Are there any studies that have been done correlating size of the electorate (or in general the population) to size of parliament and stability criteria? I was wondering which size of a parliament is scientifically deemed adequate.

I could not find any data on votes required per seat in national parliaments in relation to how well they are accepted and how stable they are. Does anybody have data to give at least a ball-park number on how many voters should be represented by one member of parliament?

  • 13
    How do you define/measure "perfect" and "adequate"? Voter satisfaction? Reelection rates? Country's GDP growth? Amount of fistfights per parlament member? :)
    – user4012
    Commented Dec 11, 2012 at 15:59
  • 1
    how well are they accepted and especially how stable are they, I would prefer the objective measure of stability (how often are there anticipated reelection?) but I could live with general acceptance of the system as proven by multiple polls. But if you come up with fistfights per member I'll take that too :P Commented Dec 11, 2012 at 16:02
  • 1
    You seem to assume the size of the parliament has to be correlated to the size of the population. I doubt there is any concrete reason why this has to be so.
    – Fela
    Commented Dec 11, 2012 at 16:29
  • Maybe it's more strongly correlated with surface area than with population.
    – gerrit
    Commented Dec 11, 2012 at 16:36
  • As this question stands now, I am going to vote to close. It's just too broad of a statement. It still is an interesting question, but perhaps a more focused approach would make it more answerable. Commented Dec 11, 2012 at 18:45

5 Answers 5


There is a rule of thumb called the cube root rule: the number of legislators in a legislature can be approximated by the cubic root of the population. Although it's essentially an observation about how the size of a population and its legislature are related, some researchers give it a normative twist (suggesting that a legislature should be the size predicted by the cube root rule).

Although the original concept is older, the modern version was established by Rein Taagapera (1973), an Estonian political scientist whose work focused on modeling legislatures. This theory comes up frequently both in academic and general interest circles. Recently Jacobs and Otjes (2014) examined it from several different angles with interesting results.

You can see the empirical evidence in a graph here.

cube root rule graph

  • 6
    But is that merely observational data? The question was about optimal size, not "existing" size (though one may argue, rightly or wrongly, that if the current size wasn't optimal it'd have evolved to more optimal over time). I'll withhold +1 since you didn't link to the paper or abstract, but if you edit that in it's worth an upvote.
    – user4012
    Commented Jan 18, 2013 at 14:17
  • 2
    It seems to derive from empirical data, but a lot of political scientists advocate it as a normative position. Commented Jan 18, 2013 at 14:43
  • 1
    Line doesn't fit data very well....
    – gerrit
    Commented Jan 18, 2013 at 14:51
  • Comparing, say, the UK with the US is not comparing like with like. The UK was (until 15 years ago) a unitary state, so it made some sense to have a relatively small number of electors per seat. In contrast, the US is a federal republic, whose states have a lot of autonomy, so it likewise makes sense to have more electors per state. Commented Jan 18, 2013 at 16:12
  • 5
    Also, how does the graph deal with unicameral vs bicameral legislatures? Plus, the House of Lords is somewhat anomalous, in that, in theory, it currently has 775 members, most of whom are not regularly present. Commented Jan 18, 2013 at 16:14

If parliament seats would be selected by lot from the population, the optimal size could be calculated like a sample size. Interestingly the sample size for populations > 1 million is basically a constant depending only on the required confidence level and margin of error.

For example if you want to be confident that in 95% of the decisions the parliament represents the will of the people within an error margin of 5%, the sample size formula suggest a parliament size of 384 people (for a population > 1 million).

Turning the reasoning around, if the European Parliament with 751 seats would be selected by lot, from the sample size formula we could see, that in 95% of the cases the will of the european people would be represented with a margin of error of about 3.5 %.

