Tell me the odds: Democracy

In a dictatorship, you have to hope that the leader will be benevolent. In a democracy, you have to hope that everyone else will be benevolent.

Democracy is very much held up as beacon of progress in governance. Many automatically assume that if leadership is elected by a majority, it minimises the possibility of tyranny. “It is the antidote to Tyranny and Oppression.” But is this necessarily true? Is it even probabilistically true?

Well. The past few years have put that notion into question.

I like to treat governance and leadership as a numbers problem. In this post, I do just that.

In my (very) simplified thought experiment, I start with the following premises/assumptions:

1. There is a set of policies designed such that anyone For the set will definitely Endorse it, and anyone Against will definitely Reject it.
2. There are three types of people in the political population: Those who are For the set; Those who are Against the set, and Those who are Ignorant-Ambivalent.
3. Those For and Against are informed supporters (i.e. they understand the intent and expected effects of the set). Those who are Ignorant-Ambivalent either do not understand the set or are not invested in its outcome, and thus are likely to choose For or Against arbitrarily.
4. A leader must be selected to Endorse the set or to Reject it. If no leader is selected, no action is taken.
5. In a Democracy, one person from the majority will be elected as the Leader. In a non-Democracy, the Leader will essentially be selected randomly.
6. The intent and expected effects of the set is beneficial for the population, regardless of its popularity amongst the population.
7. Those who are For the set of policies are considered Benevolent.
8. Those who are Against the set of policies are considered Tyrants.
9. There are four possible worlds:
   • There are more For than Against and Ignorant-Ambivalent. (A)
   • There are more Against than For and Ignorant-Ambivalent. (B)
   • There are more Ignorant-Ambivalent than For or Against. (C)
   • A Control World (S), in which there are equal numbers of For, Against, and Ignorant-Ambivalent.

Altogether, we get the following configurations, each with an equal probability of being true (1/4):

Each circle can represent an equal number of as many people as you want: Due to how elections are typically done (in a Binary manner), all votes eventually converge into either For or Against anyway.

With these premises in mind, here are the bad odds of democracy, using conditional probability:

Problem 1. The probabilities are not in Democracy’s favour.

In World (A), the population is a mostly Benevolent one. Since there are significantly more For the policy than Against, a Leader who is For the policy set will definitely be elected, even if the Ignorant-Ambivalent chose to be Against the policy set. This gives us a proability of 1.

However, this triumph is not so clear-cut in other worlds. In World (B), Those Against outnumber Those For, thereby ensuring that a Leader who is Against the policy set will be elected. A tyrant is thus sure to be selected. This gives us a Probability of 0.

In world (C), the result is dependent on the Ignorant-Ambivalent. Back-of-the-napkin calculation shows us that you only have a 2/5 probability of electing your Benevolent Leader. The Tyrant has 2/5 probability as well, while there is a 1/5 probability of a hung election, which is also undesriable. You get an outcome worse than flipping a coin to elect your Benevolent Leader

In world (S), your proability of a benevolent leader is only 1/3. Once again, 1/3 proability of a Tyrant; and 1/3 probability of a hung election. Again, less than 50/50 chance of getting a benevolent ruler.

What can we conclude here? That out of the four worlds, one world guarantees an ideal outcome (A), another guarantees a failed outcome (B), and the remaining two outcomes are left to the mercy of the uninformed and the uninvested (C & S).

Taking all these probabilities in account, you have a 13/30 chance of selecting your Benevolent Ruler.

That’s slightly worse than a coin-flip.

Problem 2. It can’t beat random selection.

Let’s compare that with a non-democratic system. Keep in mind that according to Premise 5, a Leader in a non-Democracy is essentially elected randomly. So here we start to play with probabilities:

In World (A), you have better than 2/3 probability of NOT selecting a Tyrant. In fact, you have only 1/4 chance of selecting a Tyrant (hence 3/4 odds of getting a benevolent ruler). While it is certainly worse than the certainty of not selecting a tyrant, the odds are not terrible.

A flipped situation is found in World (B), the certainty of electing a Tyrant is now reduced to 3/4 probability: You now have 1/4 probabilty of selecting a Benevolent Leader. You trade off certainty in the ideal world for hope in the worst one.

In either World (C) and (S), the outcome is actually better in a non-democratic system: you have 1/2 probability of selecting a Benevolent Leader (true also that you now have 1/2 probability of selecting a Tyrant). Moreover, there is no possibility of a hung election.

Taking the probabilities of all these possible worlds together, you get a coin flip: 1/2 chance.

And 1/2 is greater than 13/30. 1/15 probability better.

To put that into context: There are 203 countries that hold some form of elections. Assuming that each country only hold one selection in a cycle, you improve the odds for 13.5 countries if you tell them to just pick someone out of a damned hat.

Problem 3. The world is ambivalent.

Our woes do not stop there. Worlds (A) and (B) are not the closest representations of the world. Worlds (C) and (S) represent the real world more accurately than others. Many people are not informed, and most people are not as invested.

It’s not a secret that democracies suffer in a world of the Ignorant-Ambivalent. It’s why education and information is so important for a democracy to thrive. However, time and time again, we see people choose what they want to know, and very few want to invest in politics.

Another issue for democracies are that Worlds (C) and (S) have the additional problem of leading to a Hung Vote, in which no Leader can be selected. This is catastrophic; worse than a scenario where a tyrant is selected. Inaction does not generate any form of benefit. At least with a tyrant, some people will benefit, which is better than noone benefitting.

Problem 4. The defense against tyranny in a democracy is not unique to a democracy.

So far, we learned that democracy gives us bad odds. But proponents of democracy will say that democracy still trumps other systems of governance because of its unique defenses against tyranny.

Let’s unpack.

According to democracy’s proponents, a commonly used concept in many modern democracies is that of separations of power. When a leader is selected/elected, they do not gain absolute power. Instead, power is distributed between different branches of government, such that the Leader’s power is kept in check by other individuals. Trias Politica is the most common presentation of this system. In most democracies, there is the legislative, the executive, and the judiciary.

Here is the catch though: It’s not unique to democracy.

Separation of Powers is not a new concept. In fact, it has been used since the first flourishing civilization. Some societies use councils, others use church and castle, others still use feudal lords. Not every separation is equally effective, but each is an instance of Separation of Powers.

So if we accept this, what unique aspect does democracy provide?

The only world where democracy works is the world most difficult to achieve.

Democracy is the problem of putting the cart in front of the horse. Of the four possible configurations of worlds, only one world stands to be better off with democracy, and it is the world that is most difficult to achieve.

In actuality, we live in worlds more than (C) and (S), where most people are either not informed enough or not invested enough to make the best choice. With democracy, we either get worse odds, or we get odds no better than a coin-flip.

So why should we risk that instead of just picking someone at random?

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So where does this leave us?

A popular sentiment states that “Democracy is the worst form of government, second only to every other forms of government.” I strongly disagree. Democracy is very much bottom-tier. We could do much better. The question is what and how?

But what do readers think? Do you agree with the arguments? Are there any problematic premises? Is my math off?

Calculations provided here.