"Choosing the Optimal Number of Representatives in Modern Democracies"

Would having more representatives in congress improve democracy in the U.S.?:

The More the Merrier? Choosing the optimal number of representatives in modern democracies, by Emmanuelle Auriol   Robert J. Gary-Bobo, Vox EU: In representative democracies, the few decide on behalf of the many. But how few? This is not a new problem. The appropriate “representation ratio” was discussed by the founding fathers of the American constitution. In the Federalist Papers, James Madison wrote:

However small the Republic may be, the Representatives must be raised to a certain number, in order to guard against the cabals of a few; and however large it may be, they must be divided to certain number, in order to guard against the confusion of a multitude (Federalist Paper no. 10)

In a recent research paper,[1] we have derived a theory – a square-root “formula” – for the optimal number of representatives. We have then studied how this formula fits the data on populations and parliaments in a sample of more than a hundred countries. We found a surprisingly good fit. There are some “outliers”, i.e. countries for which our “formula” does not fit well, and we find that those with an excess number of representatives tend to be plagued by red tape, state interference and corruption.

In a nutshell, a parliament with too few representatives is not “democratic” enough, possibly leading to an unstable political system, in which various undesirable forms of political expression, including of course violent ones, will develop. In contrast, too many representatives entail substantial direct and indirect social costs, they tend to vote too many acts, interfere too much with the operation of markets, increase red tape and create many opportunities for influence, rent-seeking activities and corruption.

Our theory is essentially based on a statistical trade-off. Having more Members of Parliament (MEPs) improves the likelihood that a set of randomly-selected MEPs accurately reproduces the population’s preferences. Having more MEPs, however, generates direct and opportunity costs. The optimal number of representatives equalises the social value of an additional seat in parliament, which stems from a reduction of the errors made in the estimation of citizens’ tastes, and the social cost of this additional seat. The computation is made a bit more complicated than it seems at first glance because, in theory, representatives must be provided with incentives not to distort the revelation of preferences. In other words, we worry about the incentives facing MEPs; we do not assume that representatives are benevolent. As it turns out, this consideration is of secondary importance.

Under these assumptions, we show that the optimal number of representatives in a given country should be proportional to the square root of the population. The factor of proportionality decreases with higher costs of representation and is increasing in measures of the country’s dispersion of preferences. The theory should not be interpreted too literally. It says that the optimal number of seats in parliament is given by an increasing, concave, banana-shaped curve plotting the count of representatives against population size. Real-world data will not fit exactly since other factors affect the proportionality factor between the number of representatives and the square root of population size – not all of which are observed by the econometrician.

Not Penrose’s Rule

It is worth mentioning that our “square-root” theory has no connection with Penrose’s “square-root law” of fair representation, which recently attracted some attention during the debates surrounding the Nice Treaty, the Constitutional Treaty.[2] Penrose’s law is a way of solving the vote-apportionment problem in a weighted voting system like the EU’s qualified majority voting. In contrast, our banana-shaped curve gives the optimal total number of seats in the representative institution itself, under the assumption that each representative has one vote and the majority threshold is the standard 50%.

Reality check

If our theory is right and nations design their democracies with efficiency, the actual numbers of representatives in nations should roughly fit our prediction. To confront the theory with the data, we have run a number of tests on a sample of 111 countries in the year 1995. The results show that the number of representatives is nearly proportional to total population raised to the power of 0.4. Of course, 0.4 is not ½ so the best fit is not the square-root of total population; it is a somewhat smaller power. The precision and robustness of the estimates are fairly good (as can be seen on figure 1).

On Figure 1, the logarithm of the number of representatives is plotted against the logarithm of the country’s population (in millions), along with the least squares regression line. The theoretical banana-shaped curve should appear as a straight line (with slope ½) on the figure. The slope is in fact close to 2/5.

