s possible to simnply re-map a person’s probability judgment onto another probability. Perhaps the codomain needs to change to something other than [0,1], for example a poset or a von Neumann algebra.)
  • Newcomb’s Paradox — This one has a self-referential feel to it. At least as of today, the story is well told on Wikipedia. The Newcomb paradox seems to undercut the notion that “more is always preferred to less” — a central tenet of microeconomics. However, I believe it’s really undercutting the way we reason about counterfactuals. I actually don’t like this one as much as the Ellsberg and Allais paradoxes, which teach an unambiguous lesson.
 

Despite the name, they’re notreally paradoxes. They are just evidence that probability + utility theory ≠ what’s going on inside our 10^10 neurons. I don’t think Herb Simon would be surprised at that. (Simon is famous for arguing to economists that “economic agents” — both people and firms — have a finite computational capacity, so we shouldn’t put too much faith in the optimisation paradigm.)

You can find out a lot more about each of these paradoxes by googling. As is my way, I’ve tried to provide the shortest-possible intro on the subject. Twenty-two slides opening the door for you.

I also think it’s interesting how the calculus disproves Zeno’s paradox and how a proper measure-theory-conscious theory of martingales disproves the St. Petersburg paradox. I also think Vitali sets and the Banach-Tarski paradox are compelling arguments against the real numbers. Particularly since everything practical is accomplished with (finite) floats, I’m not sure why people hold on to  in the face of those results.

But personally, I’m more interested in decision theory / choice theory than those pure-maths clarifications.

 

I know I am forgetting several interesting paradoxes which have revolutionised the way people think. (Zeno thought his reasoning was so revolutionary that he concluded, via modus tollens, that the world didn’t actually exist. One of many religions that has come to such a belief, not to mention Neo and Morpheus thought so.)
And the guy sliced up a speeding car tyres with a samurai sword. You really can't argue with someone who does that.
If I’ve neglected one of your favourite paradoxes, please leave a comment below telling us about it.


hi-res




While science rightly uses empirical evidence (facts) as the ultimate arbiter of truth, those who experiment and analyse field data usually only credit or discredit ideas / frameworks that some theorist has previously invented.

Science: We finally figured out that you could separate fact from superstition by a completely radical method: observation. You can try things, measure them, and see how they work! Bitches.

Tagline. Science: We finally figured out that you could separate fact from superstition by a completely radical method: observation. You can try things, measure them, and see how they work!

Hence the name “theory-killers” for experimental physicists.

 

Where do these theories come from, though? My own experience and my observations of others lead me to believe that an economic theorist’s deep creative centre is informed, flavoured, shaped, and sullied by her own personal experiences, biases, stereotypes, and assumptions about what’s normal. If you talk to people who have deeply integrated into their psyche concepts like “opportunity cost”, “rationality”, “search”, “strategy”, “information”, “evolution”, “optimisation”, and so on, and you disagree with this statement, please tell me.

(For example: a professor of game theory told me that he cannot fathom the motivations of a suicide bomber. He can’t fathom them, so he can’t model them, so we have no theory to predict and curtail their bombing behaviour.

Example 2: Do you think Daniel Ellsberg started running psychological experiments at random until he stumbled upon his famous "Ellsberg Paradox"? No, he had the idea in his head that these two kinds of “uniform distribution” should be different—perhaps getting the idea from Keynes or Frank Knight—and
 then tested the idea.)

Since there’s a "lone genius" limit on novel* economic theories, a finite upper bound follows on how much fact-checking can improve a theory’s soul. Although one can certainly benefit from pulling on threads, reading monographs, looking at data tables and so on, ultimately I believe deep insights come from the same brain process that generates the fallacy of lack-of-imagination (argumentum ad ignorantiam). Just as people form judgments by the “Does this fit with what can I imagine” test, so too—says I—do economic theories rise from the same murky pit. Personal experiences where we’ve taken in reams of high-dimensional streaming data (like at work) feed this imaginative capacity, such that we can run and assess counterfactual dramas in our heads (sort of like a Monte Carlo). "What if the vendor had said this to my boss? Nah, she wouldn’t have reacted that way. Not like her." There are some biologists who say that our brains have an especial capability to think through such human dramas. (And in writing that sentence I used the same often fallacious imaginative faculty.) The imaginative faculty is abused by cheap stereotypes—

Ideas can be checked against experiences and personal symbols much more easily than against a tome of facts. Since theoretical creativity proceeds in inspirational flashes and needs to run verificational checks at the speed of imagination, only the checks that can be done very quickly influence the creative process.

* Of course most theories derive from the joining of ideas from the existing literature. But those aren’t “novel” ideas.

It’s my conviction, therefore, that theoretical economists would come up with better theories if they spent more time in “the real world” and less time thinking about isomorphisms.

 

The problem is more acute in economics than in physics, because economic theories are much harder to kill (so many alternative explanations / dismissals one can retreat to) — which shifts some of the burden of correctness to the theorists. If you know that

  1. a compelling idea (like “Those who spend other people’s money will be wasteful”) will be hard to falsify;
  2. it will spread memetically through influential minds;
  3. it’s important to get this right, or else the former USSR and Latin American countries (𝓞 1 billion people) will be screwed over by your idea

then you would be quite reasonable in polishing & perfecting a theory—working to cleanse yourself of biases and myopia, asking yourself if what you’re writing is really quite true, what are the underlying assumptions, and so on.

The problem is also more important for economic theorists to address because those who theorise about the human mind have, erm, direct access to the thing they’re theorising about.

image

The difficulty of killing an economic theory has been discussed much elsewhere:

and if you read the things I read, you’ve probably had similar thoughts as:

  • "Really? It took this long for ‘neoindustrial’ ideas like ‘The economics of serfdom differ from the economics of a modern web programmer’ to become acceptable?" And neo-industrial uses a totally neoclassical approach but just in a meta context—rational response to the incentives that come with a social framework, or perhaps game theory rationally optimising evolution rather than individuals.
  • "Really? People think you can just use a probability distribution to model a person’s or a firm’s thought-process?"
  • "Really? We just shrug off counterevidence to the theories by saying they’re only models?”
  • "Really? Real numbers and Lagrangians are underlying all of this?”
  • "Really? It’s so controversial that utility is derived from relative and not absolute wealth?”

and many others. Point being, if you are educated on this stuff, then I’m sure you can see how the Slutzsky decomposition is a compelling advance in “research technology”, but can’t carry over as-is to the ultimate subject of interest, which is human behaviour and feelings.

 

Am I just carping? A bit, but I also can propose something like a solution. If those who give out grants for economic research could be convinced that

  • business experience
  • time spent in poor countries
  • experience in a variety of economic roles outside of academia

were important indicators of future relevancy and correctness of research—along with knowledge of a body of literature, knowledge of mathematical/statistical/experimental methods, consulting/political experience, and/or a Ph.D.—then up-and-coming economists would have the incentive to spend time in “the real world” and find out, in a personal way, what the people they theorise about go through.