I find your answer puzzling, Ron. FPTP is concerned with individual candidates, not collective votes. E.g.
Candidate A - 40%
Candidate B - 30%
Candidate C - 20%
Candidate D - 10%
So, candidate A is elected because he/she received more votes than any other INDIVIDUAL candidate. It's clearly true that 60% of the voters in the above scenario didn't want Candidate A to win. The problem is that their vote was split among the other candidates.
AV doesn't actually solve that. It just uses a mathematical algorithm whereby the least popular candidate is discarded and their votes redistributed. This process is then repeated until one candidate is allocated more than 50% of the overall votes. At this stage, the candidate who received the most number of "first-choice" votes is HIGHLY UNLIKELY to be the winner. Under AV, the votes of the least popular candidate can play a major role in deciding who wins the election.
FPTP may not be the best system, but AV is just farcical, IMO...