The hidden mathematics behind Mamdani's victory

When Zohran Mamdani won the race for New York City mayor on 4 November, commentators immediately constructed their narratives. The most popular: voters punished Trump, who sits at 37% approval with a record 36-day government shutdown. The alternative narrative, slightly more sophisticated: people are so desperate that when centrism doesn't work and right-wing extremism doesn't either, they try the opposite extreme out of pure frustration.

Both stories look at psychology where there's pure mathematics. Both miss the structural mechanism operating beneath the surface.

Here's why they're wrong. The same day, in the same national political climate, two moderates won in Virginia and New Jersey: Abigail Spanberger and Mikie Sherrill. Former CIA and Navy respectively, classic centrists of the Democratic Party, they beat their opponents with campaigns focused on pragmatism and competence. Identical national context: unpopular Trump, government shutdown, widespread frustration. Yet in New York the democratic socialist wins with the most radical platform seen in decades, whilst Virginia and New Jersey elect precisely the type of reassuring moderates who normally win when you punish a chaotic incumbent.

The explanation cannot be psychological. If it were emotional desperation, we'd see the same pattern everywhere. If it were simply anti-Trump reaction, the three states would have produced similar results. Instead there's a sharp divergence that requires a structural explanation.

The invisible threshold

The difference lies in a number nobody is looking at carefully. In New York City, the median rent for a flat is $3,400 per month. The median household income is $6,640. Do the maths: 51% of monthly income goes to housing before paying for food, transport, healthcare, or anything else.

In Virginia and New Jersey, the rent-to-income ratio hovers around 30%. It's high, certainly. It's a significant burden. But it's fundamentally different from 51%.

There exists a mathematical threshold, somewhere around 50%, where the nature of rational choices available to voters changes completely. When you cross that threshold, political optimisation becomes binary rather than gradual.

For the median New York household, a permanent rent freeze is worth $1,700 per month in potential savings. That's 25% of total income. It's more than any politically conceivable tax cut. It's more than any realistic wage increase a mayor could produce during their term. It's more than any combination of incremental policies a moderate could promise.

At that point, what appears extreme from the outside becomes mathematically rational from within. You're not voting ideology or making a political statement. You're solving a survival equation where incremental change physically cannot shift the needle enough to make a difference in your daily life.

This is rational choice theory applied correctly. When the payoff from a policy is so asymmetric, when a single intervention can return a quarter of your income, optimisation becomes simple. The risk that the policy won't work perfectly, or will have negative long-term consequences, is heavily discounted because the alternative, continuing at 51%, is already unsustainable.

The empirical verification

If this mechanism is real, we should see it replicate in other cities with similar housing burdens. And indeed we do.

Miami has a rent-to-income ratio of 54.9%, the highest in the country. Miami's housing politics is dominated by increasingly radical proposals. San Francisco, with rents requiring 45% of income for rental and up to 78% for ownership, has seen the most aggressive housing policies emerge in California. Los Angeles, at 53% for ownership, same dynamic.

At the other end of the spectrum, Wichita Kansas has a ratio of 19.5%. Local politics is dominated by pragmatic moderates. Nobody talks about rent freezes or municipal grocery shops. Incremental policies work perfectly well when the underlying problem is manageable with marginal adjustments.

The pattern holds across different geographies, different political contexts, different demographic compositions. It's not a New York anomaly. It's a systemic mechanism with a precise, replicable threshold.

The disturbing historical analogies

Based on historical precedents, we know exactly what will happen in New York over the coming years. Because this experiment has been run before, multiple times, with consistent results.

New York City in the 1970s is the closest example. Massive rent control, political promises of affordable housing for all, anti-landlord rhetoric. The result was that developers completely stopped building new units. Why invest capital in an asset where you cannot adjust prices to real costs? The shortage dramatically worsened. Landlords, unable to cover rising maintenance costs with frozen rents, stopped maintaining buildings. Some abandoned them entirely. The South Bronx burnt, literally, because some landlords found fire insurance more profitable than continuing to operate at a loss.

The city decayed physically whilst the policies remained politically popular, because anyone inside a rent-controlled flat held onto it like family patrimony. A two-tier market emerged: insiders with 1960s rents and outsiders paying stratospheric prices for the few available units, or simply leaving the city.

Vienna in the 1920s tried something similar with Red Vienna, massive construction of public housing financed by taxes on the wealthy. It worked better than New York because the state actually built tens of thousands of units, but still created massive market distortions and eventually collapsed under the fiscal weight and political tensions it generated.

More recently, Berlin tried a rent freeze in 2020. It lasted exactly 15 months before the Constitutional Court declared it unconstitutional. In those 15 months, new construction collapsed, landlords withdrew units from the market, and the shortage worsened. When the freeze was removed, rents exploded even faster than before to compensate.

Seventy years of evidence across different countries say the same thing: rent control worsens the shortage in the long term. It's one of the few points on which economists of left and right agree. But here lies the systemic paradox.

The long-term paradox

When you're at 51% of income on housing, the long term simply doesn't exist as an operational concept. Only surviving this month exists, then the next, then the one after. The prospect that in five years the shortage will be worse is completely irrelevant if in three months you can't pay rent and end up on the street.

This creates a systemic trap that no amount of policy wisdom can easily resolve. Voters are making the rational choice given their time horizon. Developers are making the rational choice given theirs. The system produces an equilibrium where everyone optimises locally but the aggregate outcome is terrible for all.

Mamdani probably knows that the rent freeze will produce long-term problems. He's a sophisticated enough assemblymember to have read the literature. But he also knows that the voters who elected him don't have the luxury of thinking long term. And he knows that the policies that would work long term—market liberalisation plus massive construction of new supply—take years to produce effects whilst people are suffering now.

So he chooses the policy that's politically viable, even knowing it's economically problematic. Not out of cynicism but from realistic assessment of the system's constraints.

The implications for other cities

The threshold effect we've seen in New York will change American urban politics over the coming years. Not because socialism is becoming more popular in the abstract, but because more and more cities are crossing that 50% threshold where the mathematics changes.

San Francisco, Los Angeles, Miami, Seattle, Boston, Washington. All these cities are approaching or have already crossed the critical threshold. We should expect to see Mamdani-style candidates emerge in all these cities in coming electoral cycles. Not because ideology is spreading, but because the underlying economic mechanism is replicating.

Moderates trying to win in these cities with incremental platforms are bringing the proverbial knife to a mathematical gunfight. You cannot win by offering 5% improvement when the median voter needs 25% to breathe again.

Where conventional analysis fails

Don't expect moderates to compete in cities with housing burdens beyond 50% without offering equally radical interventions on the specific housing issue. The mathematics simply doesn't work. You can be moderate on everything else, but on housing you must offer relief commensurate with the pressure.

Don't confuse rational economic desperation with genuine ideological preference for socialism. Mamdani didn't win because New York became a socialist city. He won because he offered the mathematically most efficient solution to a mathematical problem. If tomorrow a Republican offered a credible way to bring the rent burden from 51% back to 30%, they'd win too.

Don't expect Mamdani's policies to work in the traditional economic sense. They'll probably worsen the shortage long term. But expect them to remain politically popular even when their negative effects become evident, because the alternative, returning to 51%, remains mathematically unsustainable for voters.

And above all, don't think this pattern is a New York anomaly or exceptionalism. It's a systemic mechanism that will replicate in every context where basic costs exceed that critical threshold. It's not a question of political culture or ideological tradition. It's arithmetic under pressure.

On 4 November in New York, an ideology didn't win. An equation did.