Ginyu makes good points, though I still voted for option 1-- option 2 incentivizes only the bare minimum. The lack of criteria shouldn't be a big issue, as voting for your favorite propaganda shouldn't be complicated-- just pick the one(s) you like best! Heck, if you like all of them, vote for all of them. I don't think voting should be restricted. The reward doesn't have to be solely determined by rank either. One way to do it would be to give X relics to each team that participated, and then maybe X+1, X+2, X+3 for 1st, 2nd, and 3rd place in the poll. Or something along those lines.
As for propaganda not being real propaganda, that's true-- it's not really meant to persuade others to join your team or root for you. Rather, it's a place to set up bragging rights and establish a team/themed spirit. Relics have had an extremely low impact in the past anyways, and the number given out for propaganda probably won't end up being significant -- just a small nudge to encourage the activity. One of my favorite teamy-spirity things was actually what Team Entropy did in War 9, with the whole avatar-ninja squad. Imo, that fits right in with what propaganda is all about.