[Debarati Roy Gupta] Scrum guide says "For Product Owners to succeed, the entire organization must respect their decisions. These decisions are visible in the content and ordering of the Product Backlog, and through the inspectable Increment at the Sprint Review".If Product Owner is not following any quantitative prioritization technique then I would try to understand from him why he is not following any Product Backlog prioritization technique and without following prioritization technique still able to order Product Backlog which visible through the inspectable Increment at the Sprint Review and adding values to the customer.
Although I would suggest him Product backlog techniques like WSJF ,Moscow etc and advice him to see whether that would bring more transparency towards Product backlog prioritization .
But final decision is Product Owner's and "For Product Owners to succeed, the entire organization must respect their decisions"

[Amit Kumar Gupta] The Product owner should be educated and convinced about the need of prioritisation and how it helps his upstream and downstream to understand his rationale and also allowing them make necessary manoeuvre without negatively affecting the value output.

While a host of prioritisation techniques are already available and in most cases one of them will be simple and fit for use; the scrum master can also enter into an exercise with PO taking stakeholders’ views into account and develop a technique which captures the variables/views weighed by the PO.

[Sahil Jain] Involving the stakeholders in the prioritisation process can create better alignment and buy-in.
Also clear communication and clarity on Product Goal will help in what is more important and valuable to focus on rather than accepting all the requests from stakeholders.
Having frequent feedback loops and ensuring key stakeholders are available in sprint review to provide feedback would also help in better prioritisation.
 

[Kushal Deshpande] The PO may have multiple source of information and inputs to his decisions, Sometimes dependencies and limitations too play a significant role into prioritization. The PO is accountable of ordering a product backlog based on 'Value' (note: This is where word prioritization is replaced by sequencing). Although Sequencing product backlog is PO's accountability, