Cube Rule

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. Mathematically the cube law works because it is an approximation to the Law Of Large Numbers .

The approximation ''can'' work well; it matched the 2002 U.S. House elections to within one seat.

However, in the 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 .

Reasons for the failure of the cube law in the UK include differential Turnout , the rise of the Liberal Democrats mostly at the expense of the Conservatives , Tactical Voting and inefficiencies in the Boundary Commission .

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Cube Rule