Required sample size

  • This assumes that each representative is well-informed on each issue, and "votes their conscience" on each issue. In practice, most legislatures are divided into parties that caucus. Furthermore, bribery and/or blackmail have historically been common, and their influence is amplified by party whipping. Would this method of selecting representatives reduce the tendency toward factionalism?
    – Jasper
    Commented Feb 26, 2017 at 23:03
  • I suppose that this method of selecting representatives would eliminate the need for "campaign contributions", and eliminate the effects of "party lists". These effects would reduce the power of parties.
    – Jasper
    Commented Feb 26, 2017 at 23:13
  • I suppose that this method of selecting representatives would make it cheaper and easier for "advocates" to "inform" representatives about "issues" than it is for the same advocates to inform the entire population about the same issues.
    – Jasper
    Commented Feb 26, 2017 at 23:16

I ran across a study that attempts to deal with idea legislature size in basic way. Check it out: http://www.voxeu.org/article/optimal-number-representatives-democracy

Also, here's a more thorough answer to your question explaining in effect that until now there are no good answers: http://aceproject.org/electoral-advice/archive/questions/replies/760379812

I think that on the whole, no one is going to attempt to calculate an optimal legislature size, but what people will do is figure out that if you change a legislature to become bigger or smaller, certain phenomena will either be muted or amplified. For example, there is evidence that legislatures become more accurately representative as they get bigger (with especially important benefits for smaller and more typically marginalized groups). At the same time, a study by Gilligan and Matasusaka (Public Choice Principles of Redistricting) suggests that larger assemblies end up spending more money because there are more members attempting to bring pork home to their constituents.

  • 1
    Hi! Welcome to Politics.SE. Can you summarize the content of those links? They may go dead at some point in the future, which would mean this answer would stop being useful.
    – Bobson
    Commented Jan 5, 2015 at 15:11
  • 1
    The article is about this paper: dx.doi.org/10.1007/s11127-011-9801-3 Auriol (2012) : On the optimal number of representatives. They derive a formula giving the number of representatives as proportional to the square root of total population.
    – asmaier
    Commented Jan 14, 2016 at 16:27

You might want to check this recent publication (preprint)

Borghesi, C., Hernández, L., Louf, R. & Caparros, F. Universality in systems with group-outcome decision making. (2013)

at http://arxiv.org/abs/1305.5476

See especially appendix S3. Assembly (both local and global) size seems to scale as n^(1/3) (so cube root). Again, only empirical observations, no optimality conditions.

  • Would you be willing to flesh this out? Mostly a link answer at this stage. Commented Oct 29, 2013 at 3:40

One way to evaluate the question is to look at the dynamics of how different sized bodies operate, and then to decide, on whatever criteria one would like, what is best.

Generally speaking, the larger the deliberative body, the most power ends up vesting in the leadership group, and the less power ends up in rank and file members. For example, in the U.S. House of Representatives, the House leadership, the committee chairs and the Rules committee control proceedings tightly, and members of the minority and members of the majority's rank and file have very little power.

Similarly, in the U.K.'s very large House of Commons, almost all power is vested in the cabinet chosen from senior members of the majority party, while "backbenchers" attend to minor, almost clerical details of legislative drafting and participate now and then in debate on the floor when they have the opportunity to do so. But, most individual MPs have little power. The Speaker's power to control debate, which is necessary, further limits the power of rank and file members.

But, in a large body, it is far less likely that everyone will overlook any key detail of legislation, because even subcommittees are quite large and have relatively modest amounts of legislation to consider relative to the number of legislators charged with reviewing it.

In contrast, in a smaller deliberative body, such as Colorado's state senate with 35 members, almost every member of the majority holds some committee chairmanship or leadership post affording that member considerable power in some particular subject matter area, committees are relativity small affording every member of any committee considerable power, and the cost of even a small number of defections from a bill that the party supports makes catering to each individual member's wishes critical for management of the body. Members all know each other on a face to face basis and the interpersonal relationships can sometimes reduce partisanship and make for relatively expeditious consideration of legislation even at a fairly deliberative pace. Most floor debate can proceed with only perfunctory attention to formal rules of procedure.

As numbers growth, the character of the body goes from one extreme to the other.

  • You make no mention of the population size, which was asked by the OP. Colorado's population is considerably smaller than the entire US population. Is it an important factor to take into account or not?
    – SdaliM
    Commented Feb 28, 2017 at 16:18
  • @SdaliM Population is virtually irrelevant. Consider New Hampshire. It has a lower house with something like 400 people in one of the smaller states and upper house with about 24. The dynamics of the legislature which affect how it works is almost entirely a function of the size of the body as a whole and not of population.
    – ohwilleke
    Commented Feb 28, 2017 at 17:38
  • Well, I think you should include this in your answer, since it was part of the original question. Otherwise a good answer :-)
    – SdaliM
    Commented Feb 28, 2017 at 17:40

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .