I understanding that the following sentence is reasonably good for expressing the given idea.
(1) This method is likely to be biased since this requires participants to bring their own laptops.
However, I was curious to know if the following is correct (given that it sounds better at least to me).
(2) This method is likely to be biased since this requires participants' bringing their own laptops.
Best Answer
This can be seen in two ways. To see how, substitute their for participants’, and then them for participants. Use the first if you want to emphasise the act of bringing and the second if you want to emphasise that it is they who are doing it.