Absolute and Relative Probability: The Conspiratorial Mind

You sit down at a card table across from one other player. Between you is a dealer with a freshly shuffled deck.

The dealer draws a card, places it face down, and asks each of you to guess the suit.

“Hearts,” you say.

“Diamonds,” says the other player.

The dealer does not reveal the card. Instead, he gives you one clue:

“The card is red.”

Immediately, your confidence rises. Hearts is a red suit. Your guess was not random noise after all. A moment ago, your odds were one in four. Now they feel like one in two.

But then you look across the table.

The other player guessed diamonds.

Their confidence has risen too.

This short example captures a distinction that is easy to miss: evidence can make your hypothesis more likely without making your hypothesis more likely than its alternatives.

At the beginning of the card game, your hypothesis was simple: the card is hearts. Since there are four suits in a standard deck, the probability of your hypothesis was 25%.

P(hearts)=25%

The other player’s hypothesis had the same probability.

P(diamonds)=25%

These two hypotheses are incompatible. The card cannot be both hearts and diamonds. One of you may be right, or both of you may be wrong, but you cannot both be right.

Then the dealer tells you the card is red. This is real evidence. It rules out clubs and spades. Your hypothesis has genuinely become more likely.

P(hearts∣red)=50%

Your confidence has doubled. But the other player’s hypothesis has also doubled.

P(diamonds∣red)=50%

So the evidence supports your hypothesis in one sense, but not in another. It makes hearts more likely than it was before, but it does not make hearts more likely than diamonds. The clue supports both hypotheses equally.

This is the distinction I want to draw between absolute probability and relative probability.

By absolute probability, I mean the probability of a hypothesis considered directly after evidence is introduced. If some evidence E makes a hypothesis H more likely than it was before, then that evidence has given the hypothesis absolute support.

P(H∣E)>P(H)

That is what happened when the dealer said the card was red. Your hearts hypothesis became more likely than it had been before.

But by relative probability, I mean the probability of a hypothesis considered against its live alternatives. Evidence gives relative support to a hypothesis only when it favors that hypothesis more than it favors competing explanations.

In the card example, “the card is red” gives absolute support to hearts, but it does not give relative support to hearts over diamonds. The evidence raises both equally.

This distinction matters because a person can be completely correct that some evidence supports their hypothesis, while still being wrong to think the evidence favors their hypothesis over someone else’s.

That, I think, is one of the central errors of the conspiratorial mind.

Conspiracy theories are often dismissed as having no evidence. Sometimes that is true. But often the problem is more subtle. Many conspiracy theories do point to real evidence: strange coincidences, missing information, institutional secrecy, conflicting reports, suspicious timing, changed stories, powerful people meeting privately, documents being withheld, or officials behaving dishonestly.

The problem is not always that the evidence is fake. The problem is that the evidence is being evaluated in isolation.

A conspiracy theorist may say, “This fact supports my theory.” And in the absolute sense, they may even be right. The fact may make their theory more likely than it was before. But that is not enough. The real question is whether the evidence supports their theory more than it supports a mundane alternative.

Suppose a government agency gives two conflicting explanations of the same event. A conspiratorial explanation might be:

“They are hiding the truth.”

And maybe the contradiction does raise the probability of a cover-up. But it may also raise the probability of a simpler explanation:

“Large institutions are messy, slow, legally cautious, and bad at communication.”

The inconsistency may fit the conspiracy hypothesis, but it also fits ordinary bureaucracy. It may even fit ordinary bureaucracy better.

So the conspiratorial thinker may be looking at real evidence. The mistake is treating absolute support as if it were relative support. They see that their hypothesis has become more likely, but they fail to notice that competing hypotheses may have become more likely too.

They hear “the card is red” and think, “My odds doubled.”

That is true.

But diamonds doubled too.

This is the difference between evidence that merely fits a theory and evidence that favors a theory. A fact fits a theory when the theory can explain it. A fact favors a theory when it is better explained by that theory than by its competitors.

Those are not the same thing.

A politician changing their story is consistent with a conspiracy. It is also consistent with confusion, dishonesty, bad memory, legal advice, public relations strategy, or learning new information.

A missing document is consistent with a cover-up. It is also consistent with bad record keeping, technical failure, negligence, or ordinary human error.

A private meeting among powerful people is consistent with secret coordination. It is also consistent with networking, diplomacy, business, or routine institutional decision-making.

The question is not merely: “Can my theory explain this?”

The better question is: “Does my theory explain this better than the alternatives?”

That is where conspiratorial reasoning often breaks down. It collects facts that are compatible with the preferred theory, but it does not adequately compare that theory against rival explanations.

This also explains why conspiracy theories can become persuasive through accumulation. A person might present twenty suspicious facts in a row. Each one seems to support the theory. Each one adds to the feeling that something strange is going on. By the end, it feels like there is a mountain of evidence.

But if each piece of evidence supports the conspiracy hypothesis and the mundane hypothesis equally, then the pile may not do what it appears to do.

The evidence may be accumulating absolutely without accumulating relatively.

It is like being told, again and again, that the card is red. That may reinforce your belief that the card is not a club or a spade, but it does not help you decide between hearts and diamonds. To decide between hearts and diamonds, you need evidence that distinguishes one red suit from the other.

Likewise, to justify a conspiracy theory over a mundane explanation, you need evidence that distinguishes conspiracy from incompetence, coincidence, ordinary corruption, miscommunication, institutional self-protection, or incomplete public knowledge.

Without that comparative step, the conspiracy theorist is not so much following the evidence as following one possible interpretation of the evidence.

This does not mean conspiracies never happen. They obviously do. Governments lie. Corporations hide information. Institutions protect themselves. Powerful people sometimes coordinate in secret. A theory should not be rejected merely because it involves a conspiracy.

The point is that conspiracy hypotheses must compete against other hypotheses.

A real conspiracy should not merely explain the evidence. It should explain the evidence better than the alternatives.

If the conspiracy were true, what would we expect to see?

But just as importantly:

If the conspiracy were false, what would we expect to see?

If both theories predict the same evidence, then that evidence does not help us much. And if the mundane theory predicts the evidence better, then the evidence may actually count against the conspiracy, even if it initially feels suspicious.

This is why alternative hypotheses matter. Without them, we are tempted to overestimate the strength of our own view. We notice that the evidence has made our hypothesis more likely, but we forget to ask what it has done to the other hypotheses on the table.

The distinction between absolute and relative probability is simple, but powerful.

Absolute probability asks: “Did this evidence make my hypothesis more likely?”

Relative probability asks: “Did this evidence make my hypothesis more likely than the alternatives?”

The card-table example shows why this matters. If you guess hearts and then learn that the card is red, your hypothesis becomes more likely. It rises from 25% to 50%. But if the other player guessed diamonds, their hypothesis rises by the same amount. The evidence supports you, but it does not favor you over them.

Much conspiratorial thinking lives in that gap. It mistakes evidence that raises the probability of a theory for evidence that raises the theory above its competitors.

But evidence does not merely need to fit a hypothesis. It needs to discriminate between hypotheses.

A fact that supports your theory and an ordinary explanation equally is not strong evidence for your theory. A fact that supports the ordinary explanation better is not evidence for your theory at all, even if your theory can be made to accommodate it.

The conspiratorial mind is not always a mind without evidence. Often, it is a mind that has confused compatibility with confirmation, and absolute support with relative support.

Evidence matters. But alternatives matter too.