Bart Massey wrote:
Peter Gavin
writes: The reason for doing it this way is that e.g. 2.5 is exactly between 2 and 3, and rounding *up* every time would cause an uneven bias toward 3. To counteract that effect, rounding to the nearest even integer is used, which causes the half of the x.5 values to round up, and the other half to round down.
Everyone keeps providing this rationale, but of course if you want "half the values to round up and the other half down" it does just as well to round positive values up and negative values down.
The rational is to have half of the expected distribution of 'related' invocations round up/down, regardless of the (adversarial) distribution of input value instances. The round to zero method provides this only when the distribution of instances are symmetric about zero. Barring random number generators, these are extremely uncommon distributions in practice. The round to even method provides this guarantee so long as the adversary can't choose between Even+0.5 vs Odd+0.5 values whenever it wants. In terms of non-adversarial distributions, this covers almost all of them, and in particular it is not biased to a particular mean for the distribution. Granted, not everyone is trying to get as close to the correct answer as possible. Sometimes it's more important to guarantee one-sided error than it is to minimize the error margins. But, IME, the most-correct answer is the general goal and when people have another goal in mind they're quite aware of it. -- Live well, ~wren