Italy assembly-size reduction: Cube root!

Based on the results of a referendum, Italy will be changing the size of its Chamber of Deputies from 630 to 400. By the cube root law (Taagepera, 1972) a country the size of Italy (around 60.5 million) should have about 392 seats in its first chamber. I’d say 400 is “about 392” and so this outcome is an obviously good thing.

Thanks to Matthew Bergman, Miroslav Nemčok, and Rein Taagepera for calling this to my attention. Rein also sent along an Italian newspaper article (PDF, a bit blurry) in which he was quoted.

The assembly reduction proposal was advanced by the Five Star Movement. As Rein said in personal communication, “sometimes populists get it right.”

Also, the Italian Senate is being reduced, to 200 (from 315, not counting appointed senators). I am not aware of any predictive model for how large a given second chamber “should be”, at least in unitary systems, but I note that in A Different Democracy, 2014, p. 214, we report that the mean second chamber in a unitary state is 0.53 times the size of the first chamber. So Italy is continuing to follow this pattern.

26 thoughts on “Italy assembly-size reduction: Cube root!

    • “Only Germany and Canada compromise between territorial and per capita representations.”
      Uh… Austria? India?
      Even Alan’s and my recent object of fascination, 1910-1994 South Africa? (or at least 1910 until 1980, when the Afrikaners abolished their Senate)
      True, India’s allocation doesn’t have any intelligible formula I can discern – Rajya Sabha seats are simply decreed by one or another of the several dozen Schedules to the Constitution – but Austria very definitely uses a mixed formula. The most populous Land gets 12 upper house delegates, and every other Land gets either one delegate per every quota (this being one-twelfth of the largest’s population) or three delegates, whichever is larger (ie,a maximum 4 to 1 range, as opposed to 2 to 1 in Germany and 1 to 1 in the USA, Argentina, Brazil, Australia, etc).
      Italy had a minimum of one Senator for the Val D’Aosta and minimum six for the other 19 Regions, the other seats being population-allocated.

      • Taagepera and Allen say that “at the opposite extreme, only Austria allocates purely on population basis n = 1, while four others do so with minor modifications. For instance, India’s subunits with population shares of 0.6%–0.9% would deserve two seats, but they actually receive three or even four, in a minor concession to the norm T is T”. So Austria goes into the population-only category, and India goes into the “mostly population” category with Belgium, Ethiopia and Spain.

        I tend to agree with Tom that this is something of a perversion of the actual Constitution. It’s possible that they’re talking about how the Federal Council allocation formula has worked in practice, but that seems unjustifiable also: Burgenland, Austria’s smallest state, seems to have considerably less than four times the population of Lower Austria or Burgenland.

      • This is from an English translation at
        Article 34 [Representation]
        “(1) Pursuant, to the following provisions, the States are represented in the Senate in proportion to the number of nationals in each of them.
        (2) The State with the largest number of citizens delegates twelve members, every other State as many as the ratio in which its nationals stand to those in the first-mentioned State, with remainders which exceed half the coefficient counting as full. However, every State is entitled to a representation of at least three members. A substitute will be appointed for each member.
        (3) The number of members to be delegated by each State accordingly will be re-calculated after every general census by the Federal President.”
        (PS: it’s one of those translations that renders “Nationalrat” as “House of Representatives” and “Bundesrat” as “Senate”… Why, out of curiosity, do we leave Germany and Austria with “Chancellors” but change Italy’s “President of the Council of Ministers” to “Prime Minister”? Maybe because the US has no “Chancellor”, but there would be confusion if you didn’t change “President of the Federal Assembly” to “Bundestag Speaker”, or “President of the Constitutional Court” to “Chief Justice”? Anyway…)

      • For some reason the Wikipedia page for the Austrian body is titled “Federal Council” while the page for the German body is titled “Bundesrat”. Wikipedia being what it is, presumably there were many pages of debate and discussion on this topic and I have no intention of challenging it.

      • I know of another example as proof for the Allen-Taagepera logical model: Chile.

        Chile, although not federal, has a senate in which seats are apportioned over regions neither proportionally with population, nor by giving every region the same number of seats. It has been a compromise ad hoc arrangement since 1988. At first some regions had 2 seats and others had 4 seats for a total of 38 directly elected seats (other senators disappeared in 2005). After a reapportionment (decided in 2015 for the half-senate elections of 2017 and 2021) the range is 2, 3 or 5 seats for a total of 50.

        With the input of 50 seats, 15 regions (a region was split afterwards) and a population of 16,4 million (census of 2012, figures from, the Allan-Taagepera model gives n=0,37 and an apportionment which is remarkably close to the actual chosen one. The model moreover makes clear the excessive underrepresentation of the “Región Metropolitana de Santiago” while the original bill as introduced in the chamber, gave that region 7 seats instead of 5 (p. 90 in, in line with the model.

    • Taagepera had another one on upper houses in both federal and unitary systems, with a specific focus on Europe:
      Taagepera, Rein, and Steven P. Recchia, 2002. “The size of second chambers and European assemblies”, European Journal of Political Research 41:2 165-185

  1. The original 1909 South African Senate had eight elected by the legislature of each Province, plus another 8 appointed by the national Governor-General. At some point (I have read somewhere) this was changed to give a population weighting, something along the lines of “one Senator for every five House of Assembly seats (or part thereof) in that Province”. So a Province with (say) 27 lower house federal seats would have 6 Senators and so on. I think there was also a floor, possibly four seats.

