There was a discussion on this a couple of years back
for anyone who wants some background/context.
Alternative vote/single transferable vote/standard transferable vote (all the terms basically mean the same thing) does have a lot going for it; it retains many of the strengths of FPTP while also mitigating some of the weaknesses. That said, it also has some pretty deep flaws (as all systems do for that matter). The most obvious is inherent to the system; elections under AV tend to be won not by the party that people like most but by the party they dislike least, with elections decided by who manages to pick up the most second, third, fourth, fifth etc preferences. In essence it becomes less about what party people really support and more about which party is most inoffensive. I don't think that's the way elections should be won... I think they should be decided by who the most people support. STV can conceivably lead to a party that has 49.9999....% of the first preference votes losing to one that has far, far less... that strikes me as being an issue. Take the below example:
10 parties, 100 votes (note, I'm using "parties" here but depending on the electoral system it could well be "candidates" instead; read one, the other or both into it)
Party A gets 46
Party B gets 10
Party C gets 9
Party D gets 8
Party E gets 7
Party F gets 6
Party G gets 5
Party H gets 4
Party I gets 3
Party J gets 2
Now, if every voter ended up ranking their second, third etc preferences onwards in reverse popularity order (so those who voted for E had J as second, I as third, H as fourth etc etc) then the eventual winner of that election would be "I"; J is eliminated first giving I five votes, then H goes giving I nine, then G goes giving I 14, then F goes giving I 20, then E goes giving I 27, then D goes giving I 35, then C goes giving I 44 and finally B goes giving I 54 and the win. But only 3% of people really
wanted I. It also presents an issue that despite J being the universal second choice and thus on paper the most acceptable answer, they're eliminated first and thus it no longer matters that everyone has them as their second choice. It can become even more complex when the votes aren't that simplistic; you'll have situations where a party wins not because they were second or third choice but because they were fifth and sixth choice. One could conceivably get around this by lessening the value of preferences beyond the first (so a first preferences counts for one, a second preference 0.5 etc etc) but that leads to horribly complicated maths.
STV also gives a huge amount more power to voters who use all their preferences compared to those who don't. A voter who ranks every single candidate has their vote counted at each runoff. Someone who votes only for the party they really like? Their vote only counts until that party are eliminated and then they are disenfranchised. One could get around this by requiring people to rank every party but that runs the risk of "donkey voting" where people eventually rank candidates merely in the order they appear on a ballot.
The main other voting system compared to STV and FPTP is some form of proportional representation. In principle this works by giving each party the same percentage of representation as their vote percentage; so a party with 4% of available votes gets 4% of available seats. This is inherently fair but comes with its own issue; you'll rarely, if ever, get an outright winner and so you'll have to have a coalition government... frequently a grand coalition featuring a large number of parties. This has two main impacts; first, it gives a huge amount of "kingmaker" powers to minor parties, because a party with 5% of the vote can decide who to form a coalition with to make a government they can demand executive positions and some of their policies implemented despite their lack of popularity with the wider public. You frequently see this is PR systems... a party which is constantly part of the government and gets some of its policies implemented despite having a tiny percentage of the vote. Secondly it also prevents parties from implementing their more radical policies; let's say a party gets 40% of the vote on the basis that it will say, abolish all taxes. Despite being the most popular party and the reason for it being that popular being that it will abolish taxes if every other party opposes that measure then the party will have to drop that policy if it wants to form a government... leaving the 40% of the electorate who voted for them on that basis disappointed. That's more an issue with coalitions then with PR itself... but PR pretty much always leads to coalitions.
To mitigate that issue in practice few systems are that
proportional (Israel is the closest to fully proportional that I know), instead putting a threshold in so a party needs to get say 5 or 10% of the vote before it can get seats. But that only mitigates it; you'll still see parties who just cross that line wield disproportionate power (arguably more in that case) and more radical policies dropped, while it also weakens the inherent fairness of PR (why should a party count if its gets 5% of a vote but not a party which gets 4.9%?).
PR also has the issue of moving power away from voters to the party. PR systems tend to use a "party list"; in the simple 100 vote system used earlier a party would list 100 people who would get seats if they won the entire vote and if it got 40% it would take the top 40 and give them seats. This has two effects... first, it removes the direct connection between me and who represents me; I didn't directly vote for them (and as a follow up it's virtually impossible to have a constituency system in PR so there's no-one who directly represents my area in power). The second is a continuation from that; because it's the party who gets to decide whether someone gets a seat or not (by changing where they stand on the party list) if there's ever an issue where the representative has to decide between standing with his party and standing with the voters there's an incentive to support the party; the party can simply move them down the list for the next election and thus almost guarantee they're not elected regardless of how popular the party is. On a side note, PR also largely prevents true independents.
There are some hybrid systems that try to get around some of these issues by combining them; AV+
is an obvious example. This works by combing STV and PR; voting is conducted as if it was simply an STV election but then the final results are "topped up" by PR following a list. So if there are 200 seats to be won that 150 would be decided entirely by STV but the last 50 would be awarded proportionately on the basis of the STV votes (so if a party got 10% of the first preferences but didn't get anyone elected through that it would get 5 representatives on the basis of 10% of 50 being 5. It's a compromise that mitigates both the strengths and weaknesses of both systems and has the additional issue of creating two classes of representatives; those directly elected and those chosen by the party.