The Role of Ideology in Experiment Selection

In addition to a means of drawing inferences from evidence, an epistemology may include a way of choosing evidence-gathering tactics (hereafter called experiments, although they may take the form of any act of observation or inquiry.) Often associated [42,43] with Bayesian statistics is an experiment selection method known as statistical decision theory, which works [14,8] as follows: for the set $S$ of available theories and the set $R_X$ of possible results of a particular experiment $X$, an uncertainty function $U(S)$ is defined, which is a function of the prior probabilities $P(T)$, $T \in{} S$, intended to represent the initial incompleteness of knowledge about which theory is true. A popular choice of uncertainty function is [14,8,44] the Shannon entropy

$$H(S) = -\sum_{T\in{}S}P(T)\log{}(P(T))\textrm{.}$$ (20)

The same uncertainty function of the posterior probabilities $P(T\vert E)$, $T \in{} S$, $E \in{} R_X$, denoted $U(S\vert E)$, can [14,44] be used to represent the remaining incompleteness of knowledge about which theory is true, once result $E$ has been obtained. For the Shannon entropy,

$$H(S\vert E) = -\sum_{T\in{}S}P(T\vert E)\log{}(P(T\vert E))\textrm{.}$$ (21)

Before performing experiment $X$, the expectation value of the uncertainty which will remain after performing experiment $X$ is [14,44]

$$U(S\vert X) = \sum_{E\in{}R_X}P(E)U(S\vert E)\textrm{,}$$ (22)

where the $P(E)$ are the marginal likelihoods, for the various results. For the Shannon entropy,

$$H(S\vert X) = -\sum_{T\in{}S}\sum_{E\in{}R_X}P(T\vert E)P(E)\log{}(P(T\vert E))\textrm{.}$$ (23)

Once all these definitions are made, one can [14] measure the expected worth of an experiment $X$, as the difference between the uncertainty before the experiment is performed, and the expected uncertainty after the experiment is performed, a quantity known as the information

$$I(X;S) = U(S)-U(S\vert X)\textrm{.}$$ (24)

If there is a choice of several experiments, and the costs, in a broad sense which includes any ethical disadvantages of performing an experiment, as well as the direct financial costs and hard work involved, are small enough to be ignored, then the experiment with the largest information should [14] then be chosen. This is statistical decision theory's means of experiment selection: it is assumed that the incompleteness of knowledge can be measured by a function of the probability distribution over theories, then experiments are chosen to reduce the incompleteness of knowledge as much as possible.

Examples of the use of this statistical decision theory to choose experiments, in the natural and social sciences, are [8] rare, although examples of its use to justify a choice of experiment retrospectively are [8] more common. It could be conjectured that the apparent rarity of the use of statistical decision theory is due to the statistical nature of natural-language arguments, used to approximate statistical arguments (section 5.3,) not being obvious.

For the purposes of this paper, the important aspect of statistical decision theory is the way in which the uncertainty function is chosen, for it is based on ideology. The ideology is [14] encoded in a loss function $L(y;T)$, which represents how bad the condition of the universe will be if a policy $y$, from a set $Y$ of possible policies, is chosen, given that theory $T$ is true. The uncertainty function is [14] then

$$U(S) = \min_{y\in{}Y}\sum_{T\in{}S}P(T)L(y;T)\textrm{,}$$ (25)

i.e. how bad the condition of the universe is expected to be, from the point of view of the ideology encoded in $L(y;T)$, if the policy is chosen which renders the condition of the universe as good as possible, on the basis of the prior probability distribution over theories. Therefore,

$$U(S\vert E) = \min_{y\in{}Y}\sum_{T\in{}S}P(T\vert E)L(y;T)\textrm{,}$$ (26)

and

$$U(S\vert X) = \sum_{E\in{}R_X}\min_{y\in{}Y}\sum_{T\in{}S}P(T\vert E)P(E)L(y;T)\textrm{.}$$ (27)

