The cube rule or cube law is an empirical observation regarding elections under the

first-past-the-post In a first-past-the-post electoral system (FPTP or FPP), formally called single-member plurality voting (SMP) when used in single-member districts or informally choose-one voting in contrast to ranked voting, or score voting, voters cast the ...

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 A two-party system is a political party system in which two 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 usually refe ...

. In a multi-party democracy operating under the

system, the cube law invariably fails, often leading to capricious results.Rein Taagepera, "Seats and votes: A generalization of the cube law of elections." ''Social Science Research'' 2#3 (1973): 257-275
online
/ref> 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, often referred to as the House of Representatives, the U.S. House, or simply the House, is the lower chamber of the United States Congress, with the Senate being the upper chamber. Together they ...

in 1942,

1996 File:1996 Events Collage.png, From left, clockwise: A bomb explodes at Centennial Olympic Park in Atlanta, set off by a radical anti-abortionist; The center fuel tank explodes on TWA Flight 800, causing the plane to crash and killing everyone o ...

, and

2012 File:2012 Events Collage V3.png, From left, clockwise: The passenger cruise ship Costa Concordia lies capsized after the Costa Concordia disaster; Damage to Casino Pier in Seaside Heights, New Jersey as a result of Hurricane Sandy; People gat ...

, the party that won a plurality of the votes actually won fewer seats in the House of Representatives. In

New Zealand New Zealand ( mi, Aotearoa ) is an island country in the southwestern Pacific Ocean. It consists of two main landmasses—the North Island () and the South Island ()—and over 700 smaller islands. It is the sixth-largest island coun ...

, 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 Mixed-member proportional representation (MMP or MMPR) is a mixed electoral system in which votes cast are considered in local elections and also to determine overall party vote tallies, which are used to allocate additional members to produce ...

, 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.

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Psephology

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