Political Entropy

All democracies end in socialism.

Instituting a democracy starts an entropic process of wealth redistribution from productive to non-productive members of the society. It is a slow process that may take generations, but it is inevitable and irreversible, unless derailed by force.

What is Entropy?

According to Merriam-Webster’s Dictionary of the English language, entropy is, among others, “a process of degradation or running down or a trend to disorder”. Broadly put, it is the tendency of an isolated system to naturally evolve toward a state of maximum uniformity. Without an external intervention, everything inside an isolated system dissipates until it becomes homogenous. You must expend energy from an outside source to oppose entropic processes.

The term was used for the first time in 1865 by the German physicist Rudolf Clausius in his formulation of the second law of thermodynamics. The second law of thermodynamics deals with the preferred direction of progress for natural phenomena in isolated systems. For instance, in a glass of water and ice, the water and ice will exchange heat until the whole mixture reaches the same temperature. By itself, a glass of water will never spontaneously heat up part of the water at the expense of cooling down the rest of the water to form ice, even if such a process does not violate any law of conservation of energy in nature.

Entropy was born out of the necessity to define a physical property for explaining such phenomena. Thus, it was postulated that isolated systems always evolve toward a state of increasing entropy or chaos/disorder/homogeneity. Rudolf Clausius invented the term by combining the words energy and trope (Greek for transformation), thus expressing the natural affinity of energy exchanges inside isolated systems. He is also the author of the best known definition for the second law of thermodynamics stating that: “The entropy of the universe tends to a maximum”.

The entropy concept has been generalized and expanded upon substantially since the 19th century, both in thermodynamics and other fields such as: information theory, mathematics, computer science, ecology or sociology. Today entropy is used widely and with various meanings, but its core significance revolves around a few basic features. Above all, an entropic process:

  • is naturally spontaneous
  • is irreversible
  • manifests through homogenization and dispersion
  • pushes the reference system toward a state of equilibrium (maximum entropy)

To see how the concept of entropy applies to the field of political doctrines, particularly to democracies, let us begin by analyzing the state’s role in society.

The State

Foundation – The Social Contract

The foundation of any state is the social contract. Political ideologies are, in essence, different types of social contracts. The social contract theory was debated by many philosophers, notably Thomas Hobbes, John Locke and Jean-Jaques Rousseau. The social contract defines the relationship between the individual and the state.

According to Thomas Hobbes, in the absence of a political society, humans are living in savagery or in a “state of nature”. Their actions are ruled only by their own power and conscience, thus they are basically free to do whatever they want. By having unlimited freedom, anyone is able to hurt his fellow man with impunity, inducing a “war of all against all” (bellum omnium contra omnes). For this reason, civilized societies are based on an agreement in which individuals surrender some personal liberties (like killing, plundering, stealing etc.) in exchange for some benefits provided by the state (notably protection from killing, plundering, stealing, etc.).

Thus, a social contract is a trade off between natural rights (personal liberties) and social rights. Various political ideologies are different interpretations of the social contract, specifically on the different degrees and methods in which public interest (defence, welfare, infrastructure, social security, education, etc.) is served at the expense of the individuals’ liberties (taxation, conscription, nationalization, jury duty, privacy breaching, etc.).

Therefore, debating political doctrines revolves around defining what is legitimate public interest (or “general will” as defined by Jean-Jaques Rousseau) and how far can the state go against individual liberties in promoting it.

John Locke in his Second Treatise of Civil Government argues that the state’s role is limited to protecting the lives, liberty and property of its citizens. For this purpose, citizens delegate to government the right to enforce order, investing the state with the mandate to retaliate with force against those who initiate force.

By preventing destructive conduct, the society as a whole benefits. Assets are protected, people are not killed or impaired, goods are not destroyed, oppressors are discouraged from living on other people’s expense, while productive people are free to enjoy the fruits of their labor. Everyone must find a productive livelihood, contributing to the overall welfare. Basically, the state prevents the society from turning against itself from the inside and protects it from being harmed from outside. To defend its citizens against internal threats, a state uses police and justice. To defend them against external threats, a state uses military and diplomacy. And the state’s set of tools (its mandate to use force against those who initiate force) is perfect for such purposes: putting away criminals while fighting, intimidating or talking things over with foreign powers. Preventing various forms of destructive conduct was historically the state’s authorities main purpose.

