How many hours before it is no longer quick? Slow or fast should make no difference in the "quality" of the counting.
Here in Denmark its done within something like 4-5 hours of the closing of the voting booths so around midnight for the final result. Everything is then being recounted for personal votes over the next one or two days or something like that. Think that is pretty similar in many other nations.
A system that still uses the good old pen* and paper for voting and AFAIK no accusations of fraud nor has the courts ever been involved (not even when an election was decided by few dozen votes on the Faroe Islands a decade ago)
Personally I prefer things to be quick as the Media running round in circles fueled by speculation and debates between "experts" is generally bad for the really important stuff like the weather or sports news...
A country like Iran does not allow outside observers and stuff like that might be something to worry more about than speed of counting.
*actually it's a pencil.
CBR
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