Maureen did not vote for McCain

Statistical applications of the kind considered here are strong only if the fig- ures are close to 100 percent or 0 percent. When the percentages are in the middle of this range, such statistical applications are weak.

A more interesting problem in evaluating the strength of a statistical application concerns the relevance of the premises to the conclusion. In the above schematic representation, F stands for what is called the reference class. In our first example, being a Republican from California is the reference class; in our second example, being a socialist from California is the refer- ence class. A striking feature of statistical applications is that using different reference classes can yield incompatible results. To see this, consider the fol- lowing example:

Three percent of Obama’s relatives voted for McCain. Marvin is a relative of Obama.

Marvin did not vote for McCain.

We now have a statistical application that gives us strong support for the claim that Marvin did not vote for McCain. This is incompatible with our first statistical application, which gave strong support to the claim that he did. To overlook this conflict between arguments based on different refer- ence classes would be a kind of fallacy. Which statistical application, if ei- ther, should we trust? This will depend on which of the reference classes we take to be more relevant. Which counts more, political affiliation or family ties? That might be hard to say.

One way of dealing with competing statistical applications is to combine the reference classes. We could ask, for example, what percentage of Repub- licans from California who are relatives of Obama voted for McCain? The re- sult might come out this way:

Forty-two percent of Republicans from California who were relatives of Obama voted for McCain.

Marvin is a Republican from California who is a relative of Obama.

Marvin voted for McCain.

This statistical application provides very weak support for its conclusion. In- deed, it supplies some weak support for the denial of its conclusion—that is, for the claim that Marvin did not vote for McCain.