The cube rule or cube law is an

empirical observation Empirical evidence is evidence obtained through sense experience or experimental procedure. It is of central importance to the sciences and plays a role in various other fields, like epistemology and law. There is no general agreement on how the ...

regarding elections under the

first-past-the-post First-past-the-post (FPTP)—also called choose-one, first-preference plurality (FPP), or simply plurality—is a single-winner voting rule. Voters mark one candidate as their favorite, or First-preference votes, first-preference, and the cand ...

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 referr ...

. 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 66.7% and B wins 33.3%, the ratio of votes A/B = 66.7/33.3 ≈ 2, but the ratio of seats is 66.7³:33.3³ ≈ 8:1. That works out to a ratio of seats of around 89:11. 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

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1996 1996 was designated as: * International Year for the Eradication of Poverty Events January * January 8 – A Zairean cargo plane crashes into a crowded market in the center of the capital city of the Democratic Republic of the Congo ...

, and

2012 2012 was designated as: *International Year of Cooperatives *International Year of Sustainable Energy for All Events January *January 4 – The Cicada 3301 internet hunt begins. * January 12 – Peaceful protests begin in the R ...

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

New Zealand New Zealand () is an island country in the southwestern Pacific Ocean. It consists of two main landmasses—the North Island () and the South Island ()—and List of islands of New Zealand, over 600 smaller islands. It is the List of isla ...

, 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 type of representation provided by some mixed electoral system, mixed electoral systems which combine local Winner-take-all system, winner-take-all elections with a Compensation (el ...

, 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

See also

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