If you have random negative and positive numbers HALF_UP is fine and the net error will tend to 0. HALF_UP is also easier for a human to understand and is often used in finance.
However, if you know you have more of positive (or negative) numbers you will get a bias. HALF_EVEN and HALF_ODD attempts to correct for this by choosing whether to rounding 0.5 up or down based on whether it is more likely to go to an even or odd number. This is statistically fairer, provided you have a 50/50 split of even and odd numbers, however harder for a human to understand.
