Revisiting the foundations of randomness and probability

30 Apr, 2019 at 14:17 | Posted in Statistics & Econometrics, Theory of Science & Methodology | 5 Comments

dudeRegarding models as metaphors leads to a radically different view regarding the interpretation of probability. This view has substantial advantages over conventional interpretations …

Probability does not exist in the real world. We must search for her in the Platonic world of ideals. We have shown that the interpretation of probability as a metaphor leads to several substantial changes in interpretations and justifications for conventional frequentist procedures. These changes remove several standard objections which have been made to these procedures. Thus our model seems to offer a good foundation for re-building our understanding of how probability should be interpreted in real world applications. More generally, we have also shown that regarding scientific models as metaphors resolves several puzzles in the philosophy of science.

Asad Zaman

Although yours truly has to confess of not being totally convinced that redefining​ probability as a metaphor is the right way to go forward on these foundational issues, Zaman’s article​ sure raises some very interesting questions on the way the concepts of randomness and probability are used in economics.

Modern mainstream economics relies to a large degree on the notion of probability. To at all be amenable to applied economic analysis, economic observations have to be conceived as random events that are analyzable within a probabilistic framework. But is it really necessary to model the economic system as a system where randomness can only be analyzed and understood when based on an a priori notion of probability?

slide_1When attempting to convince us of the necessity of founding empirical economic analysis on probability models,  mainstream economics actually forces us to (implicitly) interpret events as random variables generated by an underlying probability density function.

This is at odds with reality. Randomness obviously is a fact of the real world (although I’m not sure Zaman agrees but rather puts also randomness in ‘the Platonic world of ideals’). Probability, on the other hand, attaches (if at all) to the world via intellectually constructed models, and a fortiori is only a fact of a probability generating (nomological) machine or a well constructed experimental arrangement or ‘chance set-up.’

Just as there is no such thing as a ‘free lunch,’ there is no such thing as a ‘free probability.’

To be able at all to talk about probabilities, you have to specify a model. If there is no chance set-up or model that generates the probabilistic outcomes or events — in statistics one refers to any process where you observe or measure as an experiment (rolling a die) and the results obtained as the outcomes or events (number of points rolled with the die, being e. g. 3 or 5) of the experiment — there strictly seen is no event at all.

Probability is a relational element. It always must come with a specification of the model from which it is calculated. And then to be of any empirical scientific value it has to be shown to coincide with (or at least converge to) real data generating processes or structures — something seldom or never done.

And this is the basic problem with economic data. If you have a fair roulette-wheel, you can arguably specify probabilities and probability density distributions. But how do you conceive of the analogous nomological machines for prices, gross domestic product, income distribution etc? Only by a leap of faith. And that does not suffice. You have to come up with some really good arguments if you want to persuade people into believing in the existence of socio-economic structures that generate data with characteristics conceivable as stochastic events portrayed by probabilistic density distributions.

We simply have to admit that the socio-economic states of nature that we talk of in most social sciences — and certainly in economics — are not amenable to analyze as probabilities, simply because in the real world open systems there are no probabilities to be had!

The processes that generate socio-economic data in the real world cannot just be assumed to always be adequately captured by a probability measure. And, so, it cannot be maintained that it even should be mandatory to treat observations and data — whether cross-section, time series or panel data — as events generated by some probability model. The important activities of most economic agents do not usually include throwing dice or spinning roulette-wheels. Data generating processes — at least outside of nomological machines like dice and roulette-wheels — are not self-evidently best modelled with probability measures.

If we agree on this, we also have to admit that much of modern neoclassical economics lacks sound foundations.

When economists and econometricians — often uncritically and without arguments — simply assume that one can apply probability distributions from statistical theory on their own area of research, they are really skating on thin ice.

