The Arithmetic of Power: How Democracy and Capitalism Breed Inequality by Mathematical Necessity

The Arithmetic of Power: How Democracy and Capitalism Breed Inequality by Mathematical Necessity

 

We live inside a profound paradox: democracy promises political equality—one person, one vote—while capitalism delivers economic inequality that compounds across generations. Thomas Piketty's landmark 2013 work revealed that this tension isn't accidental but structural, encoded in a simple inequality: r > g. When the return on capital outpaces economic growth, wealth concentrates not through moral failure but mathematical inevitability. The mid-twentieth century's "Great Leveling" was not capitalism's natural state but a historical aberration born of world wars and depression. Today, as growth slows globally, we drift toward what Piketty calls "patrimonial capitalism"—a society where inheritance matters more than effort, where the escalator of compound returns lifts the already-wealthy while laborers run in place. This article explores why inequality isn't a bug in our system but its default setting, why democratic majorities cannot vote it away, and whether any peaceful path exists to break capitalism's gravitational pull toward concentration without triggering the catastrophes that historically reset the scales.

 

The Unblinking Math: r > g and the Illusion of Meritocracy

At the heart of modern inequality lies an equation so simple it feels almost trivial: r > g. Yet this inequality—where the rate of return on capital (r) exceeds the growth rate of the economy (g)—contains the entire architecture of our stratified world. Piketty's exhaustive analysis of three centuries of tax records revealed that capital historically yields 4–5% annually, while economies grow at just 1–2%. "When the rate of return on capital significantly exceeds the growth rate of the economy," Piketty writes, "as it did through much of history until World War I, then it logically follows that inherited wealth grows faster than output and income." The consequence is brutal in its simplicity: money makes money faster than work makes money.

This dynamic creates what economist Branko Milanović calls "the elephant graph of global inequality"—where the global top 1% and emerging middle classes in Asia gain while Western working classes stagnate. The worker saving $10,000 annually faces a Sisyphean climb; the heir receiving $1 million watches passive income generate $50,000 yearly without lifting a finger. As political philosopher Michael Sandel observes, "We have moved from having a market economy to being a market society—where everything is up for sale, and nothing is sacred." The meritocratic promise that effort equals reward crumbles when capital's compounding power operates on a different temporal plane than human labor.

Dimension	Labor (Human Capital)	Capital (Financial Assets)
Time Horizon	Limited by lifespan (24 hours/day)	Operates continuously, across generations
Scalability	One task at a time (surgeon, coder, teacher)	Deployed globally simultaneously
Depreciation	Physical/cognitive decline with age	Appreciates through compounding (4–5% historically)
Risk Buffer	No safety net; paycheck-to-paycheck vulnerability	Diversified portfolios absorb shocks
Growth Rate	Tied to g (1–2% in mature economies)	Tied to r (4–5% historically stable)

Nobel laureate Joseph Stiglitz captures the stakes: "We've reached a new Gilded Age. The top 1 percent have seen their incomes rise by 275 percent, while the middle class has seen barely any increase at all." This isn't about individual virtue or vice—it's about systems. As Piketty notes with chilling precision: "The past devours the future." When returns on accumulated wealth outpace new creation, yesterday's fortunes eclipse today's innovations.

The Data Archaeology: Unearthing Capitalism's True Trajectory

Piketty's revolution wasn't theoretical—it was methodological. While predecessors like Simon Kuznets examined mere decades of data and concluded inequality naturally declines as economies mature (the "Kuznets Curve"), Piketty and his team spent fifteen years excavating centuries of fiscal archives. "We had to go back to the sources," Piketty explains, "to tax records, inheritance registers, national accounts—because surveys systematically undercount the wealth of the ultra-rich." This historical depth revealed the mid-twentieth century's equality wasn't capitalism's destiny but a statistical fluke.

