My nonparametric text, Practical Nonparametric Statistics, often gives clean formulas for expectations, variances, test statistics, and the like, but includes the caveat that this only works if we ignore ties. When calculating the Mann-Whitney U Statistic, it is encouraged that you throw out tied pairs when comparing which is bigger.
I get that ties don't really tell us much about which population is bigger (if that's what we're interested in) since neither group is bigger than the other, but it doesn't seem like that would matter when developing asymptotic distributions.
Why then is it such a quandary dealing with ties in some nonparametric procedures? Is there a way of extracting any useful information from ties, rather than simply throwing them away?
EDIT: In regards to @whuber's comment, I checked my sources again, and some procedures use an average of ranks instead of dropping the tied values completely. While this seems more sensible in reference to retaining information, it also seems to me that it lacks rigor. The spirit of the question still stands, however.