Imagine the following setup. There are 3 (or more) players with an equally long road. What would happen if the longest road was broken? How is it decided who obtains the longest road from there on?
No. The rules are pretty clear about this:
Set the “Longest Road” card aside if—after a longest road is broken—several players tie for the new longest road or no one has a 5+ segment road. The “Longest Road” card comes into play again when only 1 player has the longest road (of at least 5 road pieces)
Your example exactly meets the criteria, "after a longest road is broken" and "several players tie for the new longest road".
According to the Catan FAQ it depends on a few things.
- If the player that had the longest road still has the longest road and it is 5 roads long or longer, or is tied for it, they keep it
- If the player that had the longest road no longer has the longest road and one other player has a uniquely longest road (greater than 5 pieces), that player gets the longest road
- If the player that had the longest road no longer has the longest road, and no players have a road at least 5 pieces long, or the longest road is a tie (not including the former longest road owner) the player that had it loses it and nobody gains it.
So in your case nobody would end up with the longest road.