Votes from Seats is published!

Available from Cambridge University Press. (Also available in Kindle format for only $15.90!)

(Please note that this post is a “sticky”; scroll down for new content.)

Take the number of seats in a representative assembly and the number of seats in districts through which this assembly is elected. From just these two numbers, the authors of Votes from Seats show that it is possible to deduce the number of parties in the assembly and in the electorate, as well as the size of the largest party. Inside parties, the vote distributions of individual candidates likewise follow predictable patterns. Four laws of party seats and votes are constructed by logic and tested, using scientific approaches rare in social sciences. Both complex and simple electoral systems are covered, and the book offers a set of ‘best practices’ for electoral system design. The ability to predict so much from so little, and to apply to countries worldwide, is an advance in the systematic analysis of a core institutional feature found in any democracy, and points the way towards making social sciences more predictive.

16 thoughts on “Votes from Seats is published!

  1. What is the smallest size and largest size a parliament can be? Can a lawmaking body be too small and/or too large as well as both at the same time?

    I would think the smallest size a city council is 5 members, but that is too small for a country, I would speculate no smaller than 15 members, the government has 7 seats, do all the members of the government become cabinet ministers assuming Westminster rules. I have seen no democratically elected lower house that has more members than the low to mid 700s. Is that too large, does each member have enough time to speak?

    The US state of New Hampshire has a huge legislative body whereas California is tiny for its population.

    What country in the world has a perfect size assembly for its population? Most citizens want smaller legislative bodies. Odd that New Hampshire hasn’t downsize it. Has there ever been a referendum on parliament size either to increase or decrease? NZ had a non binding one to go back to 99 members, but that was after the embrace of MMP.

    What if the cube root to population is not realistic? All this depends on the country’s population, whether there is an upper house and providences/regions/states. India’s parliament should be much larger than it is, but it has all of the above previous sentence.

    The above link says the global average is 245 members.

    We all have different opinions on this, and like Reading Rainbow, I will have to read this book.

  2. St. Kitts and Nevis has a weird parliament with two sub-chambers. There are 4 additional members referred as Senators

    • As I understand things, there is still really a single house, but with two sources of members: the elected members and 4 (or 3, I’ve seen both) appointed members. The appointed members are theoretically supposed to bring in a wider range of views than the 11 members elected from single districts are expected to have. It is really common throughout the Caribbean to have appointed senates, usually in a single chamber though.

      I have no idea how or if they differ from ordinary politicians though.

  3. Odd that St. Kitts and Nevis has 4 additional members referred to Senators, isn’t this similar to what Iceland and Norway had when they had qualified unicameralism but was recently abolish in Norway and abolished a while back ago in Iceland, but it appears that the Senators always vote with the rest of the elective members. Seems odd that countries have appointed members for unicameral and/or lower houses, does this shore up the governments majority? It would seem to me to improve on this concept would be to have random sortition of citizens at large.

    • In St. Kitts and Nevis, the prime minister appoints 2, the leader of the opposition 1, the fourth is the attorney general and not a partisan figure. So it does not, or at least should not, change the partisan balance.

      I was not aware that Iceland had qualified bicameralism, but I belie that in Norway the Storting elected 1/4 of its members as the upper house, either proportionally or through some formula. However it worked, the Lagting looked just like the Odelsting They got rid of it because they functioned more like a committee than an actual upper house.

      • Iceland had proper bicameralism, abolished in 1991. The upper house was elected concurrently using an essentially identical electoral system.

  4. I have hugely enjoyed reading Votes From Seats. For me it begs a question.. Has much work been done yet on logical models of systems that are built around biproportional apportionment?

    To make this more concrete.. Consider a system with M=2 and S=650, in which the parties’ shares of seats are established at assembly level, and the winning candidates are selected using divisor-based biproportional apportionment. It feels like such a system would be amenable to the analysis techniques showcased in the book. Has anyone given it a try yet?

    • Is this like the old Chilean binomial system? Bi proportionate system seems complicated to me, the assembly could never be an odd size if such a system is used.

  5. (The only similarity with Chilean “binomial voting” is M=2.)

    Here is a non-technical article on biproportional apportionment..
    Zurich’s New Apportionment
    And here is a short technical article on biproportional apportionment..
    Wikipedia page
    If you want to dig deeper, I recommend Friedrich Pukelsheim’s book..
    PR – Apportionment Methods and Their Applications

    Here is one way of thinking about biproportional apportionment. Imagine that A) the seats-per-district are fixed in advance, and B) the seats-per-party have been determined – at the national level – by some formula applied to how people voted. If you start with A and apply some rule in each district (EG the candidates with the most votes win the seats), you fail to achieve B. If you start with B and apply some rule in each party (EG the candidates with the most votes win the seats), you fail to achieve A. If you switch to using biproportional apportionment as your allocation rule, you achieve A and B.

    Biproportional apportionment is certainly rather technical, but I personally would not call it complicated or intricate.

    For small M – which is what interests me – biproportional apportionment inevitably gives some “discordant” allocations. For this reason, I think its M=1 variant (Balinski’s “Fair Majority Voting”) will never fly. But things ease up quite a lot with M=2. For example, I recently simulated biproportional allocation with M=2 in Wales, using the voting data from the 2017 UK General Election. In every one of the dual-member constituencies, the candidate with the highest number of votes was allocated a a seat.

    [Extrapolating from the above.. Biproportional apportionment might be an excellent allocation algorithm for the compensatory ‘tier’ of two-component systems such as evolved MMP and DMP. But that is something for a different thread.]

    • Thank you, Chris. I am glad you have enjoyed the book!

      As to your question: I assume there are no logical models of such a thing, because there’s no empirical referent.

      By the way, it would be best not to refer to a “binomial system”. That term does not describe a system. It literally describes, in Chile, either the number of candidates on a list, or the number elected from a district (or both). And I would think “binominal” (which I also have seen) would be better than “binomial”. The same objection I have to binomial applies to binominal, as well.

      The system, per se, in Chile is D’Hondt PR with M=2 and open lists.* Given the wider themes of the book, it is important to use the precise terms, signifying the families of systems to which any given specific system belongs. Similarly, “biproportional apportionment” does not seem like an accurate term for what is described in the above comment, but I am not sure I understand. In any case, it probably is not a relevant topic for this thread. It is possible that it is similar to “Dual-Member Proportional” (also a bad term!), described in a link within my PEI 2016 thread.

      (* The system up to 2013, that is. But the only thing changing is the range of magnitudes. Using the standardized terminology makes clear that just one aspect of the system is being changed in Chile–albeit a critical aspect.)

  6. Thanks for responding, Matthew. Regarding systems that are built around biproportional apportionment, you wrote “I assume there are no logical models because there’s no empirical referent”. Fair enough.. Why bother building a model if there is not yet any data to test it

    (To make sure readers don’t depart with the idea that biproportional apportionment is not in use, I note the statement on the Wikipedia page that it is being used in six Swiss cantons. For example, it has been used in Zurich since 2006. But as those elections are sub-national, they are off-topic for the seat-product model.)

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