Pluralities, majorities and how voting systems - not people - can decide elections

Here are the results from yesterday's Parliamentary elections in the United Kingdom. Note the number of votes each of the top three party received, then the number of seats in the next House of Commons they'll have as a result:

Conservative: 10,706,647 votes - 306 seats
Labour: 8,604,358 votes - 258 seats
Liberal Democrat: 6,827,938 votes - 57 seats

Let me do the math for you:

The Conservatives won one seat for every 34,989 votes its candidates received.

The Labour party won one seat for every 33,350 votes its candidates received.

The Liberal Democrats won one seat for every 119,788 votes its candidates received.

The U.K.'s political system is a bit different than ours. The government's run by a Prime Minister, not a President, who is not elected by the people. Instead, the party with control of the lower house of Parliament (the House of Commons) designates its leader as the Prime Minister.

After yesterday's election, no party has a majority in the House of Commons, so either the Conservatives or Labour will have to strike a deal with the Liberal Democrats or the other, minor parties to control enough votes to appoint a Prime Minister.

But, wow, did the Liberal Democrats get jobbed.

How did this happen? Seats in Parliament are not appropriated according to the national vote. People in the U.K. vote in districts, as we in the United States do for our Representatives. But in the U.K., whichever candidates gets the most votes wins the seat, even if that candidate did not win a majority of the votes cast. This is called the first-past-the-post system.

First past the post works well when you've got two major parties, as the U.K. has had for most of its recent history. But when votes are split among three, four or even dozens of candidates, it often delivers winners who enjoy only a slight fraction of support within a district.

Indeed, what happened in the U.K. yesterday was that Liberal Democrat candidates drew enough votes away from Labour candidates that 100 new Conservatives won election to the House of Commons. This, despite the fact that U.K. voters collectively preferred the two liberal parties over the conservative one by a margin of 60% - 40%.

Contests between two candidates (or two parties) are easy. Let the citizens vote, and whoever wins the most votes wins. But what happens when you have three or more candidates seeking a seat?

Political scientists and game theory geeks have come up with dozens of different ways to narrow a wide field of candidates to a single winner. Most involve having voters pick second and third choices, or even ranking all the candidates, from most favorite to least. Read Wikipedia for the geeky detail.

One popular system listed in that article is an "instant runoff," where the candidate getting the least first-place votes is eliminated. Then, that candidate's votes are released and re-counted for the candidates those voters had picked as their second choice. If that doesn't give any candidate a majority, then the second-least popular candidate is eliminated, and so on.

That version of an instant runoff system allows the supporters of the least popular candidates first crack at determining who gets the "second chance" votes. I prefer an instant runoff system which counts everyone's second-choice ballot equally.

Here's my ideal voting system: If more than two candidates stand for a seat, voters should select a first and second choice. If no candidate wins a majority of first-choice votes, then the seat goes to the candidate that was selected as the first- or second-choice on the highest percentage of ballots, assuming that he or she was selected as such on at least 50 percent of the ballots cast.

If no candidate was selected as a first- or second-choice on a majority of ballots, then the two candidates who got the most selections as a first- or second-choice face off in an actual run-off election four weeks later. (Holding an election is expensive, so ideally you'd have a system that minimized the need for a separate, second round of voting.)

In the U.K., it's most likely that in districts where no candidate received a majority that the Liberal Democrat voters would have picked the Labour candidate as their second choice, and vice versa. So my system would have led to more seats for the Liberal Democrats and Labour, better reflecting the overall distribution of votes in the United Kingdom.

My system likely also would have delivered the U.K. a hung Parliament. But at least the Parliament would have more accurately reflected the political slant of the U.K. people, providing stronger encouragement for a Labour/Liberal Democrat coalition.

Robert Niles also can be found at http://www.themeparkinsider.com