I am a political independent, though that does not mean that I vote willy-nilly. I have, in fact, been reliably center left for most of my adult life, save one youthfully rebellious moment when I voted Libertarian, more as a statement than a commitment to the principles of libertarianism per se. I regret that vote now, given additional exposure to the party and the kinds of people it attracts. To me, the extremes of the American political system build around radical positions, and the increasingly noxious conspiracy theories and unhinged rhetoric is nothing like the cautious, problem-solving utopia that might make me politically happy, or at least wince less.
Some might claim I am indifferent. I would not argue with that. In the face of revolution, I would require a likely impossible proof of a better outcome before committing. How can we possibly see into such a permeable and contingent future, or weigh the goods and harms in the face of the unknown? This idea of indifference, as a tempering of our epistemic insights, serves as a basis for an essential idea in probabilistic reasoning where it even has the name, the principle of indifference, or, variously, and in contradistinction with Leibniz’s principle of sufficient reason, the principle of insufficient reason.
So how does indifference work in probabilistic reasoning? Consider a Bayesian formulation: we inductively guess based on a combination of a priori probabilities combined with a posteriori evidences. What is the likelihood of the next word in an English sentence being “is”? Indifference suggests that we treat each word as likely as any other, but we know straight away that “is” occurs much more often than “Manichaeistic” in English texts because we can count words. So the a priori assumption is that words occur in texts with their given frequencies, independent of the previous or subsequent word occurrences (independence assumption). We are indifferent and naïve in this assumption in that we are not imposing any expectations on our estimates that are beyond what the data affords. We then gather evidence about the previous and subsequent words and create a posteriori estimates (count ratios) for the collocates or word pairs. This effectively updates our prior model and creates a new model that includes the pairing frequencies, normalizing them by the frequencies of all pairs of words.
Note that indifference does not always imply uniform probability; uniform probability, like the probability of any given digit arising from the toss of a fair die, is only the indifferent model for uniform probability distributions, but many other distributions are natural in the world and each has a specific form.
Indifference is one of the hallmarks of model comparison, and the cornerstone of scientific reasoning. If we have several hypotheses about a phenomenon, we might treat them indifferently (assign them equal prior weight), and then wait for evidence to move the scale. Intellectual honesty is another way to characterize this strategy. Check your prejudices and motivated reasoning at the door and then discount and update the various hypotheses as evidence accumulates.
The assignment of prior probabilities is a fraught task, however, especially when we are looking at complex arguments and hypotheses. The relative priors are themselves hypothetical and induction devolves into deduction at the edges when the structure of a syllogism is deductively valid and only the probability of the premises being accurate remains as a source of contention. There is an additional factor to consider, however. When there are many explanations, the simplest one seems a better choice intuitively than more complex ones. This is even formalized in Solomonoff induction and Minimum Description Length formulations. If each hypothesis is a logical machine that takes observations and converts those into predictions, we can enumerate the machines, assigning each to a unique integer. As long as we use a consistent encoding scheme, we can reduce them to Turing machines. Now the priors for models are a distribution also on the bit patterns for the hypothesis machines, and where many models support a given hypothesis, there is at least one with the shortest bit length (though finding it is uncomputable itself). The prior becomes exponential in the bit length.
Not surprisingly, the origin of the universe and the larger cosmos, if you will (we’ll get to the distinction shortly), is one area where there are many contending hypotheses and little guidance on how to rank them. Richard Swinburne tries to load priors in support of divine origins in a Bayesian framework, suggesting that a personal, intentional actor is simpler than a universe that is natural and requires many physical laws and fine tunings. But this ignores that there is a collective continuum for natural universes and their possible parameter sets and therefore the a priori divisor in Bayes’ formula is a conjunction of many more natural world probabilities, therefore snuffing out the prior and posterior probabilities of a single divine hypothesis.
Indifference carries with it another connotation against the biases of motivated reasoning. Indifference means waiting for more data when the terms are unquantifiable. This is where any inductive or deductive arguments fail to pass muster as reasonable concerning the origin of the universe or, given a Big Bang event in the past and some meta-structure of a cosmos that includes this universe, the origin of everything (for a modern effort, see this Rutgers dissertation that hopes that the orderliness of the universe is divine). Knowability itself may be closed to us. At the moment there are several contending theories about inflationary universes and bubbles in a larger cosmos. All of them require uniformity of physical law, which is a critical component of physics itself, and which may be incomplete or, at least, not sufficiently understood. A simplicity criteria doesn’t aid us much either. We just have to educate ourselves, participate in the process, or wait for specialists to convert our indifference into illumination.