Evolution – The State’s Role

Regardless of the type of state, societies developed naturally into establishments in which ruling classes were responsible for military, judicial, public order, law enforcement and diplomatic duties. Whether it was the ancient Greek city states, the Roman Empire, feudal states of the Middle Ages, the Aztecs, etc., rulers were exercising their authority by waging wars, dynastic marriages, passing judgement, keeping the roads free from bandits or the seas free from pirates, exchanging diplomatic correspondence and signing treaties with their neighbouring rulers.

Foreign policy aside, based on this historical view, we observe the essence of the state’s role in every society. By protecting the lives, liberty and property of its citizens, the state is to ensure that no one benefits at the expense of another. Any interaction that is not mutually agreed upon between parties is an abuse and it is the state’s role to protect its citizens from it.

Diversion – Democracy

With progresses toward universal suffrage during the 19th century, the state’s role started to elevate from preventing various forms of destructive conduct to actively supporting popular aspirations. This is how wealth redistribution came into existence. In this paradigm, the state reallocates resources between members of the society for the public good. This usually means the state picks charitable pursuits or underfinanced priorities and forces other members of the society to provide for them. For instance, the state may tax some citizens or businesses to help the unemployed, provide free education and healthcare, subsidize specific economic endeavors, etc. It may also intervene indirectly by enforcing onerous obligations between private entities, like constraining employers to provide specific benefits to employees.

However, this is also where a fundamental aberration appears. Instituting any form of wealth redistribution means legitimizing that some members of the society are in fact entitled to benefit at the expense of others. And since the state is the one to decide who benefits at the expense of whom, whoever controls the state imposes the wealth redistribution policy. In a democracy, a majority of voters controls the state.

Political Entropy

Human action is driven by self-interest or, to use decision theory jargon, by maximizing one’s expected utility. Since voting is a human act, in a democracy, a voter always supports candidates or policies that best serve his self interest. This ensures that democratic elections are won by politicians able to increase expected utility for a majority of voters.

To increase utility for the largest number of electors, politicians must maximize the pool of resources they can distribute to those voters. And when politicians hand out whatever they take from other electors beforehand (redistribute wealth), the following corollary is dictated: they need to ensure they alienate a minimum number of voters in the process of extracting these resources. Wealthy minorities are ideal for this spoliation, since their substantial wealth can be looted with little loss in popular support.

This spontaneous dynamic is inherent to any democratic system. With universal suffrage and wealth redistribution, political reasoning demands a course of action where wealth is redistributed from wealthy minorities to supportive majorities.

For instance, let’s consider a population of 10 voters, with spoliation potential (tax bases) ranging from 0 to 9 wealth units.

Voter A B C D E F G H I J
Tax Base 0 1 2 3 4 5 6 7 8 9

Without wealth redistribution, everyone hangs on to their wealth (Redistribution 0).

Voter A B C D E F G H I J
Tax Base 0 1 2 3 4 5 6 7 8 9
Redistribution 0 0 0 0 0 0 0 0 0 0 0

In an attempt to win elections however, a candidate can propose the following policy. Take away J’s 9 wealth units and give one to each of the remaining 9 electors (A to I). This will obviously upset J who will vote against such a candidate, but in exchange, the future policy maker will win 9 otherwise apathetic voters. A, B, C, D, E, F, G, H and I, who had no stake in a no-redistribution scenario (Redistribution 0), will receive 1 wealth unit each if such a policy is enacted. Consequently, they will actively support it with their votes. In other words, compared to Redistribution 0, this policy ensures the support of 90% of the voting population. By democratic standards, this is ideal.

Voter A B C D E F G H I J
Tax Base 0 1 2 3 4 5 6 7 8 9
Redistribution 0 0 0 0 0 0 0 0 0 0 0
Redistribution 1 +1 +1 +1 +1 +1 +1 +1 +1 +1 -9

Following this reasoning, the next step is to attempt to improve on Redistribution 1 in the same manner. We know that if we reduce a voter’s expected utility, we lose his support. To make this sacrifice count, we must maximize the number of votes we win in exchange. This means we must maximize the wealth we get from him by increasing taxation and/or by reducing current entitlements. To find the largest wealth pools, we add the Tax Base to the current redistribution (Redistribution 1).