If we take the “N0.4 model” as the fitted value, most countries lie within a reasonable distance of this worldwide benchmark. There are also obvious outliers, that is, countries with abnormally high or low numbers of representatives (in relative terms). We can distinguish five groups.

• The countries with an abnormally high number of seats in national parliament: France, Italy and Spain. With 898 seats in the National Assembly and the Senate taken together, France has more representatives than the United States (again adding the House and the Senate together). According to our computations, France’s optimal number is 545. Italy’s optimal number is 570, but this country has a total of 945 representatives in 1995.
• The countries with too many, albeit not a plethoric number of seats. This group includes Greece, Switzerland, Ireland and the UK (if we put the Peers aside in this latter case, and count only the MPs).
• The “good guys”, that lie more or less on the banana-shaped curve; this group includes some heavyweights: Canada, Germany, Finland, India, Japan, Portugal, Russia and Sweden.
• The group with (moderately) too few representatives: Austria, Australia, Belgium, Denmark and Norway. We invite the reader consider whether these countries have something else in common.
• The nations with abnormally sub-optimal representations: Israel, New Zealand, the Netherlands and above all, the USA. Nations in the last group are all close to a ratio of 65% of their optimal representation level. The US has 535 national representatives (if we add the House of Representatives and the Senate), but our model predicts that the Congress should have 807 seats instead. In America, a high degree of institutional rigidity seems to be the cause of the insufficient representation: the number of US representatives has been fixed by statute in 1929, and the number of voters per representative has constantly increased, through the entire US history, to reach record highs in the recent years.

The cost of deviation for the benchmark

If our theory is right, there should be a cost to nations that have too few or too many representatives. The cost from having too few is difficult to observe. In our theory, having too few representatives makes it likely that the democracy will not be sufficiently representative. Testing for this, however, would require detailed knowledge of the choices of the nations and the preferences of the population. It is easier to observe the problems of too many representatives. According to our theory, such nations should experience extra social costs.

Our preliminary study of the facts shows that a country’s excess number of representatives is significantly correlated with more red tape (a measure of the direct cost of meeting the requirements to open a new business), more state interference (a measure of whether state interference hinders business development) and more perceived corruption (as measured by Transparency International’s well-known corruption index).

Why is that true? We suggest what might be called a “quantity theory” of legislation; more lawmakers mean more law, i.e. more rules and regulations. These new rules, in turn, tend to interfere with the operation of free markets as they are motivated by the desire, for example, to protect pressure groups and various lobbies from competition. At the same time, regulations tend to create temptations and opportunities for more influence activities, cronyism, bribes, capture, and sheer corruption.

Our ideas and observations are still exploratory, and further work is of course needed to confirm the validity and robustness of these findings. Yet, our results strongly suggest that some countries, such as France or Italy, could reconsider the appropriateness and cost-efficiency of their political institutions. Another interesting question is the optimal number of Euro MPs. The total population of the EU is now 490 million; there are currently 785 euro representatives, and according to our computations, the optimal number of seats should now be roughly equal to 890.

Footnotes:

[1] The classic work on these questions is J. Buchanan and G. Tullock (1962), “The calculus of consent”, University of Michigan Press. On voting theory, see Austen-Smith and Banks (1999), “Positive Political Theory”, University of Michigan Press; see also H. Moulin (1988), Axioms of Cooperative Decision-Making, Cambridge University Press. On recent developments of the “Public Choice” literature, see Mueller (2003), “Public Choice III”, Cambridge University Press. Our own paper is available at http://www.cepr.org/pubs/new-dps/dplist.asp?dpno=6417; as far as we know, our argument for the “square-root formula”, based on Mechanism Design, is new.

[2] It was advocated Sweden in the IGC2000 leading up to the Nice Treaty and Poland last year in the negotiations of the Reform Treaty; see http://voxeu.org/index.php?q=node/262 on the logic of Penrose’s rule.

Comments

[Bruce Wilder]

Oh, my. So many considerations crowd into my mind, so much institutional complexity.

