"I'm assuming here they check each of the 15 dates for your max group size first and then check each date for max group size - n, etc. Not check your first date choice for any possible group size in your range, then second date for any possible groups size, etc. If they did the latter, you would be more likely to get a 1 person group on your first date choice than a 7 person group on your second date choice even if it was available!"

I'd be willing to bet it is the latter rather than the former. Doesn't make sense to me why they would do it the first way. I'm not sure why your hypothetical situation would be a bad thing. After you all you can set the minimum group size too. If you set the minimum group size as 1 for your first choice then why shouldn't the lottery think you would want 1 for that date above all other options? If not, just set the min and max to same number.