Translation:The voter gives an explanation of his political ideas.
A non-native English speaker has asked a question about English. I view it as useful to such an individual to know when there may be significant differences among English dialects.
To me the conceptual distinction between "explanation of" and "explanation for" in this sentence is stark, a distinction that seems mirrored in Dutch (uitleg van vs. uitleg voor), although I can certainly not speak with any authority on that point.
Yes... (Native speaker here) we usually say it's an explanation "for"... I only hear an explanation "of" when it is going to be about a topic... such as "an explanation of the Rosetta Stone"... where "for" wouldn't make sense. But in THIS context... yes, most frequently we would say "for"...