Is the quantity theory of legislation reasonable? On its face, it seems like a libertarian's delusional fantasy. How many rules there are is a function of how organized a society is -- good government does not consist in having fewer rules, but, rather, better rules. Fewer rules can only result a less organized society; better rules result in a better organized society.

There must be scale considerations in operating any decision-making assembly. Are those obviated by being the decision-making assembly of a large country? What's the point of federalism?

The U.S. has a two-party system and we obsess about efforts to gerrymander districts to reliably return Representatives from one Party or the other -- in toto, though, the proportion of Representatives in Congress from one Party almost perfectly matches the proportion of the national vote for that Party.

In the UK, by contrast, they have a 3.x party system, with two Parties that have a genuine prospect of governing, a third major Party, which, basically, has not governed since World War I, and several regional parties. The governing Party typically dominates the Parliament, if it can garner 40% of the vote -- the current Labour government achieved its majority in Parliament with just over 35% of the vote. Relieved of the need to get build coalitions that get to 50.1%, governing a metropolitan country without the constraints of constitutional separation of powers, and supported by a strong civil service, U.K. governments typically sport far more coherent policies than do some U.S. Presidential Administrations led by idiots, but does that have anything to do with the number of MPs? Seems doubtful.

[esb]

A related (and possibly more important) question involves the optimal number of effective or "strong" parties.

We know that the answer is not 1.

I have come to believe that the answer is not 2 as it appears that there is a tendency for the two to function in the manner of gangs, with an "us versus them" operational focus. Control of the government comes to be viewed as a "prize" for capture.

With a number greater than 2 the need for persuasion and cooperation permeates all strategic thinking, redounding to the benefit of all.

[Bruce Wilder]

I question the value of having more than two "strong" parties, esb. You can tell a lovely narrative of persuasion and cooperation, but it is just a story; the reality may be gridlock, or corruption, or devolution to only one "strong" party in practice, as the out-of-power opposition fractures and loses focus. The expectations built into a two-Party system help to re-build and restructure a Party, which has self-destructed, which happens frequently through history.

In multi-party democracy, there is a tendency for most of the Parties to define themselves out of a contention for a majority, leaving just one Party with a Big Tent capable of commanding a governing majority. When that Big Tent party self-destructs through corruption or whatever, political expectations support its reconstruction, but not its replacement in power. The result can be long periods of political weakness and corruption, as the one big Party struggles against the habits of corruption, and the traditionally out-of-power struggle to form an unnatural coalition with enough coherance to oust the presumptive majority Party. It can be a prolonged and ugly process.

The U.S. has a two-party system, nationally, primarily because of the structure of the Presidential election -- first-past-the-post collection of electoral votes, state-by-state. The two-party system in Congress covers a reality, where there are multiple factions, some of which have functioned at times as virtual third parties, holding the balance of power. At the State level, some States have two-party systems, but most have a clearly dominant Party, if not an effective one-Party system in place; the situation vis-a-vis Statewide offices may be quite different from the contest for control of the legislature.

The struggle to "capture" the government and power forces the Parties to morph and organize in ways that prepare them to govern, and also force the People to confront the choices facing the state and form coalitional points-of-view, that reduce the decision-space from one of mind-boggling variety to something that might be managed.

[reason]

Why is what is a guide for what should be?

[bob]

Why use representatives at all? Vote by computer. This is what happens anyway as email to Congress gives information about intensities.

[Ashish]

Assuming this theory is right - how about increasing the Senate to 250-300 members? The new members could be distributed among states on the basis of population? This would counter the over representation of small states. The rest could be added to the House.

[Winston]

It seems strange to compare the number of representatives in a unitary state like Italy to a Federation like the United States. U.S. states are unusually powerful and handle things that are handled at a national level at other countries. I wonder how things would look if the TOTAL number of elected officials were counted.

