[pzhon]

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If one theory is more likely to be true given the evidence, we don't need a heuristic principle like Occam's Razor in order to choose among theories. We can just go by the evidence in that case.

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No, simplicity is not only a tie-breaker. It's a significant indication of the merit of a theory. Ockham's Razor indicates that you should sometimes choose the simpler theory even when the evidence fits a more complicated theory better.

The best quadratic approximation to a function is better than the best linear approximation (except in degenerate situations). However, you should require a substantial increase in accuracy in order to accept the increase in complexity from 2 parameters to 3.

22/7 is a better approximation to pi than 102985/32768, even though the latter is more accurate. 22/7 is surprisingly accurate, relative to its complexity. |Pi-22/7|*7^2 is small. 102985/32768 is more accurate, but it's not even the right choice of numerator for that denominator. If 22/7 isn't accurate enough for you, 355/113 is off by less than a millionth, and it's much less complicated than 102985/32768.

There is a classic urban legend used to illustrate a sacrifice of accuracy to improve a model: When Copernicus proposed a model of the solar system centered about the Sun, his predictions were less accurate than the highly developed geocentric model accepted for thousands of years. However, he needed only about 30 circular motions rather than 80. (Epicycles were still needed because the true Newtonian motion is closer to an ellipse.) This story isn't literally true, but it spreads in part because we recognize that we should be willing to trade some accuracy for simplicity.