Economic historian Emmanuel Saez, Piketty's longtime collaborator, emphasizes the breakthrough: "By constructing distributional national accounts that reconcile tax, survey, and national income data, we could see the full U-curve of inequality across two centuries." The graph tells a story textbooks obscured: extreme concentration in the Belle Époque (1870–1914), a dramatic plunge during 1914–1970, and a steep climb back toward Gilded Age levels since the 1980s. As historian Walter Scheidel notes in The Great Leveler, "The compression of incomes and wealth during the middle decades of the twentieth century was an aberration—a brief interlude made possible only by the massive shocks of two world wars, the Great Depression, and subsequent policy responses."

The World Inequality Database, born from this effort, now tracks wealth distribution across fifty nations. Its findings dismantle comforting myths. Economist Gabriel Zucman reveals: "In the United States, the top 0.1% now owns as much wealth as the entire bottom 90%—a concentration not seen since 1929." This isn't cyclical fluctuation but structural reversion. As Piketty states plainly: "When g is small, the slightest gap between r and g generates powerful, cumulative effects over time."

The Patrimonial Trap: When Inheritance Trumps Effort

We are returning to what Piketty terms "patrimonial capitalism"—a society resembling the worlds of Jane Austen or Honoré de Balzac, where marriage and birthright determine destiny more than talent or toil. In nineteenth-century France, inherited wealth constituted 80–90% of top fortunes; by 1970, it had fallen to 40%. Today, it's climbing back toward 60–70%. "The entrepreneur is gradually replaced by the rentier," Piketty warns. This shift transforms social mobility from an elevator into an escalator moving downward for most.

The mechanism is compound interest operating across generations. An heir receiving $2 million at age 25, earning 5% annually, accumulates $13.3 million by age 65 without working a single day. Meanwhile, a dual-income professional couple saving 15% of $150,000 annually would need forty years to reach that same threshold—assuming no medical emergencies, job losses, or childcare costs derail their trajectory. Sociologist Robert Putnam captures the human cost in Our Kids: "The opportunity gap between rich kids and poor kids has grown wider over the last few decades—not because poor kids are less talented, but because rich kids get so many more chances to develop their talents."

This isn't merely about luxury consumption. Inherited capital provides what economist Daron Acemoglu calls "optionality"—the freedom to take risks that build further advantage. The trust-fund intern can accept unpaid positions at elite firms; the first-generation graduate must take the highest-paying job immediately. As venture capitalist Paul Graham observed (before facing criticism for the implication): "The startup world is full of people whose parents could support them while they tried risky things." This safety net effect compounds advantage invisibly but powerfully.

Scenario	High-Growth Economy (g = 4%)	Low-Growth Economy (g = 1%)
Wage Growth	Rapid; new opportunities abundant	Stagnant; few new positions created
Capital Returns	4–5% (still outpaces wages slightly)	4–5% (dramatically outpaces wages)
Wealth-to-Income Ratio	Moderate (3–4x national income)	Extreme (6–7x national income)
Social Mobility	"Self-made" narratives plausible	Inheritance dominates life outcomes
Political Discourse	Focus on innovation and growth	Zero-sum battles over existing resources

The Democratic Paradox: Why Majority Rule Cannot Tax Away Inequality

If most citizens rely on wages rather than capital, why don't democratic majorities simply vote for confiscatory inheritance taxes? The answer reveals democracy's structural vulnerability to concentrated wealth. Political scientist Martin Gilens demonstrates empirically: "When the preferences of the affluent diverge from those of the middle class or poor, government policy almost always follows the affluent." This isn't conspiracy—it's arithmetic. Capital buys lobbying power, media influence, and legal expertise at scales labor cannot match.

Three mechanisms prevent democratic correction:

The Lottery Illusion: Most Americans believe they'll join the top 1% someday. Sociologist Dalton Conley notes: "Even people making $40,000 a year oppose estate taxes because they imagine their garage startup might make them billionaires." This aspirational identification with capital owners fractures class solidarity.