[robertdfeinman]

The problem with the US is that the present system is not representative. Whether it was designed this way on purpose or just evolved, I'll leave to the historians.

The main problem is that in the senate there is a bias towards smaller, rural states. In fact 16% of the population controls 50% of the votes. I drew up a chart to illustrate this, if you are interested:
The Small State Senate Bias

In the house the effect is smaller, but still exists because every state must have at least one representative. This means that some congressmen represent nearly twice as many people as others.

The idea that we have a two party system obscures this imbalance. What happens is that the parties become conglomerations of groups which may share very few concerns in common. They are thus forced to be more centrist than would otherwise be the case. Take the example of the Dems. The big city states can't get programs through that would primarily benefit the urban poor because of the power of the rural and farm block. In countries where parties are much more homogeneous they tend to be less willing to compromise. I don't know which system is better.

There are things that could be done to make the present system more equitable, such as proportional representation, or the ability to assign your votes in a weighted fashion. For example, if your state had five congressional seats, you would get five votes which you could give to one or more candidates as you wished. The top five vote getters would get into office. I know of a couple of non-profits that use this system.

Even if the, say, big state urban groups wanted to change things so that they had power proportional to their population, there are too many living off the present arrangement for this to happen.

[piglet]

"The problem with the US is that the present system is not representative."

That is correct, but for other reasons than just small state overrepresentation. Basically, there is no mechanism in place that ensures that representatives represent the people, rather than the corporations that have bought them.

[Bruce Wilder]

Proportional representation does make a lot of sense for densely populated conurbations. And, how single-member districts are drawn can introduce decisive bias: for example, pie-slice districts around a city get a different kind of representation than do more "compact" schemes; geographically "compact" (i.e. square) districts can tend to increase suburban/rural "conservative" bias, I think.

Like rdf, I am not sure that the "centrism" and open-ness to internal Party compromise is a good thing or not. But, I do know that no set of rules results in a fully predictable stasis.

Game theory shows over and over that the rules of the game do not determine outcomes; how the game is played sets in motion an evolutionary process where the rules change in response to innovation in game-play and outcomes are a consequence of rule-changing artfulness or artlessness in how the game is played.

As I have mentioned before, the U.S. has never before had ideological Parties, where worldview so perfectly defined Party identity on a national basis. The compromises that the Democratic Party forged from Woodrow Wilson's day (when northern proto-liberal Progressives began migrating into the Democratic Party) through to LBJ were often breathtaking in their artfulness. Read about the Davis-Bacon Act or the account in Caro's Master of the Senate of the 1957 Voting Rights Act. But, that was a Party, where reactionary populism lived side-by-side with idealistic liberalism.

The Parties are not like that anymore. The Parties are ideologically pure. There are not more than two dozen House members, who could qualify as being "in the center" "between" the Parties. A grand total of 5 Democrats will vote to uphold Bush's SCHIP veto; and Pelosi will be hard-put to find 15 Republicans to support an override. The center has disappeared and "bi-partisan" is acquiring a bad name.

What an all-reactionary/all movement-conservative, all-the-time Republican Party did under Bush was, indeed, scary. If the Republic survives, we're going to get a taste of a what an all-liberal-progressive-moderate Democratic Party will try -- that will be just as novel, but, I hope, in a good way.

[nu]

counting senate members for France was a weird choice.. although its constitutionnal powers are broad, the lower chamber constitutionally prevails which in reality means that the french senate doesn't really matter much more than the british house of the lords. after all it has never swung to the left and that didn't seem to disturb the Left in any way.

so knowing that why exactly did they say: " With 898 seats in the National Assembly and the Senate taken together, France has more representatives than the United States (again adding the House and the Senate together). According to our computations, France’s optimal number is 545" since the difference is really the powerless senate ?

[Meh]

Bruce Wilder: I think that you're correct that everything is contingent on circumstance, you don't apply that to your own arguments. There are good examples in Europe where full PR (and 3 or more strong parties) results in reasonably compromise government, overall.

