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The cube rule or cube law is an empirical observation regarding elections under the first-past-the-post system. The rule suggests that the party getting the most votes is over-represented (and conversely, the party getting the fewest votes is under-represented). It was first formulated in a report on British elections in 1909, then extended to elections in other countries. Both in theory and in practice, the cube rule is only applicable in a
two-party system In politics, a two-party system is a party system in which two major party, major political parties consistently dominate the political landscape. At any point in time, one of the two parties typically holds a majority in the legislature and is ...
. In a multi-party democracy operating under the first-past-the-post system, the cube law invariably fails, often leading to capricious results. Suppose we have two parties which receive A and B percent of the vote. According to the cube rule, the ratio of A seats-won to B seats-won should be proportional to A3/B3. So if A wins 60% and B wins 40%, the ratio of votes A/B = 60/40 = 1.5, but the ratio of seats is 603:403 = 3.375:1. That works out to a ratio of seats of 77:23. In a close election where the popular vote is A=52 and B=48, the seats break 56:44. In other words, the winner gets many extra seats. If there are three parties the ratio of seats will also be proportional to the cube of their votes. The approximation ''can'' work well; it matched the 2002 U.S. House elections to within one seat. However, in elections for the
United States House of Representatives The United States House of Representatives is the lower house of the United States Congress, with the United States Senate, Senate being the upper house. Together they compose the national Bicameralism, bicameral legislature of the United St ...
in
1942 Events Below, the events of World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a World war, global war that lasted from 1939 to 1945. It involved World War II by country, the vast majority o ...
, U.S. House election, 1996, 1996, and U.S. House election, 2012, 2012, the party that won a plurality (voting), plurality of the votes actually won fewer seats in the House of Representatives. In New Zealand, the rule predicted the distribution of seats between the two largest parties for most elections prior to election reform. From the 1940s onwards until 1993, after which the rule was irrelevant because of the introduction of mixed member proportional representation, many elections were predicted either exactly or within one seat, with most fluctuations from this in elections where there was a strong third-party showing. However, in the United Kingdom, UK, the cube law has operated erratically. Between 1950 and 1970, elections broadly followed the cube rule, but since 1974 the relationship has broken down, almost entirely to the benefit of the British Labour Party (UK), Labour Party. Reasons for the recent failure of the cube law in the UK include differential voter turnout, turnout, the rise of the Liberal Democrats (UK), Liberal Democrats mostly at the expense of the Conservative Party (UK), Conservatives, tactical voting and inefficiencies in the boundary commissions (United Kingdom), boundary commissions.

*Duverger's law

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