In the standard analysis of the paradox of voting, votes are pivotal only in two scenarios (exact tie or win by 1).
But in reality, vote counting is difficult and messy. And in reality, close elections are often disputed and the final outcome of the election may have little to do with who won the actual vote count. (The most famous example was the 2000 US presidential election.)
In light of the fact that close elections are usually disputed and rarely settled simply by an accurate count of the vote, what do we mean by a vote being pivotal? How do we calculate this probability?
The only analysis I've come across is the one-page appendix in Gelman, Katz, and Bafumi (2004). They argue that the analysis of the paradox of voting is pretty much unchanged, even with disputed elections:
In fact, our decisive-vote calculations are reasonable, even for real elections with disputed votes, recounts and so forth. We show this by setting up a more elaborate model that allows for a grey area in vote counting, and then demonstrating that the simpler model of decisive votes is a reasonable approximation.
Are there any other analyses of the matter?
(Given the vast literature on the paradox of voting, I'm surprised the only thing I can find on this obviously-important matter is the above one-page appendix.)