# Measures of power: Nation States

So in my world I have a variety of nations states ranging from independent city-states to empires.

I am in the process of defining the socio-political landscape of the world and have a few story centric international relationships that are partially defined.

For the rest of the world and to provide more detail on those things that are already defined I am looking for a way to define (essentially give each a score) the power of each independent political entity.

• What facets of power need to be considered?
• Can each nation's score exist independently or is it necessary that they be part of a larger ecosystem?
• How would one go about automating the assignment of stats for each nation?

The best answer will have (at least for the first bullet) supporting political science literature.

For the sake of this question fantasy aspects (magic/creatures and stuff like that) may be considered non-existent.

## Deciding who lives, who eats, and who pays

Whether you live or die, what you think, and what you eat are three of the most fundamental questions that a person will need to address for themselves. All other considerations can be seen as complications of these three most basic questions. As an author, you will need to decide who has the last word on the answers to all these questions. The method described below proposes a method for answering these questions and discovering hidden features of the power relationships between competing nation-states.

Political calculations are always made in relation to other human beings. Some physical quantities about the exercise of power may be calculated independently, but the political power scores are always in the context of competition.

The three categories of power described below are roughly equivalent to the initial three questions.

## Military Power

Roughly equivalent to the power to kill, military power is the ability to enforce political will through violence and death. The power over life and death.

No bastard ever won a war by dying for his country. He won it by making some other poor dumb bastard die for his country. - George S. Patton

## Cultural Power

Cultural power is the power over how people think. A nation with cultural power is able to export their ideas in regards to how society should be run, what is culturally important and what is not. This is the power over what and how people think. It could be argued that political power is a distinct category but since laws are such an integral part of how people think and behave, I'm lumping it in with cultural power.

## Economic Power

Economic power is the power over buying and selling, more specifically over what is bought and sold. An economically powerful nation-state can push their goods and services to a broader market and command more market share than an economically weak nation-state. This is control over the flow of wealth trade goods.

How power in these three areas can be exercised will not be addressed here due to the voluminous and excellent literature elsewhere. A good start might be French and Raven's work in 1959.

## A word on distance

The farther away something is, the harder it is to influence it. In addition to the three categories of power. The method described below attempts to take into account the difficulty that great distances introduce into the exercise of power. Also, the model assumes that spheres of influence are roughly ring-shaped and projected onto a 2D map. Accounting for 3d spaces or irregular spheres adds a great deal of complexity (and this answer is long enough already).

I chose to use a log scale to ensure that this method could scale across all distances and all empire sizes.

## Calculating Power Values

1. Make a list of all the nation-states in question. This list of nation-states should be in contact with each other and in a position to compete in some way. Probably easiest to build this model in a spreadsheet of some kind.

2. For each category of power, there is a points pool defined as 5 * number of nation-states. So for a list of 5 nations, the pool would be 25. Allocate some of those points to each nation, giving more points to the more powerful nations.

3. In the adjacent column, assign values for each nation's sphere of influence ($S_i$). This value should be at least as large as the country itself though may be smaller for especially weak nations. For an earth like planet, sphere of influence values will likely range between 6 and 7.2. Using $S_i = log_{10}(d)$ You can calculate your sphere of influence values with as much precision as you desire.

4. Multiply the points column by the $S_i$ column to get your power score for that nation. Work a little spreadsheet magic to sort each power category to see the strongest and weakest.

5. Have a little fun writing out summaries for each nation based purely on the numbers you've written. You can be as detailed as you want and may end up writing a little bit of history about each nation to explain how they got to be where they are. Now, compare these values with your original intentions for each nation. If they match, great. If not, make adjustments and keep going.

## Possible Extensions of the Model

Calculate relationships between entities bigger or smaller than nation-states - As described above, this model applies to nation-states on a global scale though it can be applied equally well to purely regional relationships. To keep things as manageable as possible, keep this spreadsheet specific to a geographical scope of competitors. It's tough to keep track of regional relationships when considering global power relationships too, not impossible, just complicated. Also, the 5*number of nation-states may not work too well when comparing isolated nations who dominate their neighbors but have no contact with each other and do not compete in anyway. For example, comparing Rome with ancient China using this technique may not make too much sense.

