Happened to me in this game.
The 12 chosen cards are Coppersmith, Cutpurse, Explorer, Fool's Gold, Fortune Teller, Haven, Island, Laboratory, Minion, Saboteur, Wharf, and Young Witch.
GwinnR vetoes Fool's Gold.
Inflatable Toaster vetoes Minion.
Before he vetoed Minion, Inflatable Toaster asked me, if he should veto Minion or Saboteur. Thanks for this nice gesture, that's why I let you win ;-)
If Governor is not on the board, my GF often asks me what card I would like her to veto, regardless of who vetoes first. I still can't seem to win very often, but at least Possession is never in our games. (Unfortunately, neither is Governor.)