Even if an election could be pulled off technically (i.e., smooth ballot casting processes, etc.) given the damage to Haiti’s infrastructure, there is the interesting question of how to involve the huge displaced population: who would vote where?
Since the presidency is a winner-take-all national election, displacement cause problems that are largely technical: re-registration may be needed to ensure the identity of people. This could be a significant technical problem, but nothing compared to the political problem of elections for sub-national offices, of which there are hundreds in Haiti.
Allowing the displaced to vote in their host cities for offices below the presidency could cause lots of conflict. Specifically, people that are from PAP may find that people in the host cities do not want them voting there and influencing or changing whatever local political dynamic exists in their city (or department, etc.). For instance, I heard an Episcopal priest from Haiti last night who mentioned that Mirebalais had grown by about 50 to 60 percent! Presumably it would be hard to have them all register and vote for PAP offices while not in PAP, but the alternative is that they upend things locally if they vote for Mirebalais officials. Moreover, this problem could last several years. Ultimately, people may decide that the displaced are “long-term temporary” residents of their host cities (and the ideal is that fewer people return to PAP then lived there). If so, this will not matter as much as I fear, but it will depend on how the displaced are politically, socially, and economically integrated into local life. It will be interesting to see how many former residents of PAP begin to identify again as residents of their hometown or that of their parents.