Thanks, I've updated the OP. But it's not entirely clear to me how to determine if the accounts are connected to each other?
It would just act as a deterrent, it does not mean that you'd start looking for connected accounts that have joined your competition, you'd just have to include it as a rule so member's would understand that it isn't allowed. That doesn't mean it will stop some member's from trying to join the competition with alts, but by doing so they have broken the competition rules, and they can be tagged if they are caught.
Just take it as every other rule we have out there, it does not mean people won't attempt to break it, but it is there so if they are caught they do not say there was no rule against what they did, so that way you will reduce the number of offenders as people would not want to get into trouble, and those who go on to break the rules might be caught. Don't trouble yourself looking for connected accounts that break rules, there are members here who will do that for you.
but since there will only be one winner, it seems that concentration on multi or alt accounts is not very important because no one will be able to get the two prize
But someone that joins the competition with more than one account, with different slogans on all accounts has increased their chances.
On the topic, let me go think about a suitable slogan, i will either edit this post with it, or make a new one, cheers!