Doing the Calculus on Peace

TL;DR

1. The ethno-state fails because it has to fight a roughly 50/50 demographic fact that’s extraordinarily hard to fight. A system that needs permanent repression to survive is hard to call a system. It’s a time bomb.

2. The two-state solution fails because more than 700,000 illegal Israeli settlers and an infrastructure that has been entangled for over fifty-seven years (since the West Bank was first annexed in 1967) push the success probability mathematically close to zero. If not zero.

3. Once both options are eliminated through this kind of mathematical approach, only one remains. A One-State Democratic-Secular Palestine. Because it’s the only architecture that isn’t doomed by design.

4. No, I didn’t actually use calculus. 😢

I.

I’m not sure where to start with this, but let me be honest about what I think.

Every time people debate Israel-Palestine, it ends in the same place. Both sides shouting. Nobody moving. Everyone exhausted. Why? My guess, and I could be wrong, is that the debate begins on the wrong opening premise. Morality and religion.

Morality matters, to some extent, but it has one fatal weakness in this context. Moral claims are not falsifiable. For a lot of people, you can’t “disprove” a moral conviction with data. That’s why the debate never ends. It wasn’t designed to end.

So as a thought experiment, let’s try a different approach. Let’s treat this as a maths problem.

Take the area between the Jordan River and the Mediterranean Sea as a system. It has variables. It has constraints. It has feedback loops. The right question to ask isn’t “who has the most right to be there”. The right question is something else. Which system architecture is most likely to produce a stable equilibrium and remove the risk of ruin (the fat-tail risk)?

Here’s the central thesis. Both models, the ethno-state (Zionism) and the two-state solution, fail logically and empirically. Especially after Palestinian land has been illegally annexed by settlers who are legitimised by the Israeli government. Once both options are eliminated, only one remains. The One-State Democratic-Secular model.

I’m not going to argue from morality. I’m going to use the boring process of elimination, the same way a scientist would in a lab.

The strongest version of the Zionist argument is not “God gave us this land”. That one is easy to refute.

The strongest version is this. After the Holocaust, a group that had been systematically hunted and killed by nearly all of Western civilisation for two millennia needs a physical location that can be militarily defended. Not as a privilege, but as existential insurance. And honestly, I think that’s a reasonably valid argument. I respect it.

Now, the strongest version of the two-state argument is not nostalgia for the 1967 map.

The strongest version is this. The only way two communities with overlapping historical traumas can build healthy political identities is to first have separate sovereign space. Premature integration with no trust foundation produces Yugoslavia, not South Africa.

Both arguments are valid. I grant them in full.

Now I’m going to show that even if you accept the strongest version of each, the conclusion is still the same.

II.

The ethno-state against reality. Zionism on Palestinian land is a self-destructing system.

When Bertrand Russell wrote Principia Mathematica, he needed hundreds of pages just to prove that 1 + 1 = 2. Not because the result wasn’t obvious, but because he wanted the conclusion to follow necessarily from the basic axioms, with no room for “but my feelings tell me otherwise”.

I want to do something similar here. Not prove something complicated, but prove that a conclusion which might look controversial actually follows necessarily from premises that are already in place.

The Thermodynamics Argument

Let’s start from first principles.

In systems thinking there’s a basic concept. A closed system fighting entropy requires ever-increasing energy input. Otherwise it eventually collapses on its own. This isn’t a metaphor. It’s literally a thermodynamic principle, and it applies to a lot of things, social-political systems included.

An ethno-state, by what it is, is a system trying to maintain a particular demographic composition inside a given territory. The problem? Demographics are dynamic. They move. They change. They grow and shrink. Right now, the population data between the Jordan River and the Mediterranean is roughly 50/50. About 7.2 million Israeli Jews against 7.4 million Palestinian Arabs.

To maintain a Jewish ethno-state with the present demographic composition, the system needs one of two things.

First, permanent repression. Mobility control, legitimised discrimination, restrictions on political rights.

Second, forced change of the demographic composition. In international law, that’s ethnic cleansing.

The first option creates what systems dynamics calls a reinforcing feedback loop. Repression triggers resistance, resistance triggers escalation, escalation triggers harder repression, harder repression triggers harder resistance, and so on. The loop has no equilibrium point. It will keep escalating until one variable collapses.

The second option is a war crime in international law, and in practice it triggers an international response that accelerates the system’s collapse anyway.

