I found this article that touched on my issue.
EDIT:
It seems that some combination of installing VS 11 and some tool updates caused this problem. I was lucky and managed to get the following error message:
The type System.Web.Mvc.ModelClientValidationRule exists in both c:\Program Files (x86)\Microsoft ASP.NET\ASP.NET Web Pages\v2.O\Assemblies\System.Web.WebPages.dll and c:\Program Files (6)\Microsoft ASP.NET\ASP.NET MVC 3\Assemblies\System.Web.Mvc.dll
After some digging, I deleted the removal of โMicrosoft ASP.NET Web Pages 2 - Visual Studio 2010 Toolsโ, with the result that everything worked. Of course, it would be better to remove "Microsoft ASP.NET Web Pages - Visual Studio 2010 Tools" instead, but this is working at the moment.
I found a complete lack of information on the Internet about this type of problem, so I put it here for posterity.
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