Two vectors' bits match with probability proportional to the cosine of the angle between them.

Unlike these two methods the proportionator introduces sampling with probability proportional to size, or PPS.

This model requires that the initial niche is broken at random and the successive niches are chosen with a probability proportional to their size.

Then, it randomly draws new particles from the previous belief, with probability proportional to .

Denoting each score calculated this way by , each variable is selected with a probability proportional to its score:

Within each constituency, a polling district was selected, again with probability proportional to size.

We could sample the herds with probabilities proportional to their sizes, i.e.

But how are we to sample the primaries with probability proportional to size?

If a plane through the center is chosen uniformly at random, a disk will be crossed with probability proportional to its radius.

The first sample is chosen with probability proportional to the size of the x variate.