Most importantly, it's clear that the US system is in trouble, because it never anticipated the rise of really disciplined parties like the current Republican machine. (And likely the new Democrat machine that must evolve to take power away from the Republic party.)

Anyway, my point is, these new party forms aren't going to go away, so what's your proposal? I'll happily concede that PR/strengthening third parties/etc. isn't the way forward if you've got some better ideas?

[nu]

oh that is why:

"Why is that true? We suggest what might be called a “quantity theory” of legislation; more lawmakers mean more law, i.e. more rules and regulations. These new rules, in turn, tend to interfere with the operation of free markets as they are motivated by the desire, for example, to protect pressure groups and various lobbies from competition. At the same time, regulations tend to create temptations and opportunities for more influence activities, cronyism, bribes, capture, and sheer corruption."

OOOOH.

I guess that's why the british upper house is excluded.
I mean it's really about having "results that strongly suggest that some countries, such as France or Italy, could reconsider the appropriateness and cost-efficiency of their political institutions."

[Bruce Wilder]

Meh: "Anyway, my point is, these new party forms aren't going to go away, so what's your proposal? I'll happily concede that PR/strengthening third parties/etc. isn't the way forward if you've got some better ideas?"

I think a reasonable take-away from game-theoretic analysis of political and economic organizational forms is that evolutionary change in institutions and the rules of the game is inevitable, even when the nominal institutions and rules of the game don't change. It is simply wrong to think in terms of static ideals, when all that can happen is meliorative reform and renewal to remedy or counter inevitable corruption and entropy.

As a purely theoretical matter, particularly for the densely populated conurbations, I think "mixed proportional representation" makes a lot of sense. If I could, I would abolish the existing States, and redraw the boundaries to have about 20-odd, with Hawaii the smallest by far.

The most troubling problem political institutional problem, to my mind, is that the People are not actively engaged enough to process political debate into common thinking, shared expectations and political movement.

The U.S., though still among the youngest major nation-states, for better and worse, has some of the oldest political institutions in the world: one of the oldest written Constitutions, the Democratic Party is the oldest modern political Party, etc. France, in the same period that 110 successive U.S. Congresses have been legislating, has gone through 3 kingdoms, 2 empires, and five republics. But, even if the U.S. has not changed labels quite so often as France, there have been some major historical shifts. Politics and political institutions changed profoundly in the Age of Jackson, and again during and after the Civil War, and again during the Progressive Era of Roosevelt, Taft and Wilson, and even more profoundly during FDR's New Deal and World War II administrations. Those great transitions in political institutions required mass political action -- literally millions of people reading, marching, letting themselves be persuaded that the Union Must Be Preserved or that segregation must end or women should vote or whatever. It was a shared experience and education that undergirded change.

I don't think you have to be an exceptional visionary to see that the U.S. is at the end of an Era in a great many ways -- the economic model the U.S. relied on in building (and milking) a middle class -- mass production, electrical appliances and packaged/fast food, automobiles-highways-cheap gas, union jobs, and global dominance, is played out over most of the country. The scale and scope of that challenge overshadows the need for tinkering with institutions, but it is also the fundamental "cause" or context for the corruption of U.S. institutions, which troubles this country.

