(1) If discretionary judgments are thought to introduce subjectivity in inference, a classic strategy thought to achieve objectivity is to extricate such choices, replacing them with purely formal *a priori* computations or agreed-upon conventions (see March 14). *If leeway for discretion introduces subjectivity, then cutting off discretion must yield objectivity!* Or so some argue. Such strategies may be found, to varying degrees, across the different approaches to statistical inference.

The inductive logics of the type developed by Carnap promised to be an objective guide for measuring degrees of confirmation in hypotheses, despite much-discussed problems, paradoxes, and conflicting choices of confirmation logics. In Carnapian inductive logics, initial assignments of probability are based on a choice of language and on intuitive, logical principles. The consequent *logical probabilities* can then be updated (given the statements of evidence) with Bayes’s Theorem. The fact that the resulting degrees of confirmation are at the same time analytical and a priori—giving them an air of objectivity–reveals the central weakness of such confirmation theories as “guides for life”, e.g., —as guides, say, for empirical frequencies or for finding things out in the real world. Something very similar happens with the varieties of “objective’” Bayesian accounts, both in statistics and in formal Bayesian epistemology in philosophy (a topic to which I will return; if interested, see my RMM contribution).

A related way of trying to remove latitude for discretion might be to define objectivity in terms of the consensus of a specified group, perhaps of experts, or of agents with “diverse” backgrounds. Once again, such a convention may enable agreement yet fail to have the desired link-up with the real world. It would be necessary to show why consensus reached by the particular choice of group (another area for discretion) achieves the learning goals of interest.

Likewise, routine and automatic choices in statistics can be justified as promoting a specified goal, but it is the onus of anyone supporting the account in question to show this.

(2) The second reaction is to acknowledge and even to embrace subjective and personal factors. For Savage (1964: 178) the fact that a subjective (which I am not here distinguishing from a “personalistic”) account restores the role of opinion in statistics was a cause of celebration. I am not sure if current-day subjective Bayesians concur—but I would like to hear from them.

Underlying this second reaction, there is often a deep confusion between our limits in achieving the goal of adequately capturing a given data generating mechanism, and making the goal *itself* *be* to capture our subjective degrees of belief in (or about) the data generating mechanism. The former may be captured by severity assessments (or something similar), but these are not posterior probabilities (even if one grants the latter could be). Most importantly for the current issue, assessing the existing limitations and inadequacies of inferences is *not* the same as making our goal *be* to quantitatively model (our or someone else’s) degrees of belief! Yet these continue to be run together, making it easy to suppose that acknowledging the former limitation is tantamount to accepting the latter.

As I noted in a March 14 comment to A. Spanos, “let us imagine there was a perfect way to measure a person’s real and true degrees of belief in a hypothesis (maybe with some neuropsychology development), while with frequentist statistical models, we grope our way and at most obtain statistically adequate representations of aspects of the data generating mechanism producing the relevant phenomenon. In the former [we are imagining], the measurement is 100% reliable, but the question that remains is the relevance of the thing being measured for finding out about the world. People seem utterly to overlook this” (at least when they blithely repeat variations on “arguments from discretion”, see March 14 post). Henry Kyburg (1993) put it in terms of error: the subjectivist precludes objectivity because they he or she cannot be in error:

This is almost a touchstone of objectivity: the possibility of error. There is no way I can be in error in my prior distribution for µ—unless I make a logical error. . . . It is that very fact that makes this prior distribution perniciously subjective. It represents an assumption that has consequences, but cannot be corrected by criticism or further evidence. (p. 147)

(3) The third way to deal with the challenges of objectivity in inference is to deliberately develop checks of error, and to insist that our statistical methods be self-correcting. Rather than expressing opinions, we want to avoid being misled by beliefs and opinions—mine and yours—building on the recognition that checks of error enable us to acquire reliable knowledge about the world.

This third way is to discern what enabled us to reject the “dirty hands” argument: we can critically evaluate discretionary choices, and design methods to determine objectively what is and is not indicated. It may well mean that the interpretation of the data itself is a report of the obstacles to inference!

Far from being a hodgepodge of assumptions and decisions, objectivity in inference can and should involve a systematic self-critical scrutiny all along the inferential path. Each stage of inquiry and each question within that stage involve potential errors and biases. By making these explicit we can learn despite background judgments.

Nowadays, the reigning mood may be toward some sort of third way; but we must be careful. Merely rejecting the dirty-hands conclusion (as in my March 14 post) is not yet to show that any particular method achieves such objective scrutiny in given cases. Nor does it suffice to declare that “of course we subject our assumptions to stringent checks”, and “we will modify our models should we find misfits with the data”. We have seen in our posts on m-s tests, for instance, the dangers of “error fixing” strategies (M-S post 1, 2, 3, 4). The method for checking must itself be justified by showing it has the needed properties for pinpointing flaws reliably. It is not obvious that popular “third-way” gambits meet the error statistical requirements for objectivity in statistics that I have discussed in many previous posts and papers (the ability to evaluate and control relevant error probabilities). At least, it remains an open question as to whether they do.

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Carnap, R. (1962). *Logical Foundations of Probability*. Chicago: University of Chicago Press.

Kyburg, H. E., Jr. (1993). “The Scope of Bayesian Reasoning,” in D. Hull, M. Forbes, and K. Okruhlik (eds.), *PSA** 1992*, Vol. II, East Lansing, MI: 139-52.

Savage, L. J. (1964). “The Foundations of Statistics Reconsidered,” pp. 173-188 in H. E. Kyburg and and H.E. Smokler (eds.), *Studies in Subjective **Probability*, Wiley, New York: 173-88.

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