Sometimes (especially when thinking about evidence in baysean updates) Log odds can be useful because one bit of evidence just adds 1 bit to your log odds (in Base 2). Eliezer goes into more detail here: https://www.lesswrong.com/posts/QGkYCwyC7wTDyt3yT/0-and-1-are-not-probabilities
Sometimes (especially when thinking about evidence in baysean updates) Log odds can be useful because one bit of evidence just adds 1 bit to your log odds (in Base 2). Eliezer goes into more detail here: https://www.lesswrong.com/posts/QGkYCwyC7wTDyt3yT/0-and-1-are-not-probabilities