Prioritizing browsers for testing according to the market share and user demographics is an essential aspect in cross-browser testing. Here's an approach you can follow:

1. Research market share data: Collect dependable data on browser market share from reputable sources like StatCounter, NetMarketShare, or similar analytics platforms. These sources offer insights into the usage as well as popularity of different browsers.

2. Analyse the major browsers: Begin by going through the major browsers that have the highest market share. Basically, this includes browsers such as Chrome, Firefox, Safari, and Edge.

3. Consider platform-specific browsers: According to your target audience and the nature of your web application, you may require to prioritize browsers specific to some platforms.

4. Consider compatibility with older versions: Consider the market share of older browser versions. While it's essential to give priority to the latest versions, you should also keep in mind testing on older versions that still have a significant user base. This ensures backward compatibility and a seamless user experience for users with older browser versions.

5. Prioritize based on your project's context: Make sure to consider the specific context of your project. Factors like the nature of your application, target audience, and industry standards may influence your prioritization strategy.

Remember that market share data delivers a good starting point, but it should be combined with other considerations precise to your project and audience. Keep a check on the review and update your prioritization strategy to adapt to changing market trends and user preferences. If you are interested to know more about browser testing, you can check out some blogs by HeadSpin. Those blogs really might help you to understand.