Bargaining solutions like Egalitarian and Nash are more consistent when disagreement points change, compared to Equal Sacrifice and Kalai/Smorodinsky solutions. This was found by studying a specific type of bargaining problems called 'Constant Elasticity of Substitution'. The Egalitarian solution is the most consistent, followed by the Nash solution, while the Equal Sacrifice solution is the least consistent, followed by the Kalai/Smorodinsky solution.