Cube rule

Both in theory and in practice, the cube rule is only applicable in a two-party system.

In a multi-party democracy operating under the first-past-the-post system, the cube law invariably fails, often leading to capricious results.

If there are three parties the ratio of seats will also be proportional to the cube of their votes.

However, in elections for the United States House of Representatives in 1942, 1996, and 2012, the party that won a plurality of the votes actually won fewer seats in the House of Representatives.

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.

Expected fraction of seats won, s vs fraction of votes received, v (solid black) according to the cube rule, with a plot of the seat:vote ratio (dashed red)