2.2. Condorcet to the rescue?

Condorcet’s jury theorem, in its simplest form, says that if a jury is facing

a binary choice and each jury member makes her decision independently

and has a better-than-even chance of making the right decision, a simple

majority of the jurors is likely to make the right decision, and this will

tend toward certainty as the number of jurors tends toward infinity. We

can think of the successful linear models we have introduced as a jury: The

jury must make a binary decision about a target, and each jury member

makes her decision on the basis of a single piece of evidence. Each piece of

evidence correlates positively with the target; so each juror’s decision is

going to be right more often than not. And the linear model adds together

each juror’s judgment to come to a final decision about the target. The

only difference between the different types of models is that some weigh

certain lines of evidence more than others. Putting this in terms of our

jury analogy, some models have more jurors focusing on certain lines of

evidence than others. So given Condorcet’s jury theorem, we should expect

linear models to predict reasonably well. (Thanks to Michael Strevens

and Mark Wunderlich for suggesting this explanation.)

The Condorcet explanation leaves open at least two questions. First,

many successful linear models consist of a small number of cues (sometimes

as few as two). But Condorcet’s jury theorem suggests that high

reliability usually requires many jurors. So the success of linear models still

seems a bit mysterious. Second, why are linear models, particularly those

with a very small number of cues, more reliable than human experts? After

all, if human experts are able to use a larger number of reliable cues than

simple linear models, why doesn’t the Condorcet explanation imply that

they will typically be more reliable than the models? We will address these

questions in section 3. But for now, let’s turn to a different explanation for

the success of linear models.

Condorcet’s jury theorem, in its simplest form, says that if a jury is facing

a binary choice and each jury member makes her decision independently

and has a better-than-even chance of making the right decision, a simple

majority of the jurors is likely to make the right decision, and this will

tend toward certainty as the number of jurors tends toward infinity. We

can think of the successful linear models we have introduced as a jury: The

jury must make a binary decision about a target, and each jury member

makes her decision on the basis of a single piece of evidence. Each piece of

evidence correlates positively with the target; so each juror’s decision is

going to be right more often than not. And the linear model adds together

each juror’s judgment to come to a final decision about the target. The

only difference between the different types of models is that some weigh

certain lines of evidence more than others. Putting this in terms of our

jury analogy, some models have more jurors focusing on certain lines of

evidence than others. So given Condorcet’s jury theorem, we should expect

linear models to predict reasonably well. (Thanks to Michael Strevens

and Mark Wunderlich for suggesting this explanation.)

The Condorcet explanation leaves open at least two questions. First,

many successful linear models consist of a small number of cues (sometimes

as few as two). But Condorcet’s jury theorem suggests that high

reliability usually requires many jurors. So the success of linear models still

seems a bit mysterious. Second, why are linear models, particularly those

with a very small number of cues, more reliable than human experts? After

all, if human experts are able to use a larger number of reliable cues than

simple linear models, why doesn’t the Condorcet explanation imply that

they will typically be more reliable than the models? We will address these

questions in section 3. But for now, let’s turn to a different explanation for

the success of linear models.