Voter A B C D E F G H I J
Tax Base 0 1 2 3 4 5 6 7 8 9
Redistribution 1 +1 +1 +1 +1 +1 +1 +1 +1 +1 -9
Wealth Pools 1 2 3 4 5 6 7 8 9 0

There is nothing more we can take from J. All his 9 wealth units are already spoliated. Voter A doesn’t have any wealth. We could stop paying his 1 wealth unit handout and give it to somebody else. This doesn’t help either. We would lose A’s vote and gain someone else’s vote in exchange. With B it’s a different story. We can stop handing out his wealth unit and tax the other wealth unit he owns. We can use these 2 wealth units to buy 2 votes. So we lose a vote and win 2 in exchange. It’s a start, but we can do better. If we keep looking, we will see that voter I can provide us just enough wealth to buy every other vote. If we stop paying his 1 wealth unit handout and tax all his 8 wealth units, we have just enough to buy the remaining 9 votes. Thus, we can afford to allocate one additional wealth unit for voters A, B, C, D, E, F, G and H, and spoliate one less wealth unit from J.

Voter A B C D E F G H I J
Tax Base 0 1 2 3 4 5 6 7 8 9
Redistribution 0 0 0 0 0 0 0 0 0 0 0
Redistribution 1 +1 +1 +1 +1 +1 +1 +1 +1 +1 -9
Redistribution 2 +2 +2 +2 +2 +2 +2 +2 +2 -8 -8

With the exception of voter I, everyone is better off. If we try to give more or take less from someone, we must reduce somebody else’s cut, which will be no improvement over Redistribution 1. Therefore, Redistribution 2 is ideal compared to Redistribution 1, in the same manner in which Redistribution 1 was ideal compared to Redistribution 0. Both iterations have a popular support of 90% of the voters, as on both occasions 9 out of 10 voters get better deals compared to the previous redistribution.

If we keep this up long enough, at some point we will enter a cycle. This is a finite pool of voters with a finite number of wealth units’ permutations, so we will run out of permutations at some point, if for no other reason. In this example, after 10 iterations, we arrive back at Redistribution 0. Then, the cycle repeats.

Voter A B C D E F G H I J
Tax Base 0 1 2 3 4 5 6 7 8 9
Redistribution 0 0 0 0 0 0 0 0 0 0 0
Redistribution 1 +1 +1 +1 +1 +1 +1 +1 +1 +1 -9
Redistribution 2 +2 +2 +2 +2 +2 +2 +2 +2 -8 -8
Redistribution 3 +3 +3 +3 +3 +3 +3 +3 -7 -7 -7
Redistribution 4 +4 +4 +4 +4 +4 +4 -6 -6 -6 -6
Redistribution 5 +5 +5 +5 +5 +5 -5 -5 -5 -5 -5
Redistribution 6 +6 +6 +6 +6 -4 -4 -4 -4 -4 -4
Redistribution 7 +7 +7 +7 -3 -3 -3 -3 -3 -3 -3
Redistribution 8 +8 +8 -2 -2 -2 -2 -2 -2 -2 -2
Redistribution 9 +9 -1 -1 -1 -1 -1 -1 -1 -1 -1
Redistribution 10 0 0 0 0 0 0 0 0 0 0

It is important to realize that this is an abstract model representing the popularity of public policies. Actual public policies are influenced by a number of factors, either political, circumstantial or practical. We know politicians are always susceptible to corruption, that they are liable to blackmail, that their choices are often limited by their credibility, vested interests, incompetence, ignorance, etc. There are practical considerations to take into account as well. Costs and limitations of the bureaucratic apparatus in enforcing tax collection are often decisive. It is not feasible, for instance, to spend 2 wealth units to collect 1 wealth unit. Etc.

There are many factors at play, however, all of the above are imperfections of implementation, not of the model per se. The model indicates the policies that are most popular at any point in time. The measure in which such policies are enacted, depends on how responsive the state is to the will of the people. The more democratic a country is, the closer it will be to this ideal model. In a perfect democracy, the will of the people and the enacted policies are identical. Actual policies deviate from the model only to the extent that they deviate from democracy itself. Hence, the limitations above do not reduce the model’s relevance for democracies. On the contrary.

Also, the timing of each iteration is just a convention. It may be candidates outbidding each other during the same elections. For instance, one of them proposes Redistribution 1, then the second outbids him proposing Redistribution 2, then the first one proposes Redistribution 3 in response and so on for as long as they can change their minds while maintaining some credibility. Or there can be 2 or more political parties bidding for similar optimal policies, one election cycle at a time. They share the votes, get elected and enact Redistribution 1. Then, during the next elections, they both support policies similar to ideal Redistribution 2. And so on. Or there may be multiple candidates focusing on small electoral niches. Once in office, they have to negotiate and compromise between them in a way that best serves the electorate overall, instead of specific niches. Finally, they end up with something similar to the corresponding ideal redistribution. Etc. Actual timing is not relevant. What is fundamentally relevant, is the iterations’ succession (what comes next) and the long term (cyclical) impact.