Calculate Internal Power - Governments often have very different relationships with their own people than with neighbors, thus it is helpful to see the relationship between the government and the governed. Use the same three power categories used for comparing nation-states.

Calculate Maximal Extent of Power - Calculate or specify the maximum extent that the political entity can make its military, cultural or economic power felt.

Calculate Power Projection at specific point - By adjusting the distances in the $S_i$ calculation, it's possible to plot more detailed relationships for a specific location.

## Conclusion

As with any measure that aggregates a great deal of information down to a single number, there will be considerable loss of nuance and opportunities to argue "yeah, but...". This approach is an approximation at best though with the addition of additional aspects in $A$, its expressive power can be improved. This model also does not account for alliances that may exist between nation-states that would serve to greatly amplify the power of any one nation.

Sphere of Influence values are calculated using the below formula. This approach helps keep the math manageable $$S_i = log_{10}(distance)$$

0 = 1 meter, you human have control over yourself.

1 = 10 meters

3 = 1000 meters. Small village/town.

6 = 100K meters, comparable to but smaller than Ireland.

7.3 = 20M meters, half-way round the world

12 = 5.9 trillion meters, Pluto

26.6433 = Edge of observable universe

What facets of power need to be considered?

Dependents on your specific setting. Mana level is quite important in fantasy, while may be omitted in hard science setting. ;)

But let's think, at minimum:

-Population

-GDP per capita

-System stability (from anarchy an civil war, to a country with very well working gov with high mandate from subjects)

When trying to flesh that out a bit more:

-Unique resources

-Extra sources of soft power (like religion - Mecca / Vatican, being the country in which the main social website operates, or being a tiny state with remnant of some old, respectable, imperial dynasty)

-Additional modifier for militarization on top of simple man and economic power (Sparta, Israel)

-type of political system

Can each nation's score exist independently or is it necessary that they be part of a larger ecosystem?

In very simple model? Enough. In more advanced at least make a few types of circles to which one would include countries: -religion -ethnic group -dynastic ties

How would one go about automating the assignment of stats for each nation?

In simple version - RAND and RANDBETWEEN functions from Excel clones. Presumably with some modifiers (like city states get some bonus in wealth per capita, but have no special resources) or summing results to get distribution for GDP closer to normal distribution. I'd make list for special resources, to make excel pick, something like : 1 - oil, 2 -magnetite iron ore, 3 - uranium... 5 and more - none.

This would be especially practical if you would use it use it for province level to make bigger states nonuniform, and make the spreadsheet sum it up.

• Welcome to the site Shadow (I don't think I've said that to you before!) I like your answer and I have edited mine to clarify your question on magic. – James Dec 19 '16 at 22:27

You may want to begin by fixing a general outlook of the world, that is, the general setting in terms of technology, economic development and social customs. Do you want a world like we have it in the 21st century, with unprecedented emphasis on individual rights and freedom and with unprecedented world-wide interconnection between people and companies and nations? Do you want a world like they had in the 19th century, with a handful of Great Powers competing for domination over territory and nations? Do you want a world made up of a multitude of fragments, like they had in the Middle Ages and the early Modern period? A hierarchical world, like in the European Middle Ages? It is hard to give suggestions for books unless the general outlook of the world is specified.

In all time periods of human history there were all kinds of political structures, small and large. Even today, we have city states and small countries and mid-size countries and large countries and huge empires. Singapore is a fully independent city-state; Hamburg is a city state, member of the German federation, itself a member of the European Union confederation. Russia and China and effectively huge empires, no matter what their official names are.

## What facets of power need to be considered

The basics are population, territory, resources, economic development, and social development. They result in the four dimensions of power: Diplomatic, Informational, Military and Economic (DIME). See the Wikipedia articles on National Power and Power in International Relations.

Note that while population and territory are easily reduced to numbers, resources, economic development and social development are multifaceted. Territory is not a unidimensional attribute; while larger territory gives more power, the kind of territory is also important. Resources include climate, water, soil, wood, animals, hydropower, mineral resources, acces to the sea etc.; which resources are important depends on the general outlook of the world. The notion of economic development is also dependent on the general outlook -- up the middle of the 20th century agriculture was very important, today much less so; financial systems (what kind of financial systems aare available and how developed they are) may have a huge impact; don't forget to look at transport modes and transport networks. Social development has a great importance; aspects of social development include science, technology, education, culture, law, customs, morals and political structure; you may want to consider the categories used by the Human Development Index. Political structure, as an aspect of social development, can go in various directions none of which are inherently stronger than others.