Capital Flight: In a globalized economy, wealth is mobile while voters are not. Economist Dani Rodrik explains the dilemma: "When capital is internationally mobile but political authority remains national, governments compete to offer capital the most favorable conditions—triggering a race to the bottom on taxation." France's 2012 wealth tax prompted an exodus of 12,000 millionaires; the tax was abandoned by 2017.

Regulatory Capture: As capital concentrates, it reshapes the rules governing itself. Legal scholar Zephyr Teachout documents how "the financial sector spends $2.50 on lobbying for every dollar it pays in taxes—ensuring regulations favor asset owners over wage earners." The result? Capital gains taxed at 20% while labor income faces 37% top rates—a policy choice masquerading as economic law.

Historian Quinn Slobodian reveals the deeper architecture: "Neoliberalism wasn't about freeing markets—it was about building international legal structures to protect capital from democratic interference." Trade agreements with investor-state dispute settlement mechanisms allow corporations to sue governments that enact policies threatening profits. Democracy becomes theater while capital writes the script.

The Growth Paradox: Why Stagnation Accelerates Inequality

Counterintuitively, slowing economic growth doesn't hurt the wealthy—it empowers them. When g falls while r remains stable at 4–5%, the gap r – g widens dramatically. In a 4% growth economy, capital's advantage is modest; in a 1% growth economy, asset owners pull away five times faster than the economy expands. As Piketty notes: "Low growth is not a solution to inequality—it is its primary cause in the twenty-first century."

This dynamic transforms society's structure. In high-growth eras, new fortunes emerge constantly—tech entrepreneurs, entertainment stars—creating narratives of mobility. In low-growth eras, the existing stock of wealth dominates the flow of new income. The capital-to-income ratio soars: in Britain and France, private wealth equaled 700% of national income in 1910, fell to 200–300% by 1970, and has climbed back to 500–600% today. Economist Atif Mian explains: "When the pie isn't growing, politics becomes zero-sum. The wealthy have both the incentive and resources to defend their slice aggressively."

The consequences permeate culture. Sociologist Wolfgang Streeck observes: "Capitalism is undergoing a prolonged crisis of stagnation, leading to what I call 'the purchase of time'—where elites use wealth to insulate themselves from systemic decay while the majority experiences declining prospects." This isn't merely economic—it's existential. When young people see homeownership, family formation, and retirement security receding beyond reach despite working harder than their parents, faith in democracy itself erodes. Political scientist Yascha Mounk documents the result: "Citizens who believe the system is rigged become susceptible to authoritarians who promise to smash the corrupt elite—even if those authoritarians destroy democracy in the process."

Marx Revisited: The Spreadsheet Meets the Manifesto

Piketty's empirical work provides what Marx lacked: two centuries of data confirming capital's gravitational pull toward concentration. Both thinkers identified the same engine—capital's capacity to accumulate faster than labor can reproduce itself. As Marx wrote in Capital: "Accumulate, accumulate! That is Moses and the prophets!" Piketty quantifies this imperative: when r > g, the capital/income ratio β = s/g (where s is the savings rate) inevitably rises, concentrating ownership.

Yet crucial divergences exist. Marx predicted capitalism's internal contradictions would trigger collapse as the profit rate fell toward zero. Piketty's data shows the opposite: r remains stubbornly stable at 4–5% across centuries and regimes. Rather than revolution, Piketty foresees "a slow drift toward oligarchy"—a rentier society where a small class lives off inherited returns while everyone else scrambles for wages. As economist Paul Mason notes: "Piketty gives us Marx without the eschatology—the diagnosis without the promised apocalypse."

Piketty also identifies a modern phenomenon Marx couldn't foresee: the "super-manager." In the United States particularly, the top 0.1% increasingly earns income through labor—CEO salaries, hedge fund fees, superstar compensation—rather than passive returns. Yet this distinction proves illusory. As Piketty demonstrates, these super-salaries quickly convert to capital: "A CEO earning $30 million annually doesn't consume it all; they invest the surplus, which then begins compounding at r." Within a generation, labor income merges back into the r > g cycle. The super-manager becomes the rentier.

