The imperfect describes an action which lasted a (relatively) long period of time in the past and has finished (sometimes this just means the context has changed but sometimes that the actual piece of information is no longer true).
The present perfect on the other hand describes an action which happened in a single moment or had a single immediate effect and usually its effects are still perceived. The simple past is exactly the same with the important difference the effects are long gone (it's usually only employed in literature and for very far-away events, say your childhood when you're 50. Watch out as speakers from the South use it all the time even when the other Italians would prefer a present perfect).
So as far as this sentence is concerned here is an explanations of the differences in meaning and nuances I as a native speaker perceive:
- La maggioranza ha voluto questo. = This action is recent (or is perceived or being described as such), it is seen as one point or moment in the past. Also, the will of the majority has succeeded and produced results which have not been overturned.
In a sentence "the majority wanted this and they've got it"
Alternatively, this action may be long gone but then this tense would be chosen because this is said in a spoken, informal setting (typically said by speakers of Northern Italy).
- La maggioranza volle questo. = This action is long gone (like at least years ago, possibly decades or centuries), it is seen as one point or moment in the past. Also, the will of the majority has succeeded and produced results which have not been overturned. Finally, this is probably a written, formal style.
In a sentence "the majority wanted this and obtained it"
Alternatively, this action may be recent but said in a spoken, informal setting (speaker from the South).
As you may have noticed these two are almost the same and the thin line of distinction lies on either the remoteness of the action or the formality in style or even both.
Very very different is the imperfect tense.
- La maggioranza voleva questo. = Here the action is either recent or long gone, but has been going on for some time and subsequently has stopped. So either the majority used to want this but changed their minds or they voted for a measure and then for one reason or another the measure did not succeed. Either way the attempt at executing the action is failed and it has no more effect up to now. The style may be formal or informal, speakers from the South or the North all say this in the same way.
In a sentence "the majority used to want this but doesn't anymore" or "this is the result the majority wanted, but they failed"
Hope this helped ;)