Former Prime Minister Kim Min-seok won party-member primaries in Incheon and Jeju Island on Saturday, a week after losing to rival Jung Chung-rae, the former ruling Democratic Party of Korea (DPK) leader, as the party's leadership race enters its middle stage. Kim beat Jung 47.75 percent to 42.08 percent in votes cast by dues-paying party members in Incheon, just west of Seoul, and the southern resort island, according to party officials. Their rival, third candidate Song Young-gil, garnered 10.17 percent. With Saturday's win, Kim bounced back from his defeat to Jung in Busan, Ulsan and South Gyeongsang Province on Aug. 2, when Jung edged out Kim 46.65 percent to 43.85 percent. In the first primary, held in the central Chungcheong region on Aug. 1, Kim edged out Jung 45.05 percent to 44.61 percent. Across the three primaries held so far, Kim is slightly ahead of Jung, with 45.42 percent and 44.56 percent of the votes, respectively. The DPK's leadership race has primarily been a contest between Jung, who has long aligned himself with the party's hard-line wing rather than fully backing Pres