Conclusion from a systems-thinking lens. The ethno-state is a system that structurally cannot reach steady state. Not because the people inside it are evil, I’m trying not to make moral claims here, but because its architecture is incompatible with demographic reality. This is consistent with Nassim Taleb’s reading that the Israeli state, as currently configured, isn’t antifragile.

Logically and mathematically, define the following.

DA(t) = Arab population at time t

DJ(t) = Jewish population at time t

The demographic data shows

dDA/dt > dDJ/dt

(Arab growth rate is greater than Jewish growth rate, empirically observed.)

To maintain the ethno-state, you need a suppression level σ(t) proportional to the ratio

σ(t) ∝ DA(t)/DJ(t)

Because DA(t)/DJ(t) is monotonically increasing in t,

dσ/dt > 0 ∀t

The energy input for repression has no upper bound. It rises without limit. A system that requires unbounded input to survive is, by definition, not sustainable. This isn’t a political prediction. It’s a direct mathematical implication of the demographic data.

The reinforcing feedback loop can be represented as a simple system of differential equations.

d(Repression)/dt = α · Resistance, d(Resistance)/dt = β · Repression

where α, β > 0. The system has no stable fixed point other than total collapse. The eigenvalues are positive, which means the solution diverges, not converges.

Back to “existential insurance” from a few paragraphs ago. The legitimate need (a defensible physical location as existential insurance) is exactly what an ethno-state caught in a reinforcing feedback loop toward collapse fails to deliver. An ethno-state with 50/50 demographics is less defensible, not more. Genuine existential insurance requires a stable system. And the only path to stability, at least under this analysis, comes from constitutional hard guarantees protecting both communities, not from repression whose dσ/dt > 0 has no upper bound.

The Logical Consistency Problem

There is also a logical problem that often gets missed, and I think it’s worth sitting with.

The main Zionist argument. The Jewish people, as a group that has experienced long persecution, are entitled to self-determination on their ancestral land.

An argument that starts from their experience, I don’t want to invalidate that. But we need to apply the Kantian universalisability test. Can this principle be universalised without contradiction?

By my reading, no.

Because the Palestinian Arab population, which has also been in the same territory for centuries, has a structurally identical claim. Acknowledging the right of self-determination for one group while denying the same right to another group in a structurally identical situation is a logical contradiction, not a coherent argument.

Written in formal logic, the definitions are these.

P(x) = “group x has experienced long persecution”

H(x) = “group x has a historical claim to the territory”

S(x) = “group x has a right to self-determination on the territory”

The Zionist premise, which they assert themselves, is

_Pr_𝓏 . P(Jews) ∧ H(Jews) → S(Jews)

Now apply the Kantian universalisability test. If this principle is valid, it has to be universalisable.

Universalised. ∀x [P(x) ∧ H(x) → S(x)]

Plug in the empirical data.

P(Palestinians), empirically true, 1948 Nakba and 57 years of occupation.

H(Palestinians), empirically true, continuous presence for centuries, millennia even.

By modus ponens,

∀x [P(x) ∧ H(x) → S(x)], P(Pal) ∧ H(Pal) ⊢ S(Palestinians)

But Zionism simultaneously asserts

_Pr_𝓏 . ¬S(Palestinians)

And there is the contradiction.

S(Palestinians) ∧ ¬S(Palestinians) ⊢ ⊥

⊥ is the logic notation for contradiction. A system that produces ⊥ is, by definition, inconsistent and collapses. This isn’t about morality or empathy. It’s about Zionism, as a universal principle, producing a formal contradiction.

A common counterargument. “The historical situation is different. The claims aren’t apple to apple.”

My response. That doesn’t refute the universalisability test. It proposes that P and H need to be redefined with additional conditions. But if you add conditions so that only Jews qualify, what you’re doing is ad-hoc modification. Adding extra assumptions not for logical reasons but to save a conclusion you wanted from the beginning. A principle that only works for one case isn’t a principle. It’s an exception in disguise.

Quod erat demonstrandum.

III.

Two-State. Many Assumptions, Thin Probability.

The strongest version. “Even if infrastructure is entangled, political separation can be done in stages. Look at Czechoslovakia, which split into the Czech Republic and Slovakia in 1993 without bloodshed.” That precedent is real and often invoked.

My response. The Velvet Divorce worked because two conditions existed there that don’t exist here. Both sides actively wanted separation, AND there was no population of 700,000 illegal settlers from one side already embedded inside the other side’s territory. Without those two conditions, the Czechoslovakia analogy collapses.

