This is the likely scenario for many people when they go to vote under First Past The Post. And you only get to state a preference about one of the candidates, not give a general opinion about the whole selection.
So what do you do? You vote tactically. You don't say what you really think, and instead you vote for the candidate who you find least offensive out of those who are likely to win.
And your preferred candidate looks less popular than he or she actually is. So next time an election comes around, people won't vote for him/her yet again because they look like they don't have a chance of winning.
With the Alternative Vote, you get to be honest about your preferred candidate, and then you can also state second and third preferences for the candidates - those candidates you would have voted for tactically under FPTP.
Chances are, the same person will end up winning the seat (as it's still not a proportional system), but you'll actually have a realistic view of which candidates are people's first choice, and the winning candidate will have to get the support of 50% of the voters, even if some of that is coming from second or third preference votes.
AV wouldn't put an end to tactical voting, but it will certainly encourage more honesty about first preferences.
There has been much talk about the BNP too. Can you really imagine the BNP getting any more votes under this system than under FPTP? Are people really going to say, "Well, I wouldn't vote for them as my first choice, what with being racist and everything, but they're worth a second or third preference vote"? The BNPs are likely to sink without a trace under AV.
Less objectionable minor parties like the Greens, however, are likely to do a little bit better, as they'll win a few more first choice votes to start with, with people knowing their second preference could count, and so a vote for the Greens isn't a wasted vote. This should give a truer reflection of their support.
There has been a lot of "one person, one vote" bollocks. You still only vote once. You don't have any more votes than anyone else. Your vote may be reallocated, but doesn't count twice as much as anyone else's.
The important thing here is that a candidate who is supported by a sizeable minority, but deeply mistrusted by everyone else, has little chance of winning. This is something that didn't really matter all that much back when the vast majority of votes were split between just two parties, but when a deeply unpopular candidate can win with the support of only a third of constituents, you have to worry.
Here's a graph to illustrate how the political landscape has changed in the last 50 years, and how many more MPs are elected on the support of less than 50% of their constituents:
|Graphic illustration of why FPTP is no longer fit for purpose [source]|