I would vote for truly random, from any active member (e.g. anybody who posted 4x times in the last month). IMO anybody who "really needs" or could "fully use" a high end scope would rule out the majority of hobbyists members.
If it really is a giveaway, just email them all the qualifying members with a simple random question like"what is the voltage at point 'A' in this resistor network (+/- 5%) and leave it at that.
A word of caution to the eventual winner - I got my only scope (a lowend 100MHz jobbie) by helping somebody in the USA with a Kickstarter project. That US$350 scope it cost me around $200 in duty, clearance, GST and other charges. So if somebody in NZ won a US$10k scope, that would be up for at least NZ$2000 just in GST for getting it in the country - and I don't know about you, but I don't have that money around to spare.
If I had $2k spare to spend on hobby electronics I would use money like that to get something like a Rigol DS-1074Z, a simple function generator, a decent PSU (rather than my second hand 10+ year old DSE linear one), and a Saleae Logic Pro 8 and maybe a decent meter, and would get more value from it.
Humm, maybe then again I wouldn't - I'ld stick with what i have and buy a new hard-tail mountain bike. Got to get my priorities right