9. “All Probabilistic Methods Assume a Subjective Definition of Probability”
by Mark R. Crovelli
Abstract: In previous publications on probability, I have followed I.J. Good in arguing that probability must be defined subjectively if we accept that the world is causally deterministic. In this article I go significantly beyond this position, arguing that we are forced to accept a subjective definition of probability if we use any probabilistic methods at all. In other words, all probabilistic methods tacitly assume a subjective definition of probability.
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Probability is by definition some measure of uncertainty, and it must be subjective because some uncertainty attaches itself to everything which we regard as a cause. That we are burdened by various degrees of uncertainty however, does not mean that we know nothing. For instance, Einstein believed the moon was still there even when he was not looking at it. But it was only highly probable that the moon was still there. The modern example of this is the question of the man in the forest. If a man is in a forest and he speaks….and his wife is not present, is he still wrong? And there is only a high probability that he is still wrong.
Not sure what this has to do with libertarianism, or anything really.
The link to libertarianism, Kris, is methodological and epistemological. We libertarians, (Austrians, anyway), are extremely critical of empiricism as a justifiable epistemology for the social sciences, and probability is a central cog of empiricism today. Specifically, probability as it is utilized in conjunction with statistics (i.e., inferential statistics) is the go-to method for empiricists today. Pointing out that the central cog of empiricism today is no more “objective” than economic value undermines much of what passes for social science today.
Sounds like a good topic for a paper.
Indeed!
Thank you very much for this.
While interesting, the core contention of the paper is irrelevant to operational statistical research: so what if different mathematicians (who are not philosophers) disagree vehemently as to whether probability is subjective (observer-variant) or objective (observer-invariant)… seems to me that they have too much time on their hands and have fallen for the typical academic problem of becoming more passionate the less important the issue at stake.
One thing that can NOT be concluded from this paper, is that statistical/positive economics is using tools that have sketchy underpinnings… because it does not matter one iota if probability is taxonomically ‘objective’ or not – it only matters whether or not the inferences drawn from sample data are (a) representative [the core 'thrust' of statistics and probability]; and (b) useful.
In a sense, the subjective nature of probability is also kind of obvious: we use probability (and its cousin, statistics) when the costs of obtaining a complete characterisation of a system are prohibitive.
Example: airframe MTTF and MTBF (mean time to, and between, failure[s] respectively). Rather than run every airplane to failure, we accept less-than-complete information (i.e., more uncertainty) and instead run a SAMPLE of KEY COMPONENTS to failure, and then extrapolate.
In effect, we DELIBERATELY CONSTRAIN our information set – sacrificing certainty for empirically-robust sample-based data that (1) enables sensible inference; (2) is replicable; and (3) is operationally relevant.
And so it is with economic data: we cannot completely-characterise every process that makes up an economy, but we can make inferences from a subset of observations that are generated by economic interaction. To the extent that the analysis is performed without a ‘strong prior’ (i.e., a bias – i.e., corruption-of-process), the results will be robust. And if there IS bias in the selection of data or method (say, in Friendman and Schwarz’ ‘masterpiece’ of dodgy stats), the results can be scrutinised by well-trained individuals and the fabrication or operational inadequacy revealed.
TL;DR: it doesn’t matter if probability is subjective or not. It matters that the tools that probability gives us are useful, neutral (under certain conditions) and amenable to scrutiny.