Confirmational Holism and the Amalgamation of Evidence

Abstract

We discuss a potential application of Arrow’s impossibility theorem to the amalgamation of the evidence provided by different experimental sources. It has been suggested that, as long as there are three or more theories and at least two sources of evidence, Arrow’s negative result applies, and hence the aggregation of individual rankings is bound to coincide with the ranking delivered by one of the sources. Here we show that Arrow’s result need not obtain when dealing with the amalgamation of the evidence. To do so we discuss how different types of sources typically require different attitudes on the part of researchers regarding various auxiliary statements. Due to confirmational holism, the set of items to be ordered by level of confirmation is actually a set of structured elements. We argue that this simple fact will often impose restrictions on the domain of a reasonable amalgamation function, thus violating one of Arrow’s conditions. This phenomenon has interesting consequences at the time of considering the legitimacy of making meaningful comparisons among hypotheses that are rival in a radical way. We end by suggesting possible extensions of our framework to other contexts that require aggregating individual rankings, and in which Arrow’s theorem can be said to apply.