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I'd like to produce a model that uses very coarse inputs and produces similarly coarse outputs.

For example, if I were estimating personal sources of wealth I might say that in a given year:

    There is a high likelihood that I will earn a moderate salary.
    There is a trivial chance that I will get a high lottery payout.
    There is a small chance I will inherit a large amount of money.
    Therefore...
    Salary = b * m = m
    Lottery = t * b = t
    Inheritance = s * b = s
    Total = m + t + s = m
    Where the values are either big (b), moderate (m), small (s), or trivial (t).

This example is far from perfect but describes how I'd like the front end of the model to look. Obviously there is quite a lot more work required at the back end to ensure that the calculations are coherent.

Is there a name for this kind of model? Or a branch of mathematics that would be useful to draw upon?

The approach probably looks weird, and not very useful when we could just use numbers instead, but there are a few things in its favour:

  • Simple to operate
  • Intuitive verbal descriptions of input and output quantities
  • Easier for non-mathematicians to gain insight into the reasoning and model structure
  • Keeps the focus of analysis on big picture (rather than getting drawn into considering small differences that may be an artefact of input measurement error)
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    $\begingroup$ On the back end, would you be doing actual arithmetic (with numbers) or would you have your own "algebra" (e.g., s * b = s ... with which I am struggling a bit, as I would have guess s * b = m)? $\endgroup$
    – prubin
    Aug 3 at 22:02
  • $\begingroup$ Undecided. Ideally I'd like to reduce the arithmetic to a set of tables but even if this is achieved I'd still be looking to perform some calculations to verify that the tables are appropriate and to work out a cap for the total number of operations that can be chained. $\endgroup$ Aug 3 at 22:52
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    $\begingroup$ @P.Hopkinson, if you have faced with such a case that the input parameters are too vary, Mont-carlo simulation approach would be helpful. Have you tried that? $\endgroup$
    – A.Omidi
    Aug 4 at 8:05
  • $\begingroup$ @A.Omidi sensible suggestion and either monte carlo simulation or decision analysis would be my plan A for dealing with most of these kinds of problems. However, I've got a couple of problems that I think would benefit from a less numerical approach. $\endgroup$ Aug 4 at 10:11
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    $\begingroup$ Check out the Markowitz portfolio allocation model. It adds an element that I think is essential in this kind of decisionmaking, namely a risk aversion parameter. Would you be indifferent between a 100% chance of $10 and a 10% chance of $100? $\endgroup$
    – Max
    Aug 4 at 23:53

2 Answers 2

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It's not a direct (or even necessarily close) match to what you have described, but you might be interested in the analytic hierarchy process (AHP). There's some math under the hood, but as I recall what the decision maker sees is just stuff along the lines of "which of these is better/more important/more terrifying" and "by how much on a 1 to 5 scale, where 1 is "pretty much a toss-up" and 5 is "absolutely this one over that one". (I'm approximating from fuzzy memories here.)

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  • $\begingroup$ Thanks! It isn't what I was aiming for but it might be a better way to approach some of the problems. $\endgroup$ Aug 8 at 15:15
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A (very simple) example of coarse modelling is a Risk Assessment Matrix.

This has a few different variations but typically the severity and likelihood of individual risks are scored on a scale of one-to-five, multiplied and the result is colour coded with a verbal description to indicate the overall threat posed by each risk.

Personally I think that standard implementation is numerically dubious but it offers an example of a verbal/numerical hybrid model that is popular in the real world.

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