In many respects, the development of many of the country's economic, as well as political institutions, are at a low ebb. It is not just that Congress critters are particularly inattentive in representing their constituents (as opposed to their campaign contributors) or even that the constituents are particularly inattentive in monitoring their Congress critters (though they are). For much of American history, politics has been shaped and driven by many social organizations, with which people affiliated -- not just churches and political parties, but lots of voluntary associations mediated political influence and action. People belonged to the Elks, Kiwanis, Masons, Knights of Columbus, womens' clubs, PTA, as well as churches, unions, chambers of commerce, etc.; lots of these are forgotten -- like the Chautauqua circuit or the Grand Army of the Republic, some like the KKK, we wish they could be forgotten. My point is that social affiliation is at an historically low ebb in American life, done in by economic security, franchises, shopping malls, Wal-Mart, and television, I guess. It is not simply that giant business corporations have become more predatory in their lobbying or that television advertising is more important to political campaigns -- countervailing institutions of political organization and association that might mediate political action have withered, as have alternative channels of communication (e.g. young people don't read newspapers) and political action. Of course, people respond like Pavlov's dogs to 30-second spots; there's no context, where most people are engaged and paying attention to the looming issues of the day. Do you think Rush Limbaugh's listeners know or care about global warming?; they probably know and care more than most Americans, who don't listen to any news or public affairs programs, not even execrable ones.

Before the Civil War, no daily newspaper ever had more than 8 pages, and, though 2/3s of adults could read, only about half could read well. But, as controversy over slavery and slavery expansion grew ever more shrill and acute, almost every one in the country followed the debate in detail -- there may have been only 8 pages, but the Lincoln-Douglas debates were covered (with pro-Lincoln papers printing Lincoln's speeches nearly verbatim, and pro-Douglas papers doing the same for their man) and they were read, and re-published as pamphlets and read some more, frequently outloud. And, people met at church and in quasi-masonic political organizations and in other forums and talked.

My point is that there was a lot social and political chemistry going on, for years, to prepare the country for that conflict, and that preparation made possible the revolutionary political changes, which followed.

The Right complains vociferously about the Media, and the blogospheric Left is almost as critical. Although the critiques differ, they point to the fundamental weakness of television news and leading newspapers, both of which feel themselves in economic decline. Generational change and blatant corruption have undermined professional standards in journalism to the point that such Tribunes of the People as Chris Matthews focus on trivia, between retreats to Martha's Vineyard.

It is a serious problem, and combines with the relatively atomistic social and political lives of most Americans to create a situation in which, I fear, insufficient political chemistry is at work. Just to take one example, many of us political junkies are well-aware that some kind of carbon tax is going to be necessary to curb use of common fuels. But, most Americans have not been through the process of thinking it through -- they have not been focused on the problem, and respond with unthinking hostility to the idea of a tax -- they want cheap gas to get to their over-heated/over-cooled McMansion and to CostCo and to work a zillion miles away.

As distressed as I am with my countryman for electing Bush even after having four years of experience, and as frustrated as I am with the inability of the Democrats to restrain Bush, I actually think the country's political institutions are functioning as they should. It has taken way too long, but action is begetting reaction -- the Republicans are losing their grip on a political majority, able to elect a Congress and President, and consequently on Power.

But, I fear, that we are falling short in preparing the People for the coming need to transform the country's approach.

The transition we need to make is as great as the country faced in 1860, when they were, with the greatest reluctance, confronting imperative need to end slavery (which was a key economic institution supporting at least one-third of the country).

We are at war in the Middle East to secure oil, which will, if we actually burn it all, may make the planet uninhabitable, and we are making ourselves financially and morally bankrupt in this futile pursuit of cheap gas. Everything about that has to change.

And, most people are not engaged enough to recognize the necessity, but will be easily mobilized by reactionaries manipulating a decrepit and corrupt Media.

Hillary Clinton, whom I would vote for in a general election without hesitation, seems determined to make herself the candidate of the plutocracy -- "someone we (business) can work with" -- which may be simple realism, given the lack of political engagement in the country and the degraded state of the Media.

But, I fear that, with Media unreformed and the People unmobilized, in 2012, the U.S. will still not have national health care, will still be in Iraq, will be in an even more advanced stage of economic dis-development, and will be debating how to "reform" Social Security because no one can figure how to raise income tax rates on billionaires above 20% to stave off national bankruptcy.

As a remedial reform, proportional representation does not seem . . . proportional to the case.