Also of no relevance are the specific democratic mechanisms in play: parliamentary republic, presidential republic, direct elections, indirect elections, proportional representation, majoritarian representation, preferential voting, cardinal voting, etc. What matters is that the will of the people is enacted, which is what democracy must always provide (demos or people + kratos or power). How this happens is not important.

Now, that we have seen how wealth redistribution works in functional democracies, we can start drawing some conclusions. Is this behavior entropic in its nature? In other words:

  • Is it naturally spontaneous?
  • Is it irreversible
  • Does it manifest through homogenization and dispersion?
  • Does it push the society toward a state of equilibrium (maximum entropy)?

Naturally Spontaneous

Since every iteration is ideal compared to the previous one, the progression is naturally spontaneous. By increasing expected utility for the largest number of voters and decreasing expected utility for the smallest number of voters, the largest popular support is always ensured.

Irreversible

Let’s look at the long term wealth redistribution.

Voter A B C D E F G H I J
Tax Base 0 1 2 3 4 5 6 7 8 9
Redistribution 0 0 0 0 0 0 0 0 0 0 0
Redistribution 1 +1 +1 +1 +1 +1 +1 +1 +1 +1 -9
Redistribution 2 +2 +2 +2 +2 +2 +2 +2 +2 -8 -8
Redistribution 3 +3 +3 +3 +3 +3 +3 +3 -7 -7 -7
Redistribution 4 +4 +4 +4 +4 +4 +4 -6 -6 -6 -6
Redistribution 5 +5 +5 +5 +5 +5 -5 -5 -5 -5 -5
Redistribution 6 +6 +6 +6 +6 -4 -4 -4 -4 -4 -4
Redistribution 7 +7 +7 +7 -3 -3 -3 -3 -3 -3 -3
Redistribution 8 +8 +8 -2 -2 -2 -2 -2 -2 -2 -2
Redistribution 9 +9 -1 -1 -1 -1 -1 -1 -1 -1 -1
Redistribution 10 0 0 0 0 0 0 0 0 0 0
Long Term Wealth Redistribution
Cycle Total (10 Iterations) +45 +35 +25 +15 +5 -5 -15 -25 -35 -45
Average per Iteration +4.5 +3.5 +2.5 +1.5 +0.5 -0.5 -1.5 -2.5 -3.5 -4.5
Percentage in Tax Base +++ +350% +125% +50% +13% -10% -25% -36% -44% -50%

Over a full cycle (10 iterations), we notice how the poorer one is, the more he receives; while the richer one is, the more is taken from him. We will see later on exactly how much is taken from or given to someone. Still, we can already grasp that a wealth redistribution process based on taking from the poor and giving to the rich is not sustainable in functional democracies. To maximize popular support, politicians must increase the expected utility for as many people as possible, while decreasing the expected utility for as few people as possible.

A voter who gains something, no matter how little, will vote in favor of such a policy. A voter who loses something, no matter how little, will vote against such a policy. Therefore, when taking from someone, one must take as much as possible, since that vote is lost anyway. When giving to someone, one must give as little as possible (1 wealth unit), just enough to win the vote, in order to spread the wealth to the greatest number of supporters. Even if it is irrelevant who constitutes the supportive majority (all votes are equal), it is vital to have the wealthiest electors in the spoliated minority, so they can provide more loot.

Homogenization and Dispersion

As mentioned above, we notice how the poorer one is relative to the others, the more he receives; while the richer one is relative to the others, the more is taken from him. In our previous example, where the tax bases grew in arithmetic progression, voter J ended up losing 50% of his tax base on average. Voter I, who was a little less prosperous, paid 44% on average, voter H paid 36%, and so on.

Let’s see what happens when the wealth dispersion is higher. For instance, let’s build a model of the global wealth distribution and assume all that wealth is our tax base. Using the infamous Pareto distribution (20% of the people own 80% of the wealth) and dividing the population into quintiles yields something like this:

Quintile A B C D E
Tax Base 0 0 0 1 4
Redistribution 0 0 0 0 0 0
Redistribution 1 +1 +1 +1 +1 -4
Redistribution 2 +1 +1 +2 -1 -3
Redistribution 3 +1 +1 0 0 -2
Redistribution 4 +1 +1 +1 +1 -4
Total Redistribution per Cycle (3 Iterations) +3 +3 +3 0 -9
Average Redistribution per Iteration +1 +1 +1 0 -3
Redistribution Percentage in Tax Base +++ +++ +++ 0% -75%

In this example, the lowest 3 quintiles have close to nothing, the fourth quintile has almost something and the richest quintile has 80% of everything, which is a realistic approximation of the global wealth distribution.

