The Half-A-Loaf Approach

A common way of approaching a problem is the half-a-loaf approach. Here's an example.

Let's say a student is faced with a matching test:
========================================================================
COLORS TEST
Match the fruit with the corresponding color.

___1. Grape      A. Green
___2. Banana    B. Purple
___3. Pear        C. Yellow
========================================================================
Assume that the student knows for certain that grapes are purple. The student's paper now looks like this:
========================================================================
COLORS TEST
Match the fruit with the corresponding color.

 B  1. Grape      A. Green
___2. Banana    B. Purple
___3. Pear        C. Yellow
========================================================================
Now, the student is stumped. He doesn't know what colors bananas and pears are. So he decides to use the half-a-loaf approach. The student's reasoning is as follows.

There are four possible situations.

Possibility One: (1. B) (2. C) (3. A)   Score: 100%
Possibility Two: (1. B) (2. A) (3. C)   Score: 33%
Possibility Three: (1. B) (2. C) (3. C)   Score: 66%
Possibility Four: (1. B) (2. A) (3. A)   Score: 66%

Getting a 100% would be pleasant.
Getting a 66% would be bad, but not horrible.
Getting a 33% would be devastating to the student's average grade.

The student should avoid the 33% at all costs.

The student now has two choices: either put different answers for all the questions, or put the same answer for two of the questions.

The former gives the student a 50% chance of getting a 100% and a 50% chance of getting a 33%.

The latter guarantees the student a 66%.

The student picks the latter, securing a 66%.

Technically, the two choices are intrinsically the same, because the former choice would, on average, give the student a 66% anyway. But in a real life situation, the latter choice is better because it avoids the 33%.

This is the half-a-loaf approach: being certain of getting half a loaf of bread is better than having a chance of getting no bread.