Question: Isn't FPTP a fair system because everyone has one vote and there is only one round for it to count in?
FACT: FPTP is equal in process, but not in influence, unlike AV which is equal in process AND equal in influence.
Probably the most popular myth about FPTP is that due to it being so super simple, it must be so super fair and equal too.
It is not.
25% of the population voted for a candidate that came 3rd or worse in 2010's General Election. Their influence on the result was almost non-existant. If, however, they had decided to vote AGAINST their preference and vote tactically then they would have made more of an impact, either by increasing or decreasing the majority of the winner, or potentially even changing the winner completely.
FPTP leaves a gulf in voter power between those that vote for the top two candidates and those that don't.
AV, by comparisons, almost abolishes this unfair situation. AV is a run off voting system which means that if there are no winners (someone with over 50% of the remaining votes) in the round taking place, the least popular candidate is removed from the race and votes are reallocated to those remaining. These rounds each ask the same question, "Who's the best candidate of those remaining now?", and keeps going until a clear winner is found
It is the electoral equivalent of working out what kind of beer you want from the bar when your favourite has been discontinued because not enough people are buying it.
Because of this process everyone has the same input in to the system, everyone has the same opportunity to rank as many candidates as they like, and then everyone also enjoys a fair outcome, the same opportunity as everyone else in each round to make a statement about who is the best candidate left in the running.
FPTP is the act of making a choice, but then being left out in the cold unless you are canny enough to vote AGAINST YOUR WISHES and in line with the more popular top two candidates, creating a divide in equality between those who happen to support the top candidates and those that don't.
Worse still FPTP provides additional weight in the single voting round of FPTP for those that are willing to abandon their true desires and vote negatively and tactically, over and above those that have decided to vote with their heart.
AV is the act of letting the system know your opinion, and then being involved in a much more equitable process of fairly working out who the most popular candidate is as a group...and not assuming that the largest minority, as small as 29% in one constituency in 2010, knows what's best more than anyone else. And best of all the chance of you being punished for voting honestly and positively is almost completely eliminated.
EDIT: Some like to come and say that they wouldn't put their full preferences, so they get less say. This is wrong. While your candidate is in, you get the same amount of say as everyone else, as soon as your candidate goes out you are also out. Is this unfair? Well ask yourself this, if you wouldn't put further preferences under AV, then you'd probably not turn up (or you'd spoil) at a FPTP election where your party wasn't standing, wouldn't you?
In that case you would have actively chosen to not take part, your choice...the same is said here of AV. If you want to choose to give yourself no further influence that is not an indictment on the system, that is you having the freedom to do as you wish with your vote. The system itself hasn't disempowered you, you yourself have.