Monotone Systems

1. Monotonic systems were introduced to reflect the adjustment of negotiating power in bargaining situations, particularly in negotiations between left and right political parties. The aim is to clarify the structure of the political mechanism design. Monotonicity in this context means that if a party's bargaining power increases, then its share of the resources being negotiated also increases. Conversely, if a party's bargaining power decreases, its share of the resources being negotiated also decreases. Monotonicity ensures that the bargaining process is fair and stable.2. Monotonic systems have also been applied in data analysis. In this context, stable sets are used to provide a unifying perspective for virtual experiments. By assigning certain certificates to the elements in a stable set, virtual experiments can be performed to test the stability of the set under different conditions. This provides a basis for stability or equilibrium in the data, as opposed to volatility or fuzziness. Monotonicity in data analysis ensures that if a variable's value increases, then the outcome of the experi-ment also increases, and vice versa.