Preference Order

Preferences are conditional statements which assume a certain order in their execution. Sun Tzu uses this construct at several occasions, indicating good and not-so-good ways of performing warfare.

Definition of Preference Order

In logic and mathematics, preference is usually defined as an ordering of given elements in a set. These elements can be some objects, or possible outcomes of certain actions, and the ordering is usually defined by a utility function that weights how preferable an element is. An element A is more preferable than element B if and only if A's utility is higher than B's.

In the context of Sun Tzu, the author does not explicitly define preferences in such a rigid way. However, when multiple possible situations are being articulated, Sun Tzu indeed gives them a preference order.

We call this ordering preference order mainly for two reasons:

1. For each of the element being mentioned, you can always find a preference relation, and there's no circle-back.
   If A is more preferable than B, B is more preferable than C, then it implies that A is more preferable than C.
2. They are in coherence with Sun Tzu's general philosophy of war. Sun Tzu is not ordering these possible outcomes randomly, but follows his reasoning in evaluating these conditions.

Examples of Preference Order

We show here some examples of sentences using a preference order.

Chapter 01, sentence 26.

 Now the general who wins a battle makes many calculations in his temple before the battle is fought.
The general who loses a battle makes but few calculations beforehand.
Thus,
	do many calculations lead to victory,
	and few calculations to defeat:
	how much more no calculation at all!
        

There are three conditions to order. The most preferable one is to do many calculations that lead to victory, and the second prefer one is to do few calculations (which leads to defeat). The least preferable one, is to do no calculation at all.

Chapter 03, sentence 1.

    In the practical art of war, 
        the best thing of all is to take the enemy's country whole and intact;
        to shatter and destroy it is not so good.
    So, too, it is better to recapture an army entire than to destroy it,
        to capture a regiment, a detachment or a company entire than to destroy them.
        

This example orders five elements: 國，軍，旅，卒，伍。These five terms refer to five organizational units in the ancient Chinese armies. 國 is the entirely country, 軍 is the full army of the country, 旅 is one sub-unit of the country, the the rest two are smaller units.

For each of the elements, to keep it intact is better than to destroy it.

Taking all the five elements into consideration, to keep the higher oredered one is preferable than to keep the lower ones.

This constructs a nested preference order of the five elements.

This analysis allows us now to improve the English mind map and the translated text.

2. Chapter 3, Sentence 3.

Thus the highest form of generalship is to balk the enemy's plans;
    the next best is to prevent the junction of the enemy's forces;
    the next in order is to attack the enemy's army in the field;
        and the worst policy of all is to besiege walled cities.

This one orders four strategies. The most preferred is from the planning perspective, then the forces, then the army, and last to besiege a city.

The world is not a perfect one, therefore when the best scenario cannot happen, Sun Tzu lists a second-best one, and then the next, thus one doesn’t have to drop to the worst option immediately. By preference order, Sun Tzu provides a more refined granular view of strategies. It is not about A or not A, but we can rate from the the more preferable to the least preferable, and the possibility to make each sub-optimal scenario to happen.