Why do they ask this Politically Exposed Person (PEP) question for investment related products and robo-advisors?

Due to the position and influence PEP holds, they can potentially abuse their status for purposes of money laundering and other related offences (bribery or corruption). As a result, there is a need to go through compliance checks to prevent the occurence of such activities.

A politically exposed person is someone who is entrusted with an important public function. You can be labelled as a PEP if you are a family member or a close relative to a PEP. Once you declare yourself as a PEP, the institution will do additional due diligence on you and your transactions to prevent fraud or money laundering. Your transactions will be closely monitored so that any suspicious transactions or activities can be immediately flagged out.