## Can each nation's score exist independently?

Whether a nation's power can be considered independently of other nations depends on the general outlook of the world. In today's world it is obvious that a nation's power is highly dependent on its relationship with other nations. Consider, for example, Germany: it is a great economic power. How much of that power would remain were Germany isolated from its world-wide markets? Consider America: it is a great cultural power; doesn't this power depend on the access to other countries culural markets?

On the other hand, the closely woven world of the late 20th and early 21st centuries is not the only possible world. For a very long time people have lived in relatively autonomous economic worlds (Wikipedia article in French, sorry), which had few and essentially unimportant trade relations with each other. See also the Wikipedia article on World-systems Theory, a "macro-scale approach to world history and social change".

## Automating the assignment of stats for each nation

See Shadow1024's answer for suggestions. If you use RANDBETWEEN or similar functions don't forget to make provisions for "freezing" the results.

Power can not exists independently, if you are nation of 50 million people you could dominate many neighborhoods, but if you are placed between China & India you will be easily dwarfed.

My suggestion is to generate map of you world, split it into countries that look good to you and then assign features according to it. You will see yourself that countries who are on important waterways or navigable rivers have many advantages. On the other hand countries that are landlocked or poorly connected have many disadvantages.

It also depends a lot on who your neighbors are. If you get along with them, they will increase your power through cooperation and alliances. If you hate each other guts, they will tie part of your resources in order to keep an aye on them. Birds of feathers usually cooperate more easily. The neighbors with different races, religions or cultures usually have more difficulty to cooperate.

Empires are always multi ethnic, though they have one core ethnicity. Visit Peter Turchin site who wrote extensively about societies, his book War and Peace and War covers the formation of the empire extensively.

In the end human societies are the most complex things in the world. Choose approximation that works for you and happy world building.

# Economy is good, over-reach is bad

My citation is Rise and Fall of the Great Powers by Paul Kennedy. He goes through European history from 1500 to the cold war summarizing the reasons for the success of various nations relative to each other.

The summary version is internal peace and access to resources good, military overcommitment bad. The author focuses on European powers, and doesn't really address the issues about why the Ming/Ottomans/Mughals/Persia ended up so far behind the Europeans. However, he does have persuasive analysis for the relative power discrepancies in European struggles.

Basically, Spain rose to power becuse it was the first to the New World and looted literally entire mountains of Gold and Silver. But it struggled because it was fighting constant wars for 150 years. The wars reduced its population and caused repeated bankrupcies, which reduced internal investment and lead to other countries adapting more advanced production techniques. Population in Iberia was steady around 8 million from 1500 - 1700, while France grew from 16 million to 21 million and England from 2 million to 5 million. Eventually, Spain didn't make anything useful at all, so when the gold from the New World dried up it was destitute.

France, too, was ruined by too much warfare through the 1700s, and its population did not grow as fast as it could have. It also never pushed abroad to get access to more world resources as the Dutch and British did during this time period.

England, on the other hand, avoided major internal wars after 1651, didn't get invaded, and steadily set up colonies all over the world. So by 1800, England was firmly the richest country in the world and was able to dominate the world economy for a century.

The pattern more or less repeated itself with the United States. The US grew rapidly, generally had internal peace (except for that one Civil War thing) and due to its great size had easier access to resources like iron, coal, and timber, than most European countries. Especially after the advent of railroads, goods could be brought from remote parts of America to factories cheaply, massivly fueling America's economy. By about 1900, America was more populous and richer than the nations of Europe.

Russia had many of the advantages of the US, including a large population and ample resources, but never launched. While the population of Russia and the Ukraine absolutely exploded, increasing 4-fold between 1800 and 1900 (and was around 40 million larger than the US!), peace never found the land. Constant internal strife and poor organization meant that the railroads were never developed to move resources to factories until Soviet times. If WWI, the Bolshevik Revolution, Stalin's genocide, and WWII had not happened to Russia, it is entirely believable that there would be 400 million Russians now. Instead, there are about 140 million and they are being reduced in population, and are poorer, on average, than Brazillians, Turks, or Mexicans, all of whom were until recently considered to be in the Third World.