Not only can an uncertainty function, determining the selection of experiments, be devised on the basis of an ideology in this way, it has been shown that every continuous, concave $\cap$ uncertainty function can [14] be associated with some loss function $L(y;T)$, and therefore with some ideology, through equation 27¹⁴. Therefore, a Bayesian cannot help but suspect that any attempt to obtain knowledge without an ideology in mind (section 2.2.2,) far from eliminating ideology from the academic enterprise, conceals its inevitable role in the selection of experiments, and renders the ideology immutable. The Bayesian statistical decision theory, by contrast, is quite open about the role of ideology in its experiment selection procedure.

Again, therefore, the conclusion from Bayesian statistics is the same as that of standpoint epistemologists. In standpoint epistemology, it has been emphasized that, among other subjective influences, ideology is [29] always involved in the constitution of scientific problems and the choice of hypotheses to test; in other words, in the selection of experiments. Experiment selection methods which attempt to be value-neutral are understood [19,20,28] to conceal, rather than to eliminate, the influence of ideology on experiment selection, and standpoint epistemologists openly choose experiments [28,48,29] with the aim of providing information resources for the implementation of emancipatory ideologies. For example, a research project, by the action group ``Women Help Women,'' on physical abuse, by their husbands, of women in Cologne, was [48] inspired by the need for information on the extent of such abuse, to facilitate a decision by the municipal government about whether to fund a shelter for the victims.

In the analysis of the role of ideology in experiment selection, moreover, standpoint epistemologists have concluded that the concealed ideologies in much of the research, in natural and social sciences, that has taken place over the last three centuries, have [35,29] been patriarchy and colonialism. The present author is not, however, prepared to assert that all experiments in that period have been chosen on such anti-emancipatory grounds; Strathern [70] has pointed out that the fact that certain procedures of the universities are not explicitly codified does not imply that they implement anti-emancipatory ideologies; experiment selection systems, too, must be examined individually, rather than subjected to a universal assumption that they are anti-emancipatory, if one wishes to discover the ideology behind them. Here too, statistical decision theory can provide insights, through equation 27, which relates the uncertainty function, used in selecting experiments, to the loss function, which represents the ideology behind experiment selection. For example, the Shannon entropy, an uncertainty function which is commonly chosen for the mathematical convenience that results from its history as a tool for setting limits [44] on the performance of communication channels, rather than for its ideological associations, is associated with a loss function in which, for any given prior/posterior probability distribution $P(T)$, there is one policy $y$ with loss

$$L(y;T) = -\log{}(P(T))\textrm{,}$$ (28)

and all other policies have a larger expectation loss than does $y$.

It is difficult to imagine that patriarchy, colonialism, or any of the standard ideologies, could take this position of assigning goodness to the consequences, within theory $T$, of policy $y$, based on the probability $P(T)$ or $P(T\vert E)$ of that theory being true. The author believes that, rather than base experiment selection on the Shannon entropy, which is the optimum methodology for an ideology for which no-one, as far as he knows, has expressed support, and whose nature and relationship to standard ideologies are unclear, it would be more appropriate for researchers to arrange their research transparently to assist in the implementation of ideologies in which either they, their funding agencies, or both believe; the Shannon entropy's undoubted importance in setting limits [44] on the performance of communication channels does not imply any special position with respect to experiment selection.

Neither the author, nor proponents of standpoint epistemology [28] are neutral on the choice of uncertainty function: the author would prefer the use of an uncertainty function based on a liberal ideology, like the one set out in a convenient form for mathematical expression by Rawls [59]. However, Gibbs' inequality implies [14,44] that any experiment has an information greater than or equal to zero, from the point of view of any ideology whose uncertainty function is concave $\cap$. Therefore, the only experiments that will be unwelcome will be those with unacceptable intrinsic costs, moral or financial; fortunately for the construction of a universal science, the experiments selected by proponents of a particular ideology are also useful to their political opponents.