To show the value of a new design idea to stakeholders, I would focus on making it clear and easy to understand. I would explain how this new idea can save money, save time, or make things work better, using simple examples or data. I’d create a small demo or show real examples of how it solves problems or improves things. It’s important to talk about what matters most to each person, so I’d explain how this idea can help them specifically. I’d also address any worries they might have and show how this idea reduces risks or prepares us for the future. To make it even clearer, I’d use simple visuals or tell stories to explain how it works and why it’s better. My goal would be to help them feel confident and excited about the new design.

Design may be complex to solve complex problems. So, I would start with prototype and show case the working of simple prototype. I feel working prototype help visualizing the design better and help explain how differently and innovative way we've solved the problem. Your new design, though complex should help save time and money to stakeholders compared to existing models. Usability of new design and solution should be way simpler, however the complex internal implementation is. The products (End user interfaces or APIs) that are easy to use will be adopted faster, because it requires less learning curve, and allows people to quickly understand and utilize the features, leading to a smoother adoption process.

The proof of the pudding is in the eating! If a new design paradigm truly has merit, then it will naturally be voted by the stakeholders and consumers who will benefit; therefore, one should create a demo with the new design and juxtapose it next to the old design. Create regular, realistic workflows, and let the evidence emerge that it leads to better user experience, greater clarity, and more workflow efficiency. Needless to say, a new design paradigm is worthwhile -- by definition -- only if the users and stakeholders judge it so when juxtaposed with the extant design.

Showing the value of a new design idea is much more than simply mentioning numbers and examples. It requires a deep understanding of the audience, clear and concise communication, the presentation of concrete data, and the ability to demonstrate the positive impact of the design on the business and users.

I try to build a high trust environment so that the team can be trusted to choose whatever design they deem necessary to meet their goals. This starts by delivering value, early and often and demonstrating working software frequently. If trust is there then my experience is that discussions with stakeholders tend to be about business value and not micromanagement of design, testing strategies and other details.