This article is about the political science observation. For the U.S. congressional apportionment proposal, see Cube root rule.
"Cube law" redirects here. For the scientific law, see Square–cube law.
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 a multi-party democracy operating under the first-past-the-post system, the cube law invariably fails, often leading to capricious results.[1]
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)
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.
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.
^Rein Taagepera, "Seats and votes: A generalization of the cube law of elections." Social Science Research 2#3 (1973): 257-275. online
Further reading
Maloney, John; Pearson, Bernard; and Pickering, Andrew. Behind the Cube Rule: Implications of and Evidence Against a Fractal Electoral Geography (pdf) Environment and Planning A 2003 35: 1405-1404.
Gryski, Gerard S.; Reed, Bruce; and Elliott, Euel. “The Votes-Seats Relationship In State Legislative Elections., “American Politics Quarterly 1990 18(2): 141-157.
Qualter, Terence H. “Seats And Votes: An Application of the Cube Law to the Canadian Electoral System,” Canadian Journal of Political Science 1968 1(3): 336-344.
Rein Taagepera, ‘Reformulating the Cube Law for Proportional Representation Elections’, American Political Science Review, 80 (1986), 489–504.
Rein Taagepera, "Seats and votes: A generalization of the cube law of elections." Social Science Research 2#3 (1973): 257-275. online</ref>
External links
A Theory of Democratic Politics
December 29, 2022
cube, rule, this, article, about, political, science, observation, congressional, apportionment, proposal, cube, root, rule, cube, redirects, here, scientific, square, cube, cube, rule, cube, empirical, observation, regarding, elections, under, first, past, po. This article is about the political science observation For the U S congressional apportionment proposal see Cube root rule Cube law redirects here For the scientific law see Square cube law 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 a multi party democracy operating under the first past the post system the cube law invariably fails often leading to capricious results 1 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 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 in 1942 1996 and 2012 the party that won a 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 Contents 1 See also 2 References 3 Further reading 4 External linksSee also EditDuverger s lawReferences Edit Rein Taagepera Seats and votes A generalization of the cube law of elections Social Science Research 2 3 1973 257 275 onlineFurther reading EditMaloney John Pearson Bernard and Pickering Andrew Behind the Cube Rule Implications of and Evidence Against a Fractal Electoral Geography pdf Environment and Planning A 2003 35 1405 1404 Gryski Gerard S Reed Bruce and Elliott Euel The Votes Seats Relationship In State Legislative Elections American Politics Quarterly 1990 18 2 141 157 Qualter Terence H Seats And Votes An Application of the Cube Law to the Canadian Electoral System Canadian Journal of Political Science 1968 1 3 336 344 Rein Taagepera Reformulating the Cube Law for Proportional Representation Elections American Political Science Review 80 1986 489 504 Rein Taagepera Seats and votes A generalization of the cube law of elections Social Science Research 2 3 1973 257 275 online lt ref gt External links EditA Theory of Democratic Politics Retrieved from https en wikipedia org w index php title Cube rule amp oldid 1122955485, wikipedia, wiki, book, books, library,