The redistribution process stabilizes around a 3 iterations cycle between Redistribution 2 and Redistribution 4 (Redistribution 4 is identical with Redistribution 1). During Redistribution 2 and Redistribution 3 (when reducing expected utility for D and C respectively), there were 2 wealth units available for handouts each time. On both occasions, quintile E was on the receiving end, benefiting from tax deductions. Even so, its average fiscal burden amounts to 75% of its tax base per iteration.

If we take a closer look at the average values, we notice something interesting once the redistribution cycles stabilize. During a cycle, the average tax/handout per iteration is equal and opposite to one’s deviation from the average tax base:

  • In the first example, the average tax base is 4.5 wealth units per voter (0+1+2+3+4+5+6+7+8+9)/10 = 4.5. Voter A, with 0 wealth, receives 4.5 wealth units on average; voter D, with 3 wealth units, receives the missing 1.5 wealth units; voter I, with 8 wealth units, loses the 3.5 wealth units he had in excess, etc. Everyone is drawn to the average 4.5 wealth units.
  • In the second example, the average tax base is 1 wealth unit per quintile (0+0+0+1+4)/5 = 1. Likewise, quintiles A,B and C, with 0 wealth, each receive the average 1 wealth unit; quintile D, with wealth equal to the average is not impacted; quintile E, with 4 wealth units, loses the 3 wealth units in excess.

Democracy tends to homogenize wealth by pulling up those who fall below the average and pushing down those who rise above. The force with which one is drawn toward the average is proportional with how much one deviates from the average. This constant pressure, pushes the overall wealth distribution toward a specific state of equilibrium.

Equilibrium

To see the state of equilibrium that this homogenization leads to, we must calculate the wealth allocation over the long term (after a full cycle of redistributions). In our first example, it is constant across the board (45). For instance:

  • Voter J produces 9 wealth units per iteration and is taxed with 9, 8, 7, … 0 wealth units on each iteration respectively. This amounts to:
    (9×10)-9-8-7-6-5-4-3-2-1+0 = 45
  • Voter A produces 0 wealth units per iteration and receives handouts of 1, 2, 3, … 9 wealth units during the cycle. His total wealth amounts to:
    (0×10)+1+2+3+4+5+6+7+8+9+0 = 45
  • Voter C’s wealth will amount to:
    (2×10)+1+2+3+4+5+6+7-2-1+0 = 45
  • Voter G’s wealth will amount to:
    (6×10)+1+2+3-6-5-4-3-2-1+0 = 45
  • etc.

Likewise, in the second example:

Quintile Wealth at Cycle End
A (0×3)+1+1+1 = 3
B (0×3)+1+1+1 = 3
C (0×3)+1+1+1 = 3
D (1×3)-1+0+1 = 3
E (4×3)-3-2-4 = 3

We can see how wealth redistribution brings everyone’s wealth to the same level. After a full cycle, everyone ends up with the same amount of wealth, no matter how much wealth one produces. Democracy takes any given wealth distribution in a society and redistributes it in a manner in which everyone comes out with equal shares. This is the state of equilibrium (or maximum entropy) toward which democracy pushes society.

Conclusion

We have seen how democracy enforces an egalitarian society. Just like in the glass of water and ice, where entropy brings the whole mixture to the same temperature, an ideal democracy brings everyone’s wealth to the same level.

Regular election cycles ensure public policies are systematically updated to target any pockets of wealth (aberrations) that may have formed and disperse them in the process of building supportive electoral majorities. The larger a wealth pocket is, the faster it is eroded. In time, this flattens wealth distribution and leads to socialism.

Democracy makes it possible and, as we have seen, inevitable, for a majority to indirectly spoliate a minority by enforcing laws that are in its favor. Even if people are prevented from turning against each other directly, a majority can always use the state as a tool to extort wealth from a minority. Individual self interests always aggregate in a dynamic in which supportive majorities spontaneously build up around policies that redistribute wealth their way. In real life, this usually manifests through aspirations of social justice or equality of opportunity that institute and perpetuate policies in which below-average (less productive) members of the society systematically extort wealth from above-average (more productive) members of the society.

Since this process is entropic in democracies, it can never be opposed within the confines of democracy itself.

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