Yair Lapid, the former journalist whose new party, Yesh Atid, fared better than expected in yesterday's Knesset elections in Israel. "Better than expected" means 19 seats out of 120. (Sebastian Scheiner/Associated Press)

The results of the 19th Knesset elections in Israel are in, and the plurality winner is Likud Beitenu, the electoral alliance between the conservative Likud party and Yisrael Beitenu, a nationalist party popular with Russian immigrants. But Likud Beitenu only has 31 seats out of 120, or 25.8 percent of the Knesset.

That's not unusual. After the 2009 elections, the plurality winner, Kadima, only had 28 seats. Indeed, except for a short period in 1969 when the Labor Party merged with the leftist party Mapam, a single party has never held a majority of seats. That's why Israeli politics is characterized by short-term coalitions in which big parties make concessions to smaller parties in exchange for their participation. The numbers just don't work out any other way.

Why does this happen? It has to do with the type of proportional representation that Israel has settled on. Israel uses a dead-simple "pure party list" system. There are no geographic districts. Indeed, no voter ever votes for an actual person. Instead, every voter votes for a single party. All parties that receive more than 2 percent of the national vote is allocated seats in proportion to their vote share using an algorithm called the "D'Hondt method." The parties then allocate the seats they won to members based on an ordered list decided upon before the election. So suppose that the Labor Party puts together an 120-person list, and wins (as it did this time) 15 seats. The first 15 people on that list will thus get seats in the Knesset.

It's easy to see how this could reward small parties. Suppose there were just two parties, and one election resulted in 65 seats for Party A and 55 seats for Party B. Then Party C comes on the scene and steals six seats from Party A. Suddenly, A has 59 seats, B has 55, and C has 6, so C effectively gets to decide who forms the government. Being Party C is a pretty great deal! You only need to get 5-6 percent of the vote and you still get a lot of power. So, encouraged by this low bar for power, a lot of parties form and try to be Party C.

This doesn't happen in first-past-the-post systems like the U.S. and the U.K., because small parties usually get disproportionately few seats in such systems. For example, in 2010 the Liberal Democrats won 23 percent of the vote in the U.K. general elections, but only 9.5 percent of seats. So it's much less likely that founding a modestly popular minority party will put one in a position of power.

This observation, that plurality voting methods almost always result in stable two-party systems while proportional systems tend to have more parties, is known in political science as Duverger's law, and it's held up very well since the French sociologist Maurice Duverger developed it in the 1960s. In his book, "Patterns of Democracy," UCSD political scientist Arend Lijphart produces this chart, showing a strong correlation between a metric standing in for the proportionality of a voting system and the effective number of parties in parliament:

(Yale University Press)

That being said, it's not a perfect correlation, and a number of other factors affect the ultimate number of parties. India, for example, has a pretty disproportionate electoral system, and a huge number of parties, most likely due to its high level of ethnic and cultural diversity. Germany and Austria have systems about as proportionate as Denmark and the Netherlands', but about two fewer parties. Ljiphart argues that this has to do with the nature of cleavages within societies. It's not so much that Denmark is more diverse or hetergeneous than Austria, say, as that Austria seems to be split down the middle culturally whereas Denmark has a number of smaller divisions. This shows up in the number of parties exerting influence.

Countries with party list representation, and thus with many parties, tend to get a bad wrap, and looking at their ranks it's easy to see why. In Israel, the need to court small rightist and ultra-Orthodox parties has arguably hampered the peace process, while Belgium's proportional system, combined with its huge linguistic and cultural divide between French and Flemish speakers, led to coalition negotiations that took 541 days to conclude between 2010 and 2011. Italy's corrupt political parties and short prime ministerial terms are the stuff of legend, and even a well-governed country like the Netherlands has experienced long government formation periods due to its electoral system. Denmark seems to have fared all right, but "it only works in homogenous societies with high levels of civic trust" isn't exactly a ringing endorsement of an electoral system.

From left, Lord of the Rings director Peter Jackson, New Zealand Prime Minister John Key and Wellington Mayor Celia Wade-Brown. New Zealand has a great electoral system. (Getty Images)

But it's possible to have strong forms of proportional representation that stop short of party list representation and don't result in this kind of fragmentation. Japan, Germany and New Zealand all use a system called "mixed-member" proportional representation (or MMP) that seems to work a great deal better. In MMP, voters both choose a local representative and vote for a national party. Then, parties that have fewer seats than their national vote share suggests they should have get "add on" members chosen from a party list to compensate. So parties both have to compete regionally and get broad national support, while voters have the benefit of a dedicated, geographic representative. At the moment, that's led to a two-party system in Japan and New Zealand and a four-party (two left, two right) system in Germany which has traditionally had no trouble forming coalitions.