The purpose of most political elections is to select from the set of candidates a predetermined number $n$ of successful candidates.  (Often $n = 1$.)  In brief, my question is: 

> Has it been proved that *no voting procedure whatsoever* will allow this to be done in a reasonable way?  

For comparison, [Arrow's theorem](http://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem) states (roughly) that when each voter puts a total order on the set $C$ of candidates, there is no good way to average those orders to produce an overall total order on $C$.  This result has of course been enormously influential, spawning many other voting impossibility theorems.  However, it does not model the most common real-life situation, where the output we want is a subset of $C$ of cardinality $n$ (the top $n$ candidates, whatever "top" means) rather than a total order on $C$.

Let me emphasize how general my question is.  Suppose there are 25 candidates, 3 of whom are to be elected as our representatives.  Is there *anything whatsoever* that voters could be asked to do in the polling booth that could then be processed in some way to select the best 3, in such a way that reasonable conditions hold?  By "reasonable conditions" I mean the usual kind that appear in social choice theory, e.g. in Arrow's theorem or the [Gibbard-
Satterthwaite theorem](http://en.wikipedia.org/wiki/Gibbard%E2%80%93Satterthwaite_theorem): non-dictatorship, tactical voting unhelpful, etc.  

For instance, perhaps each voter has to mark each candidate out of 10.  Or perhaps voters are allowed to make various statements such as "if X is elected but Y is not then Z should be".  Or perhaps voters put a partial order on the set of candidates, and whenever they prefer X to Y, they choose a real number specifying how much they prefer X to Y.  There are endless possibilities, and my question is whether there's some theorem stating that *no matter what voters are required to do*, there's no good way to select the top $n$ candidates.