Ethical Holes

Though when you think about it, isn't bribing a judge effectively proof of usefulness? That's why we should judge animals by how delicious they are. As we do.

The Meed of Use

When men were chosen as judges in the contest, their role being to decide who deserved the laurels of the most useful, the nominated animals did not so much resort to bribery as leap to it. The cows called on their crow friends to find baubles, the chickens arranged with lizards for the secrets of the earth to be brought forth, and as for the pigs, they tricked the others out of many of their offerings by their wiles.
The cicadas, those gossipers, went to the gods to tell them of the shameless cheating, but the gods laughed at it. "Would they be as energetic as they are if they knew! There is no risk of favoritism from judges who will soon eat and skin them all equally, third place to first!"
Horrified, the cicadas tried to warn the world that the projects of the gods are ghoulish amusements not meant for our good. They still do. But none heed them for the annoyance.
Finis

Competition's Deepest Folds

The king proclaimed a commission with its purpose to determine how beneficial was every sport to the development of its participants with regard to the perfection of civil and martial life. Strength, obedience, adaptability, wit, numerical facility, all those were to be judged. Three superior sports would be encouraged by royal grants; banning was the fate of all the rest.
Five months later, the commissioners left their opulent homes, bought after their appointments, and met in the palace along with representatives for the various sports. They presented their conclusions, and somehow three of the sportsmen knew to smile from the outset.
The king nodded. "I congratulate the victors. Clearly you have bribed, colluded, and coerced. That is good, for my subjects must understand the world's ways. Your methods require improvement however. These others came to me directly. I have confidence you will excel in their sports, the only three henceforth permitted."
The disappointed representatives accepted the loss in a sportsmanlike fashion. As for the commissioners, they offered tournament prizes out of their wealth, not as a punishment but from their own inclination.
Finis

I Forgot One

Bribery! Just huge piles of cash. That can solve most problems. Sometimes you need to get a little more specific and get somebody moved up on the organ list or something. But how do you get the money? Violence or mind control, probably.