Inspired by President Obama's recent comments on mandatory voting, the Washington Post had the interesting idea of projecting what the 2012 presidential election results would have looked like if everyone turned out.

Unfortunately, though, they chose to use an incomplete data set, coupled it with some bad assumptions, and got some misleading results.

Take a look at the Post's map trying to project, based on racial demographics, how the election would have gone with 100 percent turnout. It shows much of the South (including Texas, Alabama, Mississippi, and South Carolina) suddenly flipping Democratic — and Maine, Vermont, and Rhode Island tipping to the GOP:

The map trying to project what the results would have been based on a partisan gender split is even more bizarre. Projecting the change in results under mandatory turnout based solely on the gender of voters, the Post finds that only four states in the country would have supported Romney:

The strange results are entirely because of some bad methodological choices by the Post.

The Post is using both Census data about demographic turnout and exit poll data on whether various demographic groups supported Obama or Romney. Basically, the Post is assuming the white voters who didn't turn out would vote exactly like the white voters who did turn out (according to exit polls), and that black, Hispanic, male, and female voters would do the same.

But here's the gigantic problem: state-specific exit poll numbers were only available for 18 states in 2012. There's also a national exit poll that offers composite results for the whole country. So for the 32 states without individual exit poll results, the Post used those national exit poll numbers to make projections.

The problem with that is that looking at how women voted nationally isn't a good way to project how women in conservative Kentucky will vote. Similarly, how white people voted nationally doesn't tell you all that much about white voters in liberal Vermont, as Josh Barro argued on Twitter.

That's why the Post's map based on racial projections comes up with the odd result of the South going Democratic and much of New England going Republican — because they had no individual exit poll data for those states. Instead, they assumed that white voters in each of them, under full turnout, would vote like white voters did nationally (59 percent for Mitt Romney).

But that's an indefensible assumption. We know white voters in the South are overwhelmingly Republican, while white voters in New England are Democratic. They don't vote like the national average.

Additionally, the gender map that seemed so inexplicable makes a lot more sense when you realize that the only four states it showed backing Romney — Indiana, Arizona, Missouri, and North Carolina — were in fact the only Romney states for which there were exit poll numbers. Every other red state flipped to a blue state based instead on the national gender split (55 percent of women nationally voted for Obama, and 52 percent of men voted for Romney).

If you remove the states without individual exit poll data, you get this much less exciting map — the winner of each state is the same as our actual election:

We did a similar modification for the race-based map. There, a couple of swing states do end up tipping:

This map shows Arizona flipping to Obama, and Pennsylvania and Ohio tipping to Romney. It's an interesting finding, and it's worth a broader discussion about whether this basic methodology makes sense. But using crude national averages to turn deep red and blue electorates purple doesn't make any sense at all.

Update: Check out the Washington Post's reply here.