The UK is voting on this today. Here is a good survey of social choice approaches to the question, and here is a survey of how AV systems work. The basics are this:
Alternative vote (AV) is a type of preferential voting in which voters are asked to rank the candidates from first to last. The basic idea is that if no candidate is the first choice of 50% + 1 voters, then the candidate who received the fewest first place votes is eliminated. This candidate’s voters then have their votes reallocated to the candidate they ranked second. This reallocation process continues until one candidate achieves 50% + 1 votes (more on this later).
Too often the social choice approaches focus on the formal properties of the voting and do not capture the actual political incentives of electoral systems, which tend to follow from imperfect information and the behavioral tendencies of voters. In this case the key change is that competition for votes becomes messier and less clearly linked to major party identities.
A long time ago I wrote this analysis of related (but not always identical) systems:
Electoral systems based upon the single transferable vote tend to produce the
• voters can express preferences for more than simply their favourite candidate
• representatives are focused towards constituency service and district policies,
rather than national policies;
• political parties are weak, non-ideological, and subject to frequent infighting;
• the ability of the legislature to check the executive is weak;
• most voters are confused by the mechanics of the single transferable vote;
• sophisticated voters have an incentive to manipulate the system and vote an
order which is not their true preference.
That is followed by a much more detailed analysis, scroll to p.56 for more. At best such systems are workable, but it is hard to see why they should bring any major advantages.