Feature	Labor (Marx's Proletariat)	Capital (Bourgeoisie/Rentiers)
Reproducibility	High (training creates more workers)	Low (land, brands, networks are finite)
Mobility	Limited by borders, family, skills	High (digital assets move globally instantly)
Time Horizon	Short-term (must eat today)	Long-term (can wait decades for returns)
Bargaining Power	Diminished by labor surplus	Enhanced by capital scarcity
Market Structure	Competitive (wages suppressed)	Oligopolistic (returns protected)

Philosopher Slavoj Žižek captures the synthesis: "Piketty has done for inequality what climate scientists did for global warming—he transformed moral outrage into measurable, undeniable fact." Yet unlike climate change, the political mechanisms to address inequality remain fractured by the very concentration of power the data reveals.

The Unworkable Prescription: Why Global Wealth Taxes Remain Utopian

Piketty's proposed solution—a progressive global tax on wealth—faces what economist Kenneth Rogoff calls "the implementation chasm." The diagnosis (r > g) is empirically robust; the cure requires political coordination that may be impossible in a world of competing nation-states. Three obstacles prove particularly intractable:

Valuation Nightmares: Taxing wages is straightforward; taxing wealth is not. How do you value a family business with emotional significance but illiquid assets? A Picasso painting? Intellectual property registered in the Cayman Islands? Economist Gabriel Zucman acknowledges: "We'd need a global financial registry—a single database tracking every asset owned by every person on Earth. The privacy and sovereignty objections would be immense."

Capital Flight: Without perfect coordination, wealth taxes trigger exodus. When France implemented a 75% top income tax in 2012, Gérard Depardieu famously renounced citizenship for Russia. Economist Emmanuel Saez concedes: "A unilateral wealth tax is self-defeating. You need near-universal adoption—which requires trust between nations that simply doesn't exist."

Liquidity Traps: A farmer whose land appreciates to $10 million due to suburban sprawl may earn only $50,000 annually from crops. A 2% wealth tax ($200,000) forces asset liquidation—not because the farmer is wealthy in cash flow, but because the tax system mistakes paper gains for spendable income. As legal scholar Rebecca Kysar notes: "Wealth taxes risk becoming poverty traps for asset-rich, cash-poor households."

Critics like economist Larry Summers dismiss the proposal as "well-intentioned but naive." Piketty himself admits it's "politically utopian" presently. Yet he insists the alternative—accepting patrimonial capitalism—is morally indefensible. The debate exposes a deeper tension: is wealth taxation redistribution (taking from some to give to others) or reallocation (preventing dangerous concentration)? As political theorist Corey Robin argues: "The question isn't whether the state intervenes—it always does. The question is whose interests that intervention serves."

Scheidel's Horsemen: The Catastrophic History of Leveling

If peaceful democratic means cannot reduce inequality, how has it ever fallen? Historian Walter Scheidel's The Great Leveler delivers a sobering answer: only through catastrophe. Analyzing millennia of data across civilizations, Scheidel identifies four "horsemen" that reliably compress inequality:

Mass-Mobilization Warfare: World Wars I and II destroyed physical capital across Europe, while conscription created political pressure for veterans' benefits and progressive taxation. Top marginal rates exceeded 90% in the U.S. and UK during WWII—not from socialist ideology but fiscal necessity.

Transformative Revolution: The Bolshevik Revolution, Mao's China, and Castro's Cuba achieved radical equality through expropriation and terror. As Scheidel notes dryly: "Violent leveling is effective but comes with enormous human costs."

State Collapse: When Rome fell, inequality plummeted—not because peasants prospered, but because elites lost everything. Everyone became equally poor.

Lethal Pandemics: The Black Death killed 30–50% of Europe's population, creating labor scarcity that empowered survivors to demand higher wages. Landlords' wealth collapsed as land lost value without tenants.

