Explanatory power is the ability of a hypothesis or theory to effectively explain the subject matter it pertains to. The opposite of explanatory power is explanatory impotence. In the past, various criteria or measures for explanatory power have been proposed. In particular, one hypothesis, theory, or explanation can be said to have more explanatory power than another about the same subject matter
if more facts or observations are accounted for;
if it changes more "surprising facts" into "a matter of course" ;
if more details of causal relations are provided, leading to a high accuracy and precision of the description;
if it offers greater predictive power, i.e., if it offers more details about what we should expect to see, and what we should not;
if it depends less on authorities and more on observations;
if it makes fewer assumptions;
if it is more falsifiable, i.e., more testable by observation or experiment.
Recently, David Deutsch proposed that theorists should seek explanations that are hard to vary. By this expression he intends to state that a hard to vary explanation provides specific details which fit together so tightly that it is impossible to change any one detail without affecting the whole theory.
Overview
Philosopher and physicist David Deutsch offers a criterion for a good explanation that he says may be just as important to scientific progress as learning to reject appeals to authority and falsifiability. To Deutsch, these aspects of a good explanation, and more, are contained in any theory that is specific and "hard to vary". He believes that this criterion helps eliminate "bad explanations" which continuously addjustifications, and can otherwise avoid ever being truly falsified. An explanation that is hard to vary but does not survive a critical test can be considered falsified.
Examples
Deutsch takes examples from Greek mythology. He describes how very specific, and even somewhat falsifiable theories were provided to explain how the gods' sadness caused the seasons. Alternatively, Deutsch points out, one could have just as easily explained the seasons as resulting from the gods' happiness - making it a bad explanation because it is so easy to arbitrarily change details. Without Deutsch's criterion, the 'Greek gods explanation' could have just kept adding justifications. This same criterion, of being "hard to vary", may be what makes the modern explanation for the seasons a good one: none of the details - about the earth rotating around the sun at a certain angle in a certain orbit - can be easily modified without changing the theory's coherence.
Relation to other criteria
It can be argued that the criterion hard to vary is closely related to Occam's razor: both imply logical consistency and a minimum of assumptions. The philosopher Karl Popper acknowledged it is logically possible to avoid falsification of a hypothesis by changing details to avoid any criticism, adopting the term an immunizing stratagem from Hans Albert. Popper argued that scientific hypotheses should be subjected to methodological testing to select for the strongest hypothesis.
