Big cities in the U.S. tend to be liberal, but there are a few exceptions.

A paper by UCLA political scientist Chris Tausanovich and MIT political scientist Christopher Warshaw, which we first saw mentioned by the Pew Research Center, cleverly combined data from seven different political opinion surveys, with a total of over 275,000 respondents from the combined surveys.

For each respondent, they used a sophisticated statistical model to estimate where the respondent falls on a left to right political scale, based on their answers to the various survey questions. Once they had the individuals' political ideologies, they were able to, using another statistical model incorporating various demographic, geographic, and economic factors, estimate the average ideology for different cities.

Here's a map showing their results for some of the largest cities in the U.S., with cities whose average ideology is more conservative than the national average in red, and cities that are more liberal than the nation as a whole in blue. The darker the color, the further away from the middle that city is:

Business Insider/Andy Kiersz, data from Tausanovitch and Warshaw, March 2014

Unsurprisingly, the most liberal big city is San Francisco, with Mesa, AZ coming in as most conservative. In general, most of the populations of big cities are, on average, more liberal than the average American. The exceptions fall mostly in the south and middle of the country, along with traditional conservative bastions like Anaheim in Orange County, California, and Colorado Springs, CO. Cities with a heavy military presence like Virginia Beach and Jacksonville also came out more conservative than other cities.

Here's a chart from the paper illustrating the big cities' average political ideologies. Cities to the left are more liberal, and cities to the right more conservative:

Tausanovitch and Warshaw, March 2014