This importantly also means that if you cannot show that data satisfies all the conditions of the probabilistic nomological machine, then the statistical inferences made in mainstream economics lack sound foundations!​

5 Comments

  1. “Those in the grip of the methodological inhibition often refuse to say anything about modern society unless it has been through the fine little mill of The Statistical Ritual. It is usual to say that what they produce is true even if unimportant. I do not agree with this; more and more I wonder how true it is. I wonder how much exactitude, or even pseudo-precision, is here confused with ‘truth’; and how much abstracted empiricism is taken as the only ’empirical’ manner of work…

    One great lesson that we can learn from its systematic absence in the work of the grand theorists is that every self-conscious thinker must at all times be aware of — and hence be able to control — the levels of abstraction on which he is working. The capacity to shuttle between levels of abstraction, with ease and with clarity, is a signal mark of the imaginative and systematic thinker..”
    ― C. Wright Mills, The Sociological Imagination

    • Great quote 🙂

  2. “Randomness obviously is a fact of the real world ”
    .
    Is it? Or is it a figment of our imagination?
    .
    Probability is an intellectual construct.
    .
    I cannot take a telescope and look at a lump of probability or randomness in some distant galaxy.
    .
    There is no such thing as a probability or randomness meter which I could use to measure probability or randomness.
    .
    I can take meter, however, for instance, and measure a current, a voltage, resistance temperature etc., etc..
    .
    Probability is not a physical property of the real world.
    .
    It is an entirely concocted means of explaining what we cannot otherwise explain.

    • I would like to add another point.
      .
      I believe the notions of randomness and probability have distracted us from studying phenomena which we dismiss as “just” random.
      .
      Who knows what we might discover in what we have discarded and essentially trivialized.
      .
      Yet undiscovered fundamental properties of nature my well be hidden in so-called randomness.
      .
      I would argue that every discernible phenomenon has a cause and hence is worthy of close scrutiny and study even if it is deemed random.

  3. According to Prof. Syll:
    “Randomness obviously is a fact of the real world”
    “in the real world open systems there are no probabilities to be had”
    .
    Sadly there are fundamental, foundational problems with these statements. These stem from the abstruse philosophy which Prof. Syll evangelises, namely “transcendental dialectical critical realism”.
    This philosophy claims that there is a truer and more real world beyond the error-prone superficial world of everyday experience and science. This “deeper reality” is supposedly a mind-independent, objective, external world, unobservable by our naked senses, i.e. without scientific theories and instruments. Allegedly there is “intransitive domain of knowledge” which has mysterious links with the world of everyday experience through “hidden generative structures” and “warranted export certificates”.
    .
    Prof. Syll, for the benefit of readers like myself who are unclear what this “deeper reality” might be, it would be very helpful if you could answer the following simple questions.
    ———-
    1. Do you have direct personal knowledge of “deeper reality”? Or is your knowledge based on second or third hand hearsay evidence?
    2. What was your earliest encounter with “deeper reality”? Was this an intense, exciting epiphany?
    3. Do you experience/enjoy “deeper reality” only occasionally, or on most days, or continuously?
    4. What are the commonest subjects of these experiences?
    5. Are these encounters accompanied by emotions or sensations. e.g. smell, pleasure, pain, joy, fear?
    6. How do you distinguish your knowledge of “deep reality” from ordinary knowledge?
    7. How do you distinguish your knowledge of “deep reality” from from fantasies and dreams?
    8. Can you reference any good accounts of “deep reality” by ordinary people?
    ——–
    9. Did “deeper reality” exist before the evolution of homo sapiens? Or before life on Earth? Or before the Big Bang?
    10. Could “deeper reality” be the same as what astronomers call “dark matter”? Or gravity?
    11. Or does “deeper reality” exist in a fifth or higher dimension beyond the reach of current science? Or perhaps in a parallel universe?
    12. Does the notion of “deeper reality” have any practical implications for science or everyday life? Or is it completely unnecessary and superfluous, i.e. a violation of the principle of Occam’s Razor?


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