How do you use emotional intelligence while influencing data driven execs?

Working with data driven execs is in many ways easier - you present facts and get alignment based on data arguments. The challenge comes when trying to influence data driven execs when you dont have sufficient data yet. This can be various reasons why - it could be a product bet or early in the product maturity cycle. Data driven execs typically follow logical arguments. As a PM, when you dont have your data-case built yet, map out your top assumptions and show how your roadmap plan is going to address resolving each assumption. The other tip is to create explicit go/no-go decision points to ensure that the execs have confidence that as a PM, you are both optimizing for your product/project and overall company goals well.

Lots of people say they are data driven, not everyone actually is. I find people are either swayed by data or by stories. Both are valid - it's easy for anecdotal evidence to mislead, but it's also easy to cherry pick or manipulate statistics. So as a PM you need to be conversant in both. 

Emotional intelligence comes into play determining how to speak with someone successfully. Listen to them for clues - how do they make arguments? Are they citing statisticis or referencing stories? Speak to them in your language for better success. 

You will need both EQ and data. More importantly, to influence data-driven execs (which, arguably, all execs are) you will need to help expand their view of the world by adding depth of understanding in your product/business area, additional layers of context that execs may not be aware of, and your ability to create clear and actionable plans with measurable results. My recommendation is not to think of EQ as a "counteract" to being data-driven, but rather use data, storytelling and clarity/depth of context to help execs expand their understanding, which ultimately may influence their viewpoints.