Why cheating is good for human computation games

After reading about Luis' new game for identifying beautiful images, it occurred to me that cheating would enhance human computation games.

The reason being is that cheating adds a new dimension to these games, namely strategy.

So in the game for identifying beautiful images, you can try to get into your partner's head based on the results of previous image pairs. This adds a new dimension to the game that is missing in the ESP Game.

So instead of combating cheating, why not encourage it explicitly by providing features to help players cheat? For example, in this beautiful image game, one can show the results of past image pairs while the game is in progress.

Even in the presence of such cheating, one may still get lots of useful data for subjective problems. In fact, one may get more as the games would have a new dimension to them.