How large should a country's representative assembly be? The question is not trivial. Assembly size has measurable effects on the representation of political parties. Especially, in smaller magnitude systems (such as single-member districts, but also small multimember districts) having more seats means more districts in which smaller parties with localized support have greater chances for representation. An assembly that is too small for the country may thus shut out important interests. Regardless of district magnitude, a small assembly may create a feeling of 'distance' between representatives and voters, even voters who favor large parties. On the other hand, an assembly that is overly large may create an unwieldy legislative process and generate a need for more complex intra-assembly committee structures or encourage the delegation of more legislative authority to the executive branch. Thus the question arises of what is the 'optimal' assembly size for a given country of a given population.
One of the most important activities of a legislator is communication. A legislator is engaged in communication with both constituents and other legislators. Obviously, there are other persons with whom legislators communicate and there are other activities in which legislators are engaged besides communication. Nonetheless, a crucial feature of the working life of a legislator is to perform the representation function - communicating with constituents - and to perform the lawmaking function in which a legislator must communicate with other legislators. Assembly sizes that are small for a given country will minimize communication channels among legislators, and hence streamline the lawmaking function, but at the expense of multiplying the communication channels with constituents. Conversely, assembly sizes that are large for a given country will reduce communication channels with constituents - hence, other things equal, 'improving' representation' - but will make the lawmaking process less effective due to multiplication of communication channels involving other legislators. In between assemblies that are 'too small' and those that are 'too large' for a given country, there is an optimal size that minimizes the total number of communication channels.
Actual Assembly Sizes and Nations' Populations
The reasoning above would suggest that there would be a systematic relationship between assembly size and population. A study of actual assembly sizes for established democracies in the advanced industrial states revealed the following cube-root relationship between population and assembly size:
where S is the number of seats in the lower or sole house of the assembly, and P is the total population of the country. However, it was also found that for countries in the developing world, this appealingly simple relationship overpredicted the size of assemblies. The reason appears to be that what is relevant is not the total population, but the 'active' population, Pa. The active population - that portion that can be assumed to be actually involved in market exchange and therefore in seeking political representation - can be estimated as:
where L is the literacy rate and W is the working-age fraction of the total population. Thus, if a country had a population of ten million, with a 90% literacy rate and 55% of the population of working age, its active population would be Pa = 10,000,000 x .90 x .55 = 4,950,000. If a country had a population of ten million, 55% of which was of working age, but its literacy rate was only 75%, then its active population would be Pa = 10,000,000 x .75 x .55 = 4,125,000. In developed countries, there is little difference between active and total population, but in developing countries, there may be a difference. When all countries with assemblies were investigated, the following relationship between active population and number of seats in the assembly was revealed:
Thus to take our two examples above, the country with the active population of 4,950,000 would be predicted to have an assembly of 215 members, while the country with the active population of 4,125,000 would be predicted to have an assembly of 202 members.
Very few countries have assemblies that are larger than twice the size predicted by this equation and only a few have assemblies that are smaller than half the predicted value. So, the equation may be thought of as a useful predictor of the suitable size of a country's assembly, once the active population of the country can be ascertained.
A Theoretical Model
Now the question that remains is whether this relationship is purely empirical, or if it can be given a theoretical foundation. There is indeed a theoretical basis for the equation: The 'communications channel' model, alluded to above, allows us to derive the relationship.
If S is the number of assembly seats and Pa the total active population, then the average constituency of one assembly member consist of Pa/S active citizens. Because the assembly member is both a sender and receiver of information, the total number of constituent communication channels, cc, is 2Pa/S.
Inside the assembly, every member communicates with S-1 other members, again in a dual capacity as both sender and receiver of information. He also monitors the channels connecting the other S-1 members to one another. The total number of channels inside the assembly, cs, is:
- cs = 2(s-1) + (S-1)(S -2)/2 = S2/2 + S/2 -1,
which may be simplified to S2/2 for any value of S large enough to be a realistic national assembly size (because the term, S/2 -1, will have negligible effect) . So the total number of channels making demands on the assembly member is:
- c = cs + cc = S2/2 + 2Pa/S.
The assembly size that is optimal is the one that minimizes the total number of communication channels for a given active population. That number may be determined by calculating the derivative dc/dS and making it zero:
The result is 2Pa = S3, which then gives us the model:
Obviously, as with any theoretical model, much detail is left out. Yet the empirical fit is quite good, and so the model tells us that we might expect pressures to change assembly size if a given country's assembly falls too far above or below the model's prediction. If a country were to set its assembly size according to this model, and to adjust its assembly size periodically according to the model as active population grows, pressures to change the size of the assembly would be less likely to result than if other methods are used, or periodic adjustments are not permitted.
