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Start with curiosity
Pushing back on a senior person starts with curiosity. Does that person have context you lack? Confirming that you understand their prior, and asking what they know that you do not, puts everyone on the same baseline before the debate starts.
Made up or open
Then it helps to find out whether their mind is made up or open to input. If it is made up, picking a fight for the sake of it gets nowhere. If they are open, the terms are clear: fresh data gets a hearing, and a strong belief with no data behind it calls for asking why you hold it, or going to get the data.
The CPO and CEO
The CPO and CEO relationship tends to go badly when the CPO competes with the CEO for vision and the two end up at loggerheads. The CPO's job is translating the founder's vision and intuition into reality, which takes an art of pushing without competing.
Why does the highest-paid opinion often win?
Analytics writer Avinash Kaushik popularized the acronym HiPPO, for the highest-paid person's opinion, in the mid-2000s. Ron Kohavi, who ran experimentation at Microsoft and Amazon, later used it widely when arguing for A/B tests. The idea is that without data, rank decides who is right. Experimentation is often presented as a way to give a junior person's idea a fair test against a senior person's.
Why does knowing someone's prior matter in a debate?
Bayes' theorem, published after the minister Thomas Bayes died in 1761, describes how a belief should shift when new evidence arrives. Two people with different starting beliefs can see the same evidence and still end up in different places. Asking what the other person knows reveals what their starting belief rests on. Once both sides share that baseline, the disagreement narrows to the actual evidence.
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