To "enjoy a majority" means to (in a democratic political system) have the largest share of voters supporting you. In your sentence, there is a political party ("his party) that might not have more voters backing than the other relevant parties. It's difficult to say more without context.

you mean kurdish ?

hola, espero poder hacer un intercambio de idiomas contigo, hablo espanol nativo y necesito practicar mi noruego. un barazo