The Compounding Assumptions Problem

Occam’s Razor gives us a tool. Between two hypotheses that can both explain reality, pick the one that requires fewer assumptions.

Not because the simple one is always right, but because every additional assumption is another source of error.

The two-state solution requires all of the following assumptions to hold simultaneously.

• A₁. The more than 700,000 illegal Israeli settlers in the West Bank can be relocated, or can accept Palestinian citizenship, peacefully.

• A₂. The water systems, road network, and electric grid that have been entangled for 57 years can be logistically disentangled.

• A₃. Gaza (under Hamas) and the West Bank (under Fatah) can function as one coherent state entity.

• A₄. Two separate economies can stand on their own without sabotaging each other during the transition.

• A₅. There is enough political will on both sides to execute all of the above simultaneously.

Even if we are generous and assign each assumption a 70% success probability (which is already very optimistic), the cumulative probability of all of them holding together is

P(two-state succeeds) = 0.7⁵ = 0.168 ≈ 17%

Intuitively people calculate this as 0.7⁵ = 17%, but that contains a statistical error. It assumes A₁ through A₅ are independent, when in fact they are positively correlated. A more precise framing.

Borrowing Taleb, every assumption above is a single point of failure. Picture a chain with five critical links. You don’t need all of them to break for failure. One is enough. And if you ask which link is weakest, A₁ alone is sufficient. More than 700,000 illegal Israeli settlers already have roads, water, electricity, and internet integrated into the Israeli system. This is no longer a question of political will. This is an infrastructure problem. There is no precedent in modern history where a settlement this complex and this large has been peacefully disentangled.

Formally, define S as the event “two-state succeeds”. So

S ≡ A₁ ∧ A₂ ∧ A₃ ∧ A₄ ∧ A₅

This is a conjunctive necessary condition. All assumptions have to hold simultaneously. Which means

¬Aᵢ ⊢ ¬S for any i ∈ {1,2,3,4,5}

Every Aᵢ is a necessary condition. Failure of any one is sufficient to fail the whole. This isn’t probability multiplication. It’s a much stricter logical condition. You don’t even need to know the probability of each. You only need to show that one condition isn’t met, and the argument is finished.

And for A₁, relocating or integrating 700,000 embedded settlers is a condition that, by all available historical base rates, has never been successfully done in a comparable context.

∴ ¬A₁

∴ ¬S.

This isn’t ideological pessimism. It’s basic base-rate thinking, plus a formal proof.

But, the Confederation Model?

Meaning two sovereign states with shared institutions and open borders. This is often proposed as a fourth alternative. Functionally, a confederation with sufficiently deep shared institutions is a one-state with extra bureaucratic layers. If the institutions are weak enough to preserve full sovereignty, we are back to two-state with all the same failure modes. A confederation isn’t a stable midpoint. As far as I can see, it’s an unstable equilibrium that converges to one of the two endpoints. The disjunction remains exhaustive.

IV.

This is the part I’m most nervous about, and you might also be worried about me. That I sound like someone who got too excited about game theory and forgot that real people are losing their families on the ground. That I have no skin in the game.

I’m aware of that. I feel sad. I’m doing what I can. And it’s precisely because of that that I think structural analysis like this matters. Not to replace empathy, but to explain why empathy alone is not enough.

People on both sides of this conflict don’t refuse peace. The problem is that the system doesn’t give them room for it. That is what has to change.

Borrowing a phrase Scott Alexander uses often at SSC / ACX, we are stuck inside the Moloch trap. In game theory we call it the multipolar trap.

Iterated Prisoner’s Dilemma

The current situation, at least as I read it, can be modelled fairly accurately as an Iterated Prisoner’s Dilemma, one of the most powerful frameworks in game theory.

The setup. Two players. Two choices (cooperate or defect). The payoff matrix looks roughly like this.

The numbers represent utility. The higher the better. The ideal outcome for both sides is (3, 3), both cooperate, both win. But look at the structure.

Whatever B does, A is always better off defecting. If B cooperates, A gets 5 (defect) versus 3 (cooperate). If B defects, A gets 1 (defect) versus 0 (cooperate). Defect always dominates cooperate. This is what game theory calls a dominant strategy.

Because the logic is symmetric for both sides, the Nash equilibrium sits at (1, 1). Both sides keep defecting. Both sides keep losing. Not because they are stupid or evil, but because that’s the rational response to the present incentive structure.

