Does that mean that the respondant doesn't pay any of the fees for a single-member panel, only when they request 3? I didn't really understand that part.
Single member panel - Complainant pays entire fee.
Three member panel - Respondent pays 1/2 fee.
The fees are different at the NAF and WIPO.
In a single member panel, the panelist is chosen by the dispute resolution provider.
A three member panel at WIPO is composed as follows:
Respondent picks three panelists - one of those is selected for the panel.
Complainant picks three panelists - one of those is selected for the panel.
Then, both parties are provided with a list of five panelists and asked to rank them according to preference. WIPO then purports to select the presiding panelist based on a maximization of preference.
At NAF, both parties provide a list of three, and then are asked to strike two names from a list of five provided by the NAF.
If you think about it long enough, there should be no functional difference between the NAF and WIPO presiding panelist selection mechanisms. Under a maximization of preference, WIPO should never seat a panelist who was ranked lower than third on either parties' preference list. Hence, ranking any two panelists as four and five should have the same consequence as striking them, as at the NAF. Neither the NAF nor WIPO understand that.
As far as results go, you can divide UDRP cases into several categories for analysis, and this was done at my suggestion in a paper by Prof. Milton Mueller at Syracuse University entitled "Rough Justice". Looking at:
Single member, default cases
Single member, contested cases
Three member, respondent requested, contested cases
he found that the third scenario resulted in a win percent for the respondent over 60% - the only combination in which the majority of results were in the respondent's favor.
Now, since requesting a three member panel requires payment of a fee, that result may reflect, as Duckinla points out, a determination by the respondent that it has a strong case and thus does not want to risk getting a relatively unreflective panelist. There is a wide variation of thoughtfulness among UDRP panelists, hence having a measure of control over the panel composition can make a big difference.
The absolute best part, though, is that even though the parties are not supposed to communicate their strikes/preferences to the other side, it turns out that more often than not the complainant will copy his/her strikes to the other side. So, by waiting until the deadline for submitting your strikes, you can often effectively pick the presiding panelist by using your two strikes to eliminate two of the remaining three on the list of five.
If you have a defensible case, then going with a single member panel is like driving without seatbelts.