What is the difference in sense between
Une majorité d'électeurs
Une majorité des électeurs
La majorité des électeurs
This form is actually accepted because when you say “d'électeurs”, i.e. “de électeurs”, what you're considering the “électeurs” word as an unnumbered group of people like liquids (think of the difference between much and many in English).
I'm not sure this is good French by « l'Académie » standards, but this is definitely used, mostly in the media. Somehow, I guess what you say in fine prints is that you don't know how many voters there was in the pool of voters.
Whereas, by using “des électeurs” you say “de les électeurs” which points and numbers the voters, which implies you know how many they were. (I have no sources for that, that's only from my humble understanding as a native French speaker).
This work the same way for “d'études” vs “des études”. You use the former when you cannot quantify how "many" studies, like in “Combien d'heures d'études as-tu travaillé ?”.
they both mean the same thing. Usually, it means that this is what we call "relative majority", i.e. a plurality in English. (i.e. if after a vote you have 30%, 30%, 40% as result, 40% is “une majorité”, but not “la majorité”).
This means that a majority is "absolute", i.e. a true majority, which means over 50% of the votes.
The second form in unlikely to be used for it mixes definite and indefinite articles.
My opinion is that the definite form (the 3rd) tends to stress the fact that the 50% bar was passed, and the decision cannot be discussed: The majority decided; when the indefinite (1st) implies that the outcome is a result of the ongoing circumstances: A majority decided.
Edit: the indefinite form can also account for a "relative" majority i.e. when the candidate or party received most votes but less than 50% of the (valid) votes
I do not have an authoritative reference, but I believe that the first expression
would be used in the sense "the majority of voters..." — you are talking about "the population of voters" — people who might show up at the polling station. When you search for this exact expression in Google, you get 3.3M hits. I think that means it is "not uncommon". Specifically, Linguee suggestions contain many examples of its use (with the English translation); these include numerous quotes from the European parliament.
is talking about "people who came out and cast their ballot" — and specifically "more than 50%" of those people.
Finally, the difference between the second and third might be like "the majority" and "a majority" — the former being an absolute (>50%) and the latter relative (more than any other).