In any case, the discussions of economy were salient to the book, because they completely determined the result of all wars since 1500. If you had more people and higher tax incomes, you won the war, eventually. So the only thing you really need to track is the economy. If it is medieval/early modern, then you need to account for population and tax revenue. And remember that tax revenue is related to merchants, not to the size of the nations. Milan, Florence, and Venice were likely all richer than France in 1500, despite France's 10 to 1 (or more) numerical advantage. As a result, any of the those powers could potentially take on France in a war and win, as can be seen in the Italian wars.

Once the Industrial revolution hits, the metric becomes raw industrial power. The US was always going to win WWII, no matter how many Rommels or Yamamotos the enemy could throw at them. Japan built 15 heavy and 10 light carriers before and during WWII. The US built 27 and 110. Germany and Japan combined made 22,000 tanks and almost 200,000 aircraft. America made over 300,000. Thats not even counting that Britain and the USSR matched what Germany and Japan did between them. The US's overwheliming industrial advantage guaranteed that they would win the war....and I might point out that while building more ships, aircraft, and tanks than anyone else, the US also found the time to invent and develop some atomic bombs.

# Conclusion

Economics dominates who wins wars in the long run. Having lots of people, lots of tax income, and lots of industrial production makes you the most powerful country in the world.

A common measure of a nation's power is in the DIME format:

• Diplomatic
• Information
• Military
• Economic

Also worth considering religious power, and the fact that it's very hard to be diplomatically significant without at least some power in the other measures.

In game theory there is a branch called cooperative game theory

This is applicable when you want to describe the amount of power a party (in your case a political entity) has with respect to the others.

The idea is that except the raw power* of the party, a second criterion should be considered and this is the cooperation possibilities of this party. For example, a party that has 49% of the raw power but all the other parties are it's enemies, it might actually be pretty weak.

The assumption in this theory is that a coalition will be formed. I'm assuming that since you're trying to measure the power of the entities, there's some kind of competition going on, and if so this is a likely assumption. In this case, you can calculate the strength of each entity using it's Shepley value which is calculated using the number of coalitions the party can form, and it's relative importance in them (i.e. how easily could they have been formed without them)

Note that since what you're talking about is more than political power, you should factor that in by giving each entity a weight that also represents it's raw power. For example if you decide a coalition must have a strong army, then all the army-less entities should have a much lower value, such that a coalition can't be formed without a strongly armed entity, and the Shepley value would reflect that.

• Row power includes military, natural resources etc.

There are many different kinds of power to consider. There's economic power, military power, the power that comes from alliances, "soft power", religious power, cultural power, organizational power, technological power, and so on. In traditional Japanese culture there are kinds of power that we don't even have words for in English.

In just a single Political Science journal "Foreign Affairs" in a single year you can find multiple articles just on the subject of recent Chinese attempts to promote "soft power". And they won't even agree with each other. Soft power is the kind of power a country gets from things like culture and setting a good example. None of the authors attempt to quantify it because there isn't a good way to.

Power is too general an undefined to quantify. Let's compare the power of the Vatican to that of Taiwan. Taiwan has a larger military; the Vatican doesn't have one at all. When the leader of the Vatican speaks the entire world listens; when the leader of Taiwan speaks nobody outside of Taiwan listens. Taiwan is more likely to be invaded and lose it's sovereignty; this is not going to happen to the Vatican anytime soon. What's more powerful, Taiwan or the Vatican? If religious power is what you care about then the Vatican is more powerful. If you care about the number of active fighter jets then it's Taiwan. If it's sovereignty then the Vatican. If it's economic power then Taiwan. If you gave each of them a number it would say much about your biases and nothing about the political states of the Vatican and Taiwan.

What kind of power do you want to compare and quantify? What is the most important thing to the political entities in this world of yours?

If you're creating statistics for a game then you can give nations arbitrary values for whatever stats are important to this game. What these stats are will vary depending what the game is about. "Settlers of Catan" and "Diplomacy" are games about political entities and the stats they use do not overlap. If you're not designing a game then this is better thought of in terms of people and the systems they care about.