We've had a bit of a situation in a tournament and I just wondered how other people would have solved it. See attached image for details. We had 3 teams who were very equal on many/all of the tournament rules we had available (also below). I'd love to know how others would approach/work-out/solve this situation.
First of all, it's a bit unclear how iii. is to be interpreted. If "the results" only refers to the number of points the teams in question have earned while playing against each other, then the three teams (Athletic, United and City) are still tied because they've all won only one match each against the other two teams. So we should go straight to iv., but this one cannot be applied because more than two teams are tied.
Since this path leads to a paradox (the tie cannot be resolved without further tiebreakers, like drawing of lots), I believe the correct way to read iii. is the following: "re-apply all the above criteria only to the matches between the teams that are still tied". In which case, after seeing how Atheltic, United and City are still level on points (3 each), you won't go straight to iv., but you'll instead check which teams has scored the greater number of goals (i.e. you'll be applying i.), which is United (two goals for, as opposed to Athletic and City that have only scored one).
This means that United certainly qualifies as the winner.
But now you have to decide which team is the runner up, and at this point you have again two possibilites: either you go on with the criteria, thus using iv. to decide whether Athletic or City advances to the next stage together with United (since they're only two teams, a penalty shoot-out can take place), or you re-apply the criteria from the beginning again, solely to the teams that are still tied (that are, Athletic and City); in this case, the tie is immediately broken because only one game has been played between the teams in question, and it was won by Athletic.
However, the latter solution usually needs to be clearly stated in the regulations like this (example taken from the Regulations of the UEFA European Football Championship):
if, after having applied criteria a) to d), teams still have an equal ranking, criteria a) to d) are reapplied exclusively to the matches between the remaining teams to determine their final rankings.
And since these regulations don't seem to state a provision like this anywhere, the first thing I said is the only one that's coherent with the rules you provided: that is, a penalty shoot-out must take place in order to decide whether Athletic or City should advance to the next stage as the runner up.