Also, not all social actions work in the sense you say - that the lower statted player gets two second chances.
For example, when loitering suspiciously, the player sending the invitation gets two Hastily Scrawled Warning Notes and the person accepting gets one, regardless of stats.
For Chess and Sparring Bouts, the winner gets one of the relevant second chances and the loser gets two. As far as I know, the formula for who wins isn’t clear, although I have heard that it sets a challenge for one player based on a difficult level benchmarked against the other player’s stats. So in other words where the stats of the two players are very different you might be able to manipulate who wins and who loses by having one or the other player send the invitation. By doing that it’s possible to ensure that the higher statted player loses more often (and therefore gains more second chances) than they would if the other player was doing the inviting.