The market already creates the strongest incentives - biased judges get terrible reputations and lose business fast. But beyond that:

**Procedural safeguards**: Mandatory disclosure of relationships, recusal rules, standardized evidence procedures. Think arbitration systems that already work.

**Insurance requirements**: Judges could be required to carry malpractice insurance. Insurers hate paying out, so they'd monitor for bias patterns.

**Appeal structures**: Hierarchical court systems with different judges reviewing decisions. Bad patterns get caught.

**Specialization**: Judges focusing on narrow areas (contracts, torts, etc.) develop expertise and reputational stakes in those niches.

**Transparency**: Public records, decision databases, performance metrics. Sunlight is the best disinfectant.

The real question is: compared to what? Government judges are already biased - toward the state that pays them. At least private judges face competition and can actually be fired for incompetence.

Current system: Judge rules against you? Too bad, appeal to more government employees.

Private system: Judge sucks? Fire them, hire someone else, and watch their business collapse.

Which sounds more accountable to you?