First, a review of the claims that Tony Hsieh and Zappos make about density:

CREATE RESIDENTIAL DENSITY OF GREATER THAN 100 PEOPLE PER ACRE.

When people live closely with one another, the opportunities to interact serendipitously increase which increases the sharing of knowledge, ideas, and improves productivity.

ADD DENSITY OF GROUND LEVEL ACTIVITIES, SPACES, AND BUSINESSES.

Urban residential density of at least 100 people per acre combined with ground-level gathering places such as cafes, interesting small businesses, and public spaces increases economic output and happiness. ...

... URBAN DEVELOPMENT

Inspired by the book Triumph of the City and thinkers like Richard Florida, we aim to create a dense urban core with residential density of at least 100 people per acre and ample ground level spaces to gather. Interlaced in every project we envision is a respect for the environment, opportunities to connect with nature, and connectivity infrastructure that reduces the need to use a car.

Our primary goal is to help to create an environment that encourages serendipity…the opportunity to unexpectedly collide with people from different backgrounds. Serendipity encourages people to connect with each other, exchange ideas, and accelerates learning. This means that a community must remain accessible to people from all economic backgrounds.

A truly great city must not only be financially sustainable, but also environmentally sustainable. With that in mind, we're planning green roofs, urban gardens and parks to enrich the lives of the passionate people who call Downtown home.

Connectivity is key to sustaining a vibrant community, so we're partnering with the Regional Transportation Commission and others to make it easier to walk, bike, and take public transit—building a community where people can live, work, and play without needing a car.

Emphasis added. Greater density will improve productivity and enhance innovation. Thus, Las Vegas will be financially sustainable. As for the issue of environmental sustainability, there are placemaking and transit oriented development. Note the disconnect between greater density and environmental sustainability.

Now turn from Las Vegas to San Francisco:

A visit to San Francisco over the past few days really crystalized in my head the important distinction between increased efficiency in the allocation of resources and fundamental innovation. Either can produce economic growth, but in the long-term it's the latter that matters most of all. But while conventional economics has a lot to teach us about efficiency I don't think economists really know much about innovation and they end up doing the world a disservice—and ultimately discrediting their own mastery of the subject they really do know—by confusing the two.

San Francisco is a hotbed of inefficiency and what any economically literate person would recognize as bad public policy. In the Tenderloin District, for example, you have huge swathes of what's got to be some of the most valuable land in the country occupied by low-income individuals living in dilapidated structures. A more sensible policy paradigm would allow the replacement of those structures by bigger, nicer, more modern, denser structures and by doing so would unleash a quantity of financial wealth that's more than adequate to pay off the beneficiaries of current rent control policies. The much bigger and denser San Francisco of the future would make California in particular and the United States in general a much more prosperous place by using market forces to better allocate scarce land.

That said, while San Francisco is a hotbed of inefficiency it's also a hotbed of real innovation. The corridor that starts in San Francisco and runs down to San Jose is the premiere cluster of technological innovation in the world and has been for some time. Digital technology has given us tools that are impressive in their own right, and its influence is spreading wide day by day. And in the long run, this is where prosperity comes from. New technologies are developed and diffused and they create high living standards wherever they go.

Emphasis added. Well said, Matthew Yglesias. Greater density promotes the more efficient allocation of urban land. The result is more prosperity. Along those lines, an economist such as Matthew Kahn might highlight how greater density promotes environmental sustainability. Without a doubt, there are all kinds of benefits from greater density.

We confuse efficiency and innovation, thus confusing the discussion about density and sprawl. While economists may struggle to understand innovation, geographers do not. How does knowledge diffuse across space? From a geographic perspective, density doesn't have a lot to say on that score. Migration does. See, "Networking Regionalised Innovative Labour Markets (Regions and Cities)."

Innovation is spiky. Geography matters. From economists at the World Intellectual Property Organization:

The American advantage is even greater when only migrants from countries outside the Organization for Economic Cooperation and Development are accounted for, reflecting sizeable inflows into America by skilled Indian and Chinese inventors, the report said.

The findings help dilute concerns expressed by such economists as Robert Gordon of Northwestern University that the U.S. is approaching a period of weak economic growth that requires immigration of high-skilled workers to avoid.

At a time when American universities have warned it's getting harder for students to secure visas, the study says in its conclusion that "restrictive immigration policies may have some negative effects on the inflows of skilled workers."

The pool of talent is probably growing too. Data from the United Nations shows the estimated migrant population worldwide was 213 million in 2010, a 58 percent increase from 1990. The migration rate of inventors reached as much as 9 percent in the 2000s, the economists said.

That shows migration is a "critical pillar of the ongoing process of globalization," they said.

Emphasis added. Migration connects two places, two cities. That network is how "new technologies are developed and diffused and they create high living standards wherever they go." One doesn't encourage greater density in South Asian cities to address poverty. One seeks better connectivity between cities.

Concerning innovation, Downtown Las Vegas doesn't need greater density. It needs better connectivity with innovative labor markets. San Francisco ("a hotbed of inefficiency") has that, in spades. The obsession with the sprawl problem is informing bad urban policy.