28. “Can Probability Be Subjective and Objective at the Same Time? A Reply to Arnold Baise”
by Mark R. Crovelli
Abstract: My claim that probability ought to be defined as a purely subjective measure of human belief has been challenged in a recent and interesting article on these pages by Arnold Baise (2011). Baise argues that probability ought to be defined, not as a purely subjective measure of human belief, as I have claimed, but rather in the following way:
Probability P(A|I) is a number between 0 and 1 that indicates how plausible it is that proposition A is true, based on information I. In addition, one could add that a probability of 1 indicates certainty that the proposition is true, while a probability of 0 indicates certainty that the proposition is false. (2011, p.3).
The reasoning that leads Baise to advance this definition for probability, however, is seriously and apodictically flawed. As a consequence, his definition for probability must be rejected as a viable alternative to my purely subjective definition.
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It is clear that individuals feel more or less certain about the truth of various propositions (whether about what is, what was or what will be). This “subjective probability” is rightly the concern of the social scientist who is concerned with how people think and how what they think affects their behaviour.
The question is whether in addition to this it is philosophically meaningful to talk of an “objective probability” of something happening.
If you believe that reality is non-deterministic, that God really does throw dice, then the probability of something happening is indeed a property of the universe.
But most of us tend to think that instead the universe is governed by deterministic laws of cause and effect. Under this hypothesis, probability is a function of our models of the universe and their adequacy (related to the size of the error term, the bit we can’t adequately explain). Such models can be written down and critiqued, judged to have or not have predictive value – they are one step more “objective” than the ideas in somebody’s head.
I’d argue that it is philosophically meaningful to say that one person’s subjective probability is more accurate (more reliable) than another’s subjective probability of the same event. Which tends to imply an objective something which is used as the yardstick to judge our subjective perceptions.
In a Heisenbergian universe, it may be impossible to know whether or not it will rain in Denver tomorrow. A probability may be the best we can do.
Or, in a more relaxed version, it may the best we can know with the computing power available to us – an information theory limit rather than a physical one.
The glaring problem with claiming that some people’s probabilities are “more accurate and reliable” than other people’s is that not everyone agrees with you. As I note in the article, for example, some people think frequentist probabilities are always “more accurate and reliable,” while other people (myself included, obviously) would not dogmatically endorse frequentist probabilities as “more accurate and reliable” in all circumstances.
In other words, just because you might think some probabilities are “more accurate and reliable,” does not mean that everyone agrees with you. To assume that everyone agrees with you is to assume the very thing you are trying to prove. The burden is on you, after all, to prove that certain probabilities are “objective” in some sense, in spite of the glaring fact that not everyone believes this.
There is ample room for disagreement when we are dealing with uncertain events and phenomena. And this is just another way of saying that probability is a measure of subjective belief.