Minimizing Tracking Error with Index Construction

Consider a large institutional investor that is looking to construct a passive equity portfolio that closely tracks a broad market index. The investment team is debating between different index construction methodologies and wants to ensure that they address the issues of liquidity, sector exposure, and tracking error. They have identified three popular methodologies to potentially use: Market Capitalization Weighting, Equal Weighting, and Fundamental Weighting.

As an equity portfolio manager, your role is to assess the impact of each methodology on the resulting index's characteristics and performance. Given this context, which index construction methodology is most likely to minimize tracking error relative to the underlying index while maintaining a relatively stable level of sector exposure?