Option 1:
Use the last two digits of some commonly available public number that was, essentially, random or at least unpredictable and not controllable. A good example today would be the cents portion of the SP500 index.
Options 2:
Tally up which of the numbers had the least amount of money bet on it and then make that the number.
You can guess which of the two options the more nefarious organizations used.
Interesting related note: back in the first half of the 20th century, there used to be a game in the newspapers where you were presented with a grid of faces, each one being numbered. The goal was to pick the face that you though OTHER people would pick most often. In other words, if you picked the most popular face, you would win. This led to lots of "well which face do I think other people will think is most popular etc"
John Maynard Keynes used the game above as a proxy for the stock market with stocks being the faces e.g. you were trying to pick the stock you thought that everyone else would buy.
I mean, pretending that it's random is fraud, but if you were honest about the affair, that would actually make for a mildly interesting game.
But if the game were that you need to pick others consider the least popular....
It happened more than once that the marketing side would come back and ask for a new winner because of a situation like us doing a drawing for a prize from an ISP, and the winner's email being "@competitorisp.net".
As far as I know (and I've got a reasonable basis for this), the clients never requested this or anything. It was purely our marketing guys not liking the optics of telling the client that a competitor's customer won.
And yeah, for some giveaways and stuff they'd take a list of people and trawl through their social media accounts to figure out who'd have the most impact.
Again, don't think the clients had requested this, it just made the job we're doing look better to show the client "Yeah this person won and look at all the social media buzz it created!" rather than "Yeah we gave it to someone that looks like a troll, has no media presence, and the only people that will probably hear about this are a few people in an IRC chatroom."
If it's not regulated (or small enough that the regulators won't notice), I'd assume any contest/etc like this is probably rigged. Marketing is, generally, an industry full of lies. The contests are no different.