This is, I think, fairly close to where Israel and Palestine sit today. Reduced to its skeleton, violence and repression are the dominant strategy not because either side “doesn’t want peace”, but because under the current game, unilateral cooperation means existential vulnerability.

One-State Changes the Game Itself

The solution isn’t to persuade the players to “be nicer”. The solution is to change the structure of the payoff matrix itself.

One-state does precisely that. When both groups become a single legal-constitutional entity, the incentive structure changes fundamentally.

Economic sabotage against the other group becomes sabotage against yourself, because they are now inside the same tax network, supply chain, and labour market.

Political extremism becomes electorally irrational. To win a parliamentary majority, every party has to win cross-ethnic votes. The system forces moderation through self-interest, not through moral persuasion.

Terrorism loses its rational calculus, because target and perpetrator now sit inside the same legal and economic system. The blowback is symmetric.

In incentive design, this is called preference alignment. The system is deliberately structured so that individual interests automatically line up with collective ones. The principle is the same as giving directors call options so that their interests align with the company’s.

The result is what I’d call Mutual Assured Construction. Like Mutual Assured Destruction but reversed. Not “if you collapse I collapse so we don’t fight”, but “if you rise I rise, so we have a reason to cooperate”.

V.

Demographics Are a Likelihood, Not an Opinion

Bayesian reasoning, at the most basic level, goes like this. You have a prior belief. You update that belief based on the likelihood of incoming data.

Our prior. “An ethno-state can be sustained in the long run.”

The likelihood from the demographic data. A 50/50 population with the Palestinian Arab growth rate consistently higher. Which means every decade that passes, sustaining the ethno-state requires increasingly intense repression. The trend is monotonically increasing. There is no natural reversal point without extreme intervention.

Posterior belief after the update. The probability that an ethno-state can be sustained in the long run without apartheid or ethnic cleansing is very low, close to zero.

De Facto Reality on the Ground

The 700,000-plus Israeli settlers in the West Bank are not a political figure. They are an infrastructure reality. Roads, water systems, electric grid, internet in the West Bank have all been integrated into the Israeli system. Physically, the de facto one-state has existed for several decades. What’s missing is only the de jure version. The formal legal and constitutional recognition.

The two-state solution isn’t continuing the status quo. It’s reversing a reality that has already taken shape. The probability of reversing infrastructure this complex in the current political climate, even after being generous, is close to zero, as calculated above.

Historical Base Rate

The two cases I find most relevant are these.

South Africa (1994). The transition from an apartheid ethno-state to a democratic one-state proved that constitutional integration can stop an existential conflict. Was the outcome perfect? Honestly, far from it. Economic inequality is still massive, crime rates are high, and several indicators show a concerning state fragility. But the point stands.

Northern Ireland, the Good Friday Agreement (1998). A conflict between Catholic-Nationalists and Protestant-Unionists that had run for centuries was resolved not by physical separation of territory but by constitutional power-sharing. Legally guaranteed distribution of power. Identity conflict, it turned out, is far more effectively resolved by institutional integration than by geographic partition.

Historical base rate. Democratic-integration models have a better track record at stopping existential conflict than partition does. Not a guarantee, but in the Bayesian sense, a strong prior.

VI.

Boundary Conditions, So It Doesn’t Become Yugoslavia 2.0

One-state isn’t a silver bullet that automatically works. If you’ve taken chemistry, you know that a reaction requires certain conditions to run. There are hard constraints that, if violated, will make the system collapse into another version of the same conflict.

One. A Super-Rigid Secular Constitution.

Religion and ethnicity have to be completely decoupled from political rights. Not “a state that is tolerant of religion”, but a state that is constitutionally blind to ethnic and religious identity when it comes to civil, political, and property rights. This is non-negotiable. Without it, any demographic majority will dominate the minority, and we are back to a zero-sum game.

Two. The Integrated State’s Monopoly on Violence.

Joint security forces. Mixed-composition military and police. Ideally with third-party international oversight for the first one to two decades, or at minimum a commissioner-like oversight board. A power vacuum during the transition is the most dangerous condition, because it will be filled by the most extreme actors from both sides.

Three. Convert Historical Conflict into Economic Language.

The right of return for Palestinian refugees, if interpreted as mass physical relocation, creates a new zero-sum game identical to the one we are trying to fix. The solution is to convert it into economic language. Economic property reparations. Documented financial compensation, not a fresh round of displacement that would trigger the next cycle. This turns identity conflict into a finite, solvable transaction.

