“Let's get an objective opinion. Tom, what do YOU think?”
You and your sister are discussing a family trip to Spain. You're debating whether to take a side trip to France while you're there. You can't agree with each other, so you want a 3rd person (Tom) to help you choose. You say this to ask Tom his opinion.
Let's get an objective opinion. Tom, what do YOU think?
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When someone decides "objectively", they're just thinking about the facts, not their own feelings. When you ask for an "objective opinion", you want to hear the opinion of someone who doesn't already have strong feelings about a subject, and who won't gain or lose anything because of the decision.
Objectivity is an important idea in American and Western culture. People usually value objective decisions and opinions more highly than biased or emotional ones.
When you want someone to tell you their opinion, you say that you want to "get" their opinion:
Hey, can I get your opinion on this? Which one's better - the orange or the green?
what do you think?
You probably already know this, but you should ask "What do you think?" instead of "how". This can be confusing, because you use "how" in other situations:
How do you feel about that?
But just remember: "what" and "think" go together.