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The first vote implicitly shows that he would have, as it is clear that a majority in the town wanted him gone independent of who would then replace him. It's almost certain that the second-placed candidate, at least, would have beaten our incumbent in a head-to-head battle.
The mathematical theory behind such voting anomalies is well-established, and I'd encourage you to read into it at some point. But for the time being it should be clear that the two votes, head at the same time, are inconsistent with each other. If the town wants a particular person to go, then the electoral system should be able to reflect that. It very clearly did not in this case.
To tie it in with Brexit, imagine if the people had been asked two questions on June 23rd: firstly whether they wanted to leave, and secondly which of several futures they wanted to pursue. It is safe in that case to say that there would have been at least *some* level of division amongst the Leave voters, and enough, too, to squeeze it out of contention as compared to Remain. In that case we would have remained because of the lack of agreement among *how* to leave, and the question would have been considered dead.
In both cases, granted, one way around it is to insist that the second question can only be asked assuming that the "incumbent" decision must be excluded, or perhaps there must be a delay between the two questions being asked, so that the "incumbent" supporters are invited to reconsider their vote in light of defeat. So this particular vote in Fall River is also flawed in ways beyond merely using an FPTP system. But the point I am making is that the two votes could well have been held at the same time, and not delivered such a stark contradiction within other voting systems, that don't belong to PR but instead are "preferential" voting systems.