Imagine a group of people want to choose something, like what to have for dinner or a person to represent their interests. They choose a simple voting system: each voter votes for one candidate, and the candidate with the most votes is the winner. That's simple and straightforward so it's a good system, right?
Wrong! This voting systems is called First Past the Post (FPTP) or Plurality, and it's a terrible, terrible system. To explain why, consider the country of Dystopia, which divides its people into constituencies, each of which elects one member of parliament. At the last election in the All Stations South constituency there were 2 candidates, from the Bad Party and the Worse Party. The election went like this:
votes
Bad Party 12000
Worse Party 11000
So Bad won. But now it’s a few years later, and many voters don't like either of these alternatives. They are closer to the Bad Party, in that they dislike it but dislike the Worse Party even more. So these voters form their own party, the Better Party, and field candidates at the next election.
Because the Better Party is closer ideologically to the Bad Party than the Worse Party, more voters from that party switch over. The Better Party manages to attract 2000 non-voters (who were fed up with both of the alternatives), 2000 from the Bad Party and 500 from the Worse Party.
The next election goes like this:
votes difference
Worse Party 10500 -500
Bad Party 10000 -2000
Better Party 4500 +4500
Oh noes! The Better Party's intervention has made things go from Bad to Worse. Because the Better Party were ideologically closer to the Bad Party than the Worse Party, more people switched from Bad->Better than from Worse->Better, so Worse is now the winner.
The Spoiler Effect
This is called the spoiler effect and it's a main reason which FPTP is such a bad system. When the existing parties don't care much about an issue, if a new party comes in they will draw more votes from whichever of the existing parties they are ideologically closer to, making that party less likely to win and making things (from the new party's point of view) worse.
CGP Grey has a video on the spoiler effect and why FPTP leads to there being two big parties:
Because of these issues, countries with FPTP tend towards having 2 major parties, in what's called Duverger's Law. In Britain these are the Conservative and Labour parties, in the USA the Democrats and Republicans, in Canada the Conservatives and Liberals, and in all cases, the power of the 2 main parties becomes entrenched: they are very hard to replace, no matter how unpopular they get.
Politicians know FPTP is crap
Politicians know all this of course. So if a politician tells you FPTP is a good voting system, my advice to you is to laugh in their face. When they are actually saying is "fuck you voters, us and the other big party deserve to continue alternating in power forever, no matter how unpopular we get."
If you want proof that politicians know FPTP is crap, consider Britain's Conservative and Labour parties. Both support FPTP for elections to the Westminster parliament. Both have internal elections for their leaders. They are free to choose any system for these elections that they like -- they could choose their leader by consulting a ouija board if they so desired, or use FPTP if they wanted to. They both choose not to use FPTP.
Labour uses the Alternative Vote for its leadership elections, and the Tories use a multi-round system with the lowest-scoring candidate being eliminated in each round. Both of these are transferable voting systems, in which if a voter’s vote is to a losing candidate they can transfer their vote to another candidate who is better placed to win.
So if a Labour or Tory politician tells you that FPTP is a good voting system, after you have finished laughing, you should ask them “if it’s so good, why don’t you use it for your own elections?”