If it’s alright with you, I’d like to think through this together, and I invite our readers to think through it with us in the comments.
First, let’s consider the survey. I’m going to assume that the purpose of your survey is to gather reliable data. Reliable data is uncorrupted, which means it’s free of errors and bias.
Second, let’s consider the Six Sources of Influence. They are personal, social, and structural levers that can be used to affect motivation and ability.
So, there's a bit of irony in your question. In essence you’re asking how you can influence people in a situation where, if you want reliable data, they shouldn’t be influenced at all—unless it is to tell the truth as they see it.