Scheidel's conclusion is stark: "Throughout recorded history, the only way to substantially reduce inequality has been through violent shocks." Peaceful reforms—land redistribution, education expansion, progressive taxation—produce marginal improvements at best. This challenges liberal optimism at its core. As political scientist Francis Fukuyama admits: "We hoped history had ended with liberal democracy's triumph. But if inequality inevitably rises without catastrophe, perhaps history hasn't ended—it's just entered a new, more dangerous phase."

The Realist's Dilemma: Managing Inequality as Systemic Risk

If inequality is capitalism's default state and only catastrophe resets it, what should policy aim for? The emerging consensus among pragmatic economists isn't utopian equality but what political scientist Jacob Hacker calls "risk mitigation." Inequality itself isn't the problem—it's inequality's destabilizing effects: eroded social trust, political polarization, and economic stagnation as the middle class loses purchasing power.

This reframes policy as engineering rather than morality. Economist Thomas Philippon argues: "We don't need to eliminate r > g—we need to build institutional shock absorbers that prevent its consequences from triggering system failure." Three strategies show promise:

Pre-distribution over Redistribution: Rather than taxing wealth after concentration occurs, reshape markets to generate more equitable outcomes initially. Antitrust enforcement prevents monopoly rents that inflate r. As Lina Khan, chair of the FTC, argues: "Market structure determines who captures value. Breaking up dominant platforms forces capital to compete, lowering returns toward g."

Human Capital Investment: The only sustainable way to raise g is through education and health. Economist Claudia Goldin demonstrates that "countries investing in universal early childhood education see both higher growth rates and lower intergenerational inequality." When labor becomes scarce and highly skilled, its bargaining power rises—narrowing r – g.

Institutional Buffers: Compare the United States and Denmark—both capitalist democracies subject to r > g, yet with vastly different inequality outcomes. Denmark's combination of strong unions, portable benefits, and active labor market policies creates what sociologist Gøsta Esping-Andersen calls "social investment"—not handouts but capabilities that let workers capture more value. The result? Top 1% income share is 18% in the U.S. versus 6% in Denmark.

Country	Top 1% Income Share	Wealth Tax?	Union Density	Public Services	Intergenerational Elasticity*
United States	20%	No	10%	Limited	0.50 (Low mobility)
United Kingdom	14%	No (abolished 2006)	23%	Moderate	0.45
Germany	12%	No	18%	Strong	0.32
Denmark	6%	Yes (0.7%)	67%	Universal	0.15 (High mobility)
Sweden	7%	Yes (0.4%)	64%	Universal	0.20

*Intergenerational elasticity measures how much parents' income predicts children's income (0 = perfect mobility, 1 = none)

The goal isn't eliminating inequality—it's keeping it within bounds that preserve social cohesion. As political economist Daron Acemoglu warns: "When the top 1% captures most growth while the bottom 50% stagnates, you create the conditions for populism, xenophobia, and democratic backsliding." Managing inequality becomes national security.

The Iron Law of Oligarchy: Why Every System Concentrates Power

Sociologist Robert Michels' 1911 "Iron Law of Oligarchy" predicted this impasse: in any complex organization, power concentrates among a few who then manipulate rules to preserve advantage. This applies equally to democracies and autocracies—just through different mechanisms. In market democracies, capital buys influence; in autocracies, proximity to the ruler determines privilege. As political scientist Jeffrey Winters documents in Oligarchy, "The wealthy have always found ways to translate economic power into political protection—whether through campaign donations, lobbying, or, in premodern times, private armies."

The feedback loop is self-reinforcing. Rising r generates wealth concentration → concentrated wealth captures political institutions → captured institutions enact policies (tax cuts, deregulation) that further increase r → repeat. Economist Luigi Zingales calls this "the revolt of the elites"—where those benefiting from globalization actively undermine the institutions (unions, public education) that once moderated capitalism's excesses.

