I know the point of no-luck cyclic move order is to completely eliminate luck, but I think there are some situations where it actually increases the amount of luck. One example is in the Small Earth games, where one pick is clearly the best one. In that case players will often only pick 2 starts, rather than the normal 4, in order to get the picks more quickly. However, if your picks overlap with your opponent, you will end up getting a random starting spot, which could be good or terrible based on which one you get.
Here's an example of a game where I only picked 2 starts. I ended up getting both of them since I picked faster and he didn't take my second spot in his top 3, but but I also likely picked faster because I didn't bother to pick 4 starts as he did.https://www.warlight.net/MultiPlayer?GameID=8871031
I think you should be required to pick the total number of starts that all players will get. That would rule out possible luck in getting random picks.
Edited 6/8/2015 20:38:31