The current British electoral system- first past the post (FPTP)- gives a Parliament that is only approximately what the voters choose. Several times in the past, the party with the largest number of MPs, and which therefore becomes the government, has received a lot fewer votes than the supposedly second party. Sometimes MPs can be a elected when three quarters of those who voted chose someone else. In other words, FPTP does not accurately reflect how people actually vote- and it therefore fails a major test of democracy.
The Liberal Democrats- and many others in all parties- believe that the electoral system should give a result that is proportional to how people vote: if 40% of people vote for a party, then it should have 40% of the seats in the House of Commons, not 70%, which is often what happens now.
The way we would prefer to do this is for voters to list in order of preference their candidates, and instead of dividing up regions: Edinburgh West, South, North, East, South West etc, we would have five MPs chosen for the whole of Edinburgh. So in this example, each party would put up five candidates in Edinburgh, and voters chose between them. If voters chose five MPs of a single party, then five would be elected only from that party, and if they chose to vote for an independent candidate and they gained the roughly one fifth of the votes need to qualify, then an independent could be an MP. Sometimes, voters might split their ticket, voting in favour of candidates from different parties, because they like one individual's personal characteristics even if they don't much like their party. The point about this is that it leaves the choice up to the voters themselves, and it guarantees that all parties, and independents, can expect to compete fairly. This system, known in crampingly dull jargon of electoral politics as "the single transferable vote in multi-member constituencies", usually, and mercifully shortened to STV, is fair, open and widely used- including in the UK, for Scottish local elections. It is easy to vote: you just list in order of preference, but the counting of the votes is relatively complicated, involving the elimination of the candidates with the lowest number of first preferences and the transfer of their votes proportionately to the other candidates until the final tally, where (in the Edinburgh example, five), MPs are elected having achieved a number of votes and transfers that exceeds the quota (in the Edinburgh example, roughly one fifth of the total votes and preferences cast).
The problem for STV is that neither the Labour Party, nor the Conservatives, like the idea that voters can chose between candidates of the same party. The party barons fear that they can not impose "party discipline" on MPs who have a popular local mandate which has been tested against other candidates of the same party. These popular MPs are indeed far more likely to rebel against the party line.
Yet FPTP is manifestly unfair and all parties at various times have been the victim of it. The result has been that Labour, and a few in the Conservatives have been scratching around for a -rather messy- compromise. This has resulted in the emergence of the Alternative Vote- (AV). Here the method of voting is the same as STV: the voters list in order of preference, but only one MP gets elected for each constituency- in other words we still break up cities and counties into smaller units, with all of the boundary commission disputes and the rest of it. The only real advantage of AV is that in order to win, they must essentially reach a quota of 50%+1, so more MPs would be chosen by the majority of their voters, rather than, as now, where it is happened that MPs have been elected on as little as 25% support.
AV is barely an improvement on FPTP, in that it will not deliver a result that is proportional to how people actually voted, and it allows the party barons to impose more discipline on rebel MPs.
However, FPTP is so unfair that it has to be changed, and getting voters to list in order of preference for one MP is but a short step to listing for several MPs- that is the STV system. So the referendum is critical, because if it fails, it means that voters are essentially too apathetic to care about what happens to their vote. All of the complaints that people have made: from the expenses scandal to poor legislation, to the disconnect between the rulers and the ruled are in part the result of an electoral system that fails to hold the politicians to account. Without the even fairly small change that AV represents, then British politics will be unreformed, and may in the end by unreformable.
So in the final analysis, at this referendum it is necessary for the British people to show their political leaders that the current system has failed and must be reformed. Although the change to AV is actually pretty small, it would be a statement of intent: that the British people want to see an improvement in their democracy.
Unless they do that, the outlook for our political system is bleak indeed. So, even though I think AV changes little in practice, I have registered from overseas and will be voting "Yes" because without that small step no further change is likely for many years- and given the scale of the crisis in the UK, I don't think we can wait that long.
It is the last chance, but it is a chance, and we should grab that chance with both hands.