There are three Royal Lineages: Red, White, and Blue. The first king is drawn from the Red line. The second king is drawn from the White line. The third is Blue. And then it cycles: 4th is Red. 5th White. 6th Blue. And then a Red king takes the throne, the Seventh King of the Rotating Kindom and Third King of the Red line. And so on.
When the Red King dies, it is the children of the Red King who are of age to ascend to the throne. The grandchildren of the Blue King are also the right age. But it is the White line that supplies the next King. It is the great-grandchildren of the previous White King who are the princes of the Kingdom.
The descendents of the Blue King meet to choose a new King from among the White princes. When, in the fullness of time, the White King dies, the descendents of the Red King will meet to choose a new King from among the Blue Princes. The cycle continues with the each King succeeded by a prince of the next colour chosen by a conclave of KingMakers, all of the previous colour
Under traditional rules of succession, the eldest son becomes King. When the eldest son is stupid, that hurts the Kingdom three ways. First the new King is stupid. Second we worry about the new King's sons. They vary. Some are better than him, some worse, but choosing the eldest makes a random choice. The capability of the subsequent Kings wanders randomly through the stupidscape until the Kingdom falls. Third, there is some hope that the coutiers may bully the King into marrying a clever woman and thus repair the blood line. But where are the incentives? The King may stubbornly chose a beautiful woman over a clever one and have handsome, stupid children.
Do schemes in which the new King is chosen wisely from among the sons of the old King really help? Imagine that the Royal couple usually have four children. Two sons. Two daughters. There is an alternative if the eldest son be unsuitable. That is not much of a choice. But four children imply sixteen grandchildren and sixty-four great grandchildren. Now there are 32 sons and some hope a picking a wise and good King.
The complexities of the rotating triple crown fail to create incentives around the Kings choice of Queen. One of his great grandchildren will be King, no matter how poorly he choses. But the King's children are set in competition with each other. Each hopes that one of their children will be the parent of the next King of their colour. The Kings grandchildren are also set in competition with each other. Each hopes that their son will be the next King of their colour. The King's children must encourage all their children to conduct themselves regally and choose a mate to be parent to the future king. The King's grandchildren must follow through by choosing a suitable spouse and grooming their sons to be ready to take the throne.
All three problems of the stupid eldest son are solved. The King makers have a choice, so the stupid eldest son does not take the throne. The line of succession follows the choice. The stupidity of the eldest son is not inherited. If the choice proves to be bad, there are two generations available to repair the blood line and some incentive to do so.