A see-saw stat is a stat that moves between two extremes, both of which are beneficial, but in different ways. I got the idea from Pendragon's passions, but they can be applied in any game system.
To set up the see-saw stat, you need two opposed qualities - Honor/Practicality, Piety/Worldliness, Kindness/Cruelty, etc. - depending on what would be important in the game. Both qualities must be beneficial in different circumstances, so stay away from qualities that are universally good or bad.
Next, set up your number range. We'll be using this as a bonus, so the number range must not be unbalancing when taken to extremes. For example, for a percentile system, 10 or 20 points would be reasonable, depending on how the bonus is to be applied. The number range is a total - both stats added together would always equal the total. So if one is increased, the other must be decreased by the same amount. I like even numbers for the total, so both sides can start even.
The application of the bonus is simple - add the number on one side of the see-saw to your chance or quality, whichever is appropriate. However, you need to delineate what that bonus can be added to. The two sides need to be applied to different things.
Now as the game goes along, the GM (or group if you prefer) award a point of one or the other whenever a character does something strongly inclined in that direction. Each point tipping the see-saw further in one direction. Some characters move strongly in one direction, some in the other, and some hover around the middle. All of these are winning strategies, because the result is always a bonus.
For example, I used Honor/Practicality in my In Harm's Way military games. This reflects the duality of a mindset in which both qualities are very important, but are never applicable in the same circumstances. Taking the honorable course when there is a choice adds 1 to the PC’s Honor score, and subtracts one from the PC’s Practicality score. Conversely, choosing the practical course adds one to the PC’s Practicality score and subtracts one from the PC’s Honor score.
The character can add his Honor score to any rolls where the PC’s Honor might help, such as convincing superior officers of the need for a certain action, dealing with VIPs and diplomacy, or for any Leadership roll.
The character can add his Practicality score to any rolls where the PC’s Practicality might help, such as dealing with criminals, brutes, and minor officials, bribing, finding information from low lives, intimidating, or any Discipline roll.
Honor plus Practicality always equals 20.
The see-saw stat is a type of abstract tactic used in social situations. How the PC chooses to live his life gives him certain advantages in certain situations.