But What About Lebanon?

A very fair question. Lebanon, constitutionally, looks similar on the surface to what I’m proposing. Multi-community, one state, power-sharing. The result? Fifteen years of civil war, repeated state collapse, and a very fragile present.

But this isn’t a counterargument to one-state. It’s empirical evidence that boundary condition one above isn’t optional.

Lebanon failed not because it was a one-state, but because its confessionalism codifies sectarian identity directly into the constitution. Parliamentary seats are divided by religion. Executive positions are divided by ethnicity. Permanently and rigidly. That isn’t a secular one-state. That’s a one-state whose architecture actively amplifies communal identity as the basis of power. The opposite of what I’m arguing.

Lebanon isn’t a refutation of one-state. Lebanon is a case study of what happens when boundary condition one is violated. It strengthens the argument, not the other way around.

VII.

The Transition Problem

I want to be fully honest here. This might be the most important game-theoretic question of all. In an Iterated Prisoner’s Dilemma, the transition period is when both sides have maximum incentive to defect. Precisely before the new system locks in and changes the payoff matrix. Before constitutional guarantees feel real, before joint security forces have built authority, and before economic integration has produced enough mutual dependency. That window is the most dangerous one.

I’m not going to pretend I have the technical blueprint. But there is one thing that is logically necessary from the game-theory analysis above. The transition period requires an external enforcement mechanism. Not to rule, but to act as a commitment device that makes defection too costly during that window. A UN mandate, an international guarantor, or a similar structure with a specific and time-limited mandate.

This isn’t an argument against one-state. It’s an argument about how, not whether. And it’s exactly the issue boundary condition two above is written to address. I openly admit this is the weakest point of the argument on the implementation side. But a weakness in implementation isn’t an argument that another option is better, especially when those other options have already been shown to be structurally infeasible.

VIII.

One-state is often called utopian by both sides at once. Or too “anti-Zionist” from the Israeli and Western side. That framing misses the point of the argument.

To restate it. This isn’t a moral argument. It’s a process of elimination.

A priori. The ethno-state fails the universalisability test and breaks the principle of sustainable systems. The two-state solution fails on the compounding probability of too many assumptions that must hold at once. The Israeli state as currently driven by the idea of Zionism is not antifragile, and it carries significant ruin risk.

A posteriori. A 50/50 demographic. More than 700,000 Israeli settlers embedded in the infrastructure. The historical base rates from South Africa and Northern Ireland. Everything points in the same direction.

If two options have already been eliminated logically and empirically, what’s left is the third option. Not because the third option is perfect, but because it’s the only one not structurally doomed from the start.

Maybe this is how peace actually works. Not because everyone suddenly becomes kind, but because the system is designed so that violence becomes irrational and cooperation becomes the only sensible move.

The maths here doesn’t require humans to love each other. The maths only ensures that destroying the other side means destroying yourself. And sometimes, that’s more than enough.

This is what’s called Disjunctive Syllogism.

(Exhaustive disjunction). E ∨ T ∨ O

where E = ethno-state, T = two-state, O = One-State Democratic Secular.

From Section II,

¬E. Proven. Cannot reach steady state. Generates ⊥ via universalisability.

From Section III,

¬T. Proven. ¬A₁ ⊢ ¬S. Infrastructure is not reversible.

By Disjunctive Syllogism,

E ∨ T ∨ O, ¬E, ¬T ⊢ O

This is a deductively valid inference. No probability, no induction required. If you accept the exhaustive disjunction premise and both negations, O follows necessarily.

Without class analysis. Without flipping the colonial-imperialist narrative. Without falsifying religious silliness. Without a moralising shouting match.

A One-State Democratic-Secular Palestine is the solution that, when analysed mathematically, does not collapse under the weight of its own assumptions.

If you want to reject this conclusion, and I am genuinely open to that because I might well be wrong, there are a few ways you can do it.

1. Show where my axiom is wrong.

2. Show that the disjunction isn’t exhaustive. Show another option I haven’t considered.

3. Show that ¬E or ¬T can be falsified. Show where my logic breaks.

4. Show a historical precedent in which an ethno-state with 50/50 demographics has been sustained in the long run without apartheid or ethnic cleansing.

I’m writing this as someone trying to think clearly, not as someone who thinks he is already right. If you can show a fundamental flaw in the argument, I’ll happily revise my position. That’s how thinking should work.