You have a misunderstanding. Watermarking does not bias the responses in any way. How is this possible?

Before: "He leaped at the chance" - 33%. "Jumped at the opportunity" - 66%.

After: "He leaped at the chance" - 33%. "Jumped at the opportunity" - 66%.

But if you refresh your response from Anthropic 100 times:

Before: "Jumped at the opportunity" He leaped at the chance" "Jumped at the opportunity"

After: "He leaped at the chance" "He leaped at the chance" "He leaped at the chance"

The second one is detectable as being watermarked.

davmre has a good explanation that's more in-depth.