Economically, America’s most prosperous regions are more dominant than ever. Politically, they’re not.

Amazon divided its second headquarters evenly among what are likely the two most powerful urban areas in the U.S. It seems like yet more evidence that the economy’s rush to agglomeration will reduce the nation to a hollow core of “American carnage," as famously described by President Trump in his inaugural address, flanked by space-age big cities on the two coasts.

But that vision collides head-on with an alternative view. A centuries-old political compromise has ensured America’s elite cities and the densely populated states around them are getting increasingly less say in how the nation is governed.

Their economic success is leading to diluted political power in the Senate, where two seats are given to each state regardless of population, and in the electoral college, where votes are based on a state’s representation in the Senate and House of Representatives.

Others have explained the economics of why companies such as Google, Apple and Amazon, whose founder and CEO, Jeffrey P. Bezos, owns The Washington Post, prefer to expand into cities which are already economic superstars. But how does that square with the electoral impact of concentrating American professionals in just a few urban areas?

Unlike the U.S. economy, the U.S. political system penalizes growth. The effect is easiest to see at the state level, where senators are selected. Commerce Department figures show that the five largest states have less representation — relative to the national average — than at any other time on record. Comparable figures begin in 1968.

As Silicon Valley corporations rose to dominate the national conversation, senators in California gained well over 600,000 constituents in a typical two-year span. That’s more than senators in Vermont or Wyoming represent, total.

In 2015 and 2016, the most populous states also accounted for the highest share of the nation’s income on record. And their collective income, which we’re using as a proxy for household economic output, has grown faster than income in any other decile of states since the Great Recession.

There is a similar but smaller effect in the House. Seats there are reallocated once a decade, and tend to lag population growth. The electoral college reflects both chambers.

Clara Hendrickson, who studies governance at the nonpartisan Brookings Institution and helped author a new report on regional economic inequality, described a “troubling imbalance between the places that enjoy economic power and the places that enjoy political power.”

“Coming out of the 2016 election, the debate has focused on whether forces of economic anxiety or cultural anxiety have contributed more to Trump support,” she said. “And I think regional inequality is an important part of that debate. It reflects both economic and cultural divides.”

But, she said, “If we go too far to pursuing a political solution which tries to give more power to the regions that are winning in today’s economy, we’re discounting our obligations to people who today live in economically underperforming regions.”

In a recent paper in the Cambridge Journal of Regions, Economy and Society, Jason Spicer, now of the University of Toronto, observes that the flow of people from rust-belt states interacted with the state-level winner-take-all electoral system to give older, whiter voters outsize influence in the 2016 election. This type of government allows regional inequality to build up to higher levels than in countries with proportional representation, Spicer said.

“It is no accident that the first and most powerful shocks of the backlash to neoliberal globalization came in the U.S. (Trump) and the U.K. (Brexit),” two countries with winner-take-all elections, Spicer said via email.

“We shouldn’t gloss over that the emerging knowledge economy is inherently an urban one,” said Mark Muro, a senior fellow at Brookings. “That accentuates the stresses of the founding fathers’ system.”

“We’ve never been here before,” Muro said. “We’ve never had a digitally oriented, agglomeration-driven economy.” The political side effects, he said, “are becoming an impediment to efficient economic growth.”

In 2016, the most recent year covered by the Commerce Department, the five biggest metro areas by population were in the five largest states: California, Texas, Florida, New York and Illinois. Voters in the sixth-largest metro, D.C., are under-represented in national politics.

The country’s most economically important cities aren’t even guaranteed to determine their state’s national representatives. Sen Ted Cruz (R-Tex.) won the state’s contested Senate seat by a 2.6-percentage-point margin earlier this month, despite heavy support for Democrat Beto O’Rourke in Dallas and Houston, two of the largest cities in the country.

The stellar election maps from the Post’s graphics and engineering teams show a similar pattern in another large state, Florida, though the outcome of the Senate contest between Republican Rick Scott and Democrat Bill Nelson remains unclear.

To be sure, there are ways to convert economic strength into political influence. “Most campaign contributions come from the major urban areas,” according to the Center for Responsive Politics. Residents of large cities flex their muscles through political spending, lobbying and positions in the Federal bureaucracy.

There are plenty of exceptions on both sides. Some small states thrive while some large ones flail. We’ve simplified things here to illustrate the paradox at the heart of the country’s economic bifurcation.

The real tension is between regional inequality and a functioning democratic system, Hendrickson said. “Ensuring the health of American democracy might depend on achieving a certain level of geographic cohesion.”