Core Viewpoint - The article discusses the political situation of Shigeru Ishiba, the leader of the Liberal Democratic Party (LDP) in Japan, following a significant defeat in the recent House of Councillors election. Despite the loss, Ishiba maintains a higher cabinet approval rating than the LDP, indicating a potential support base that may influence internal party discussions regarding leadership elections [1][6][12]. Group 1: Cabinet Approval Ratings - Ishiba's cabinet approval rating stands at 32%, which is 8 percentage points higher than the LDP's support rate. Even when combined with the support rate of the Komeito party, the cabinet's approval still exceeds the total by 5 percentage points [6][12]. - The "Prime Minister Premium" metric, which reflects the level of support for the cabinet over the ruling party, has remained positive since Ishiba took office, indicating a stronger direct support for him compared to the LDP [4][10]. Group 2: Support from LDP Constituents - Following the LDP's defeat, Ishiba has garnered understanding and support from the LDP's base, which may impact ongoing discussions about an early presidential election within the party [3][12]. - In a survey, 57% of respondents expressed a desire for Ishiba to continue as Prime Minister, with 78% of LDP supporters favoring his continued leadership. This contrasts with a general sentiment where 36% wish for a change in leadership [9][12]. Group 3: Political Stability Indicators - The "Aoki Rule," which suggests that when the combined approval ratings of the cabinet and the LDP fall below 50%, governance becomes challenging, indicates that Ishiba's administration has consistently maintained a rating above this threshold since he took office [10][12]. - The LDP's support has reached its lowest level since 2002, which raises questions about the sustainability of Ishiba's support and the potential for a shift in party dynamics [12].