Even communism proved no escape. As historian Stephen Kotkin observes of the Soviet Union: "The abolition of private property didn't eliminate inequality—it transformed it from wealth-based to power-based. The nomenklatura enjoyed dachas, special stores, and healthcare unavailable to ordinary citizens." Autocracy trades a wealth gap for a privilege gap—often more rigid because political loyalty, unlike capital, cannot be earned through market activity.

This reveals a deeper truth: hierarchy may be unavoidable in complex societies. The critical question isn't whether inequality exists—it's whether positions at the top circulate or ossify. Piketty's true fear isn't wealth concentration per se but patrimonial concentration—where the same families remain on top for centuries. As political theorist Daniel Markovits argues in The Meritocracy Trap: "When elites reproduce themselves across generations through inheritance and exclusive institutions, they transform temporary advantage into permanent caste."

Reflection

We stand at a crossroads defined not by moral failure but by mathematical inevitability. Piketty's r > g is not a call to revolution but a diagnosis of capitalism's gravitational constant—a force as real as gravity itself. The mid-twentieth century's equality was not the system's natural state but a historical accident born of unprecedented destruction. Today, as growth slows globally and capital compounds across generations, we drift toward a world where birth determines destiny more than effort—a reality our meritocratic myths cannot obscure.

Yet fatalism is unwarranted. History shows that while inequality's trend may be structural, its slope is political. The United States and Denmark both operate under r > g, yet produce vastly different societies through institutional choices: unions, inheritance rules, education investment. These don't abolish inequality—they build friction against its most destabilizing effects. The goal isn't utopian equality but what political economist Robert Reich calls "a moral minimum"—ensuring that even in an unequal society, everyone has healthcare, education, housing security, and meaningful work.

The deeper challenge is geopolitical. Capital's mobility has outpaced democracy's reach, creating what sociologist Saskia Sassen terms "expulsions"—where global elites operate beyond any single nation's regulatory grasp. Solving this requires either unprecedented international cooperation (a global wealth registry, coordinated tax floors) or re-embedding markets within democratic control through capital controls and production reshoring. Neither path is easy, but the alternative—accepting patrimonial capitalism as inevitable—guarantees the very instability Scheidel's horsemen represent.

Ultimately, democracy's purpose isn't to achieve equality but to manage inequality's tensions so catastrophe remains unnecessary. As Piketty himself concludes: "The history of inequality is political, not economic. When we choose to act, we can bend the arc." The arithmetic of power is real, but so is human agency. Our task isn't to repeal r > g—that's impossible—but to build societies resilient enough that its consequences don't tear us apart. The alternative isn't stability—it's the slow-motion collapse that precedes the horsemen's arrival.

References

Piketty, T. (2014). Capital in the Twenty-First Century. Harvard University Press.

Scheidel, W. (2017). The Great Leveler: Violence and the History of Inequality from the Stone Age to the Twenty-First Century. Princeton University Press.

Saez, E., & Zucman, G. (2019). The Triumph of Injustice: How the Rich Dodge Taxes and How to Make Them Pay. W.W. Norton.

Milanović, B. (2016). Global Inequality: A New Approach for the Age of Globalization. Harvard University Press.

Stiglitz, J. (2012). The Price of Inequality: How Today's Divided Society Endangers Our Future. W.W. Norton.

Gilens, M. (2012). Affluence and Influence: Economic Inequality and Political Power in America. Princeton University Press.

Acemoglu, D., & Robinson, J. (2019). The Narrow Corridor: States, Societies, and the Fate of Liberty. Penguin.

Piketty, T., et al. (2022). World Inequality Report 2022. World Inequality Lab.

Hacker, J., & Pierson, P. (2010). Winner-Take-All Politics: How Washington Made the Rich Richer—and Turned Its Back on the Middle Class. Simon & Schuster.

Winters, J. (2011). Oligarchy. Cambridge University Press.