。
Koizumi was elected as the new president of the ruling LDP.
Literal
Koizumi [subject-が] ruling-party LDP [attributive-の] new president [as-に] was-elected-[passive-された].
Political news. 与党 ('ruling party') contrasts with 野党 ('opposition party') — the fundamental binary of parliamentary politics. 自民党 ('Liberal Democratic Party,' LDP) is Japan's dominant conservative party. 総裁 ('president') is specifically the head of a political party; 総理大臣 is the prime minister (head of government). 選出する ('to elect'). The passive ~された describes the outcome from Koizumi's perspective.