  2. Are all Federations bicameral? If they are all bicameral, then are the states, regions, providences, and etc have weighed representation or equal representation? Are all upper houses elected or appointed, perhaps sortition of citizens or state representatives might be a new suggestion? Italy’s problem is that the Prime Minister requires confidence in both chambers separately, what was the origin of this? Romania requires a joint sitting. Any other parliamentary democracies have strange quirks like this? I heard that the Senate had a 6 year term and was shorten to 5 to align with the lower house.

    • Micronesia and Venezuela (under its Chavista constitution) are the only unicameral federations I know of. The latter is, of course, no longer a democracy (and perhaps is dubiously federal), and the former is, well, micro.

      • Arguably the EU if we are only looking at the Parliamentary Assembly, but if we include the Council of Ministers and (with its extensive regulatory powers) the Commission, it’s really more like tricameral.
        Mutandis mutatis with the UN.
        And historically, of course, the US under the Articles of Confederation had a unicameral Congress.
        Point of order: I could only view the first page of Allen & Taagepera (2017) but it seemed that they were talking about the formula for allocating seats in an upper house – “N per State/ Province”, “1 per N thousand population”, or some mix of the two. But subsequent comments imply they were discussing the size of the legislative chamber. The two topics intersect at some points (eg, “50 US States” x “2 Senators per State” = “a Senate of 100 members”) but are conceptually distinct.

      • But Tom, the articles weren’t federal. They were confederal. As far as I know the vast majority of confederations have been unicameral.

      • I also am unable to access the Allen and Taagepera, probably because it is published by Elsevier, and our access to this publisher’s journals is severely restricted by an ongoing subscription dispute.

        As for the EU, I think a case can be made that it is in fact bicameral. The Council of the European Union is its “senate” or perhaps we might say its Bundesrat (given rough similarity in how it is constituted).

      • I am not absolutely convinced that confederations exist, except in the history of Inner Asia where the usage is subtly different from the federalism literature. I do not wish to cause any head explosions so I won’t mention that the Xiongnu, Hun, Goktürk, and Mongol polities are generally referred to as confederations by historians.

        A majority of polities that identify as confederations are actually federations with federal laws that operate directly on citizens (Switzerland, the Confederate States of America, North Germany before 1870, the EU) or are sui generis (the Holy Roman Empire, the US before 1787, Argentina before 1860, the Confederation of Independent States).

      • Alan, though I’ve certainly seen that distinction made, there are also other definitions of federations and confederations which have the benefit of being more useful. Confederations are best defined as state unions which do not have an independent government, which can be operationalised quite effectively by the absence of directly-elected positions. For example, the US under the Articles of Confederation did not have any direct elections; the Congress was not an independent govt so much as an assembly of ambassadors representing the state governments. If a union of states has even one directly-elected veto player, it becomes meaningful to call it a federation.

      • What a confederation or federation calls itself is, of course, completely irrelevant.

      • jd

        That’s a more reasonable definition than the traditional formula I relied on. I blame Dicey, but I do that a lot anyway.

    • The cube root law is a deductively derived model of what is optimal, and on average, it is very accurate empirically. Some countries’ assemblies are too small, some are too large, and some are just right. Canada–and now Italy–are just right.

      I suppose the most “representative” assembly would be one for which S=P, where S is the size of the assembly and P is the population. But this poses certain difficulties in terms of efficient operation. The most efficient would be S=1, but this poses certain other problems, including being pretty unrepresentative. The model of the cube root law of assembly size is about balancing these needs (in Taagepera’s terms, communication channels with constituents and communication channels with other assembly members). Note that the balance, as it works out in the model, says a country is better off being closer to the S=1 end than the S=P end, or else we might have expected a simple square root law. But the cube root it is.

      Within a wide range around the predicted value for a given population, the more important criterion for “representativeness” is, of course, the seat product–i.e., the assembly size multiplied by the mean district magnitude.

    • Ah, but do they exceed the Droop Quota?
      What are their preferences?
      MSS, your comments filter seems to be under-inclusive as well as over-inclusive.

      • Meanwhile said filter traps my witty, informative, brilliantly-crafted, fully-sourced-with-hyperlinks comments like general Zod in the Phantom Zone.

  3. Matthew, this is all very interesting in the abstract, of course, but the real question is… what will this do to Italy’s number of parties???

    • From my Google Translate reading of the amendment itself, it looks like the amendment itself only reduces the constitutionally mandated number of seats, and doesn’t delve further into the details of how seats will be allocated amongst the two tiers. It appears that the legislature has passed a law to provide that the proportion of seats allocated in each tier will stay the same regardless of how many seats are in each chamber (expand the section entitled “Legge/Law 51/2019”). That site also shows two tables of how that law will translate into seats allocated to each region (which is not district magnitude). Essentially, what this means is that the district magnitude for the Chamber’s PR tier will fall (since Chamber seats are allocated on a nationwide basis) from 386 to 245. In the Senate, where PR seats are allocated to parties within the regions, this means (I think) that the average district magnitude will fall from 9.65 to 6.1.

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