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representative democracy means the House of Commons represents the people, with a margin of error only for pragmatic reasons. That isn't true (2015: most MPs don't have more than half their vote, the party vote share doesn't match the party seat share, the governing party has less than half the national vote) so the voting system needs improving, but with what? There are many alternatives.

reformify helps to see the wood for the trees. It lists the basics of the main electoral systems, so you can easily compare what they do and don't do. Each system has properties it achieves by design (sometimes things aren't so bad simply by chance). The checkboxes select all with that property, or sort by some variable. Overall the simplification aids clarity but not completeness: please follow the wikipedia links for that.

summary if you're in a real hurry - to guarantee majority representation you need either only two candidates or a transferable vote system (SV, AV, AV+, STV); to get proportional representation you need either a list system (CLPR, OLPR), a top-up system (AMS, MMP, AV+), or STV.
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MR Majority Representation means your MP has more than half the constituency vote, or the equivalent, and therefore represents the whole constituency by there being more in favour than against, by being above average, by democracy is the rule of the majority. See note about majority. The MR percentages are of MPs who have a majority, currently in that country. The main reason this doesn't happen is there being more than two candidates.
PR Proportional Representation means nationally the party MP share matches the party vote share, and that as many voters as possible should be represented, meaning the House of Commons better represents the voters. The main reason this doesn't happen is not counting in bigger areas than constituencies & uneven geographical vote distribution. The PR percentages mean how much Proportional Representation is currently in that country. It is calculated using the Gallaher Index (but then inverting by subtracting from 100% since that formula gives disproportionality).
Open the voter chooses who represents them, i.e. you vote for named people you've met personally or could meet. The opposite - Closed - is being able to vote only for a party (sometimes you get the list of candidates but you can't choose amongst them), which some say means an MP is more beholden to their party than to the voters for their place. Some systems have both.
Equal all MPs are equal in being voted for in the same way for the same role & responsibility to voters. The opposite - Unequal - is having more than one route to becoming an MP.
Threshold the system has a mechanism for excluding fringe extremists, or stopping very small parties from getting disproportionate representation, maybe a national threshold (typically 5%) or as a natural property of the system.
Constituency link Sorts smaller to larger. Smaller is better. How much the voter will feel connected to their local MP is partly the size of the constituency and partly whether they agree with them, or if not whether the MP has a democratic majority. Conversely to get PR you're looking top-down at the whole country, so there's a trade-off here. Some systems have both local and non-local parts.
Choices Sorts more to less. More choices is better. The more choices the voter has the more the result is what the voter really thinks. And if there's less risk of vote splitting there is less need to resort to tactical voting to get something you prefer or dislike less.
Clarity Sorts most to least. Simpler is better. This is jointly the simplicity of how you vote and of understanding how the count works. But you may want a particular property even though how it works is a bit complicated. "Everything should be made as simple as possible, but not simpler." - Albert Einstein
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  1. This page isn't about direct democracy systems (as in Switzerland) - the UK has too many people for that in general.
  2. abstaining mean "don't care, mind or know" - any result is OK. It includes there being no point voting in safe seats. The voter might be wanting to say None Of The Above, i.e. no result is OK. Currently (2015) in the UK about 15% aren't registered to vote, and the turnout at General Elections is about 65%, meaning about 55% vote.
  3. "majority" has (at least) two definitions in the dictionary. One is "more than half", the other is "more than the second candidate". So "Democracy is the rule of the majority" has become ambiguous. A clarifying thought is that if there are only two candidates, or if it's a yes-or-no answer, then the two meanings are the same: having more votes than the other candidate automatically means having more than half. This page understands "X represents Y" to mean "most people at Y agree with X", i.e. there are more in favour than against, more than half. The technical term for "highest score even if not more than half" is "plurality".
  4. tactical voting You may have to vote tactically for a candidate or a party you don't like if you judge a party you dislike even more might otherwise win. A constituency may be so much for one party that your vote, if different, may have no effect besides publicity. Applies to FPTP, and any system that uses that, also other systems but to a much less extent. In May 2015 the Electoral Reform Society surveyed it at about 9%, more than the difference between the Conservative & Labour vote.
  5. transferable voting a.k.a preferential voting. You vote for a sequence of candidates in order of preference, but your vote counts against only one candidate at any one point in the count. It starts with your first preference and is transferred down the sequence only if necessary in order to achieve other things, like a democratic majority or maximising the number of voters getting some representation. Whether you think this compromise is worth making depends on what you think of the other things. You don't have to vote for more than one candidate or for all of them (you do in some Australian variations but that's their problem). The sequence of counting rounds is logically equivalent to a series of FPTP votes with the last candidate knocked out each time (a.k.a Runoff voting). That's what the French do, if no-one's got 50%, except they knock out all but the top two and everyone has to vote again.
  6. vote splitting is when similar choices A & B split the anti-C vote, such that C wins even though A + B > C. Think two left-wing candidates against a right-wing one. You can get this in all electoral systems but FPTP is easily the worst. Transferable voting mostly stops this since you have to get more than 50%, though it's theoretically still possible. wikipedia.
  7. The d'Hondt and Saint Laguë systems are ways of dividing up a vote proportionally without having fractions of MPs or seats and whilst being fair to the remainder.
  8. Q: if it's such a good idea why hasn't it happened before? A: the turkeys have never voted for Christmas. Each party leader can't risk losing power, by causing there to be fewer MPs for their party, without being swiftly ejected. The Queen, who should have an interest in her Governments representing her Subjects, can't interfere whilst remaining above party politics. So there's no-one in charge of this entire level, except We The People.
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Some things that can be done:
  1. The intention is to turn this page into a Facebook app, when you'll be able to: Record your preference here:
  2. Join the Electoral Reform Society, they've been doing it for years.
  3. Sign (="like") the Not in our Name page, a general-purpose "we agree there's a problem" petition.
  4. On Facebook: Voting Reform Team for reform activity, Voting Reform: the options for comparing voting systems (which is where this page comes from).
  5. Read Roy Jenkins' report on the UK voting system in 1988. It is amusingly wordy, but gives a good introduction to how experienced legislators see the problem.
  6. Read Michael Meadowcroft's updated write-up on the subject.
  7. Read Simon Hix & John Carey's 2011 paper The Electoral Sweet Spot, on the question of how small/big a voting area has to be to get useful nationally PR, if you want to get into some serious academic stuff. Short version: 5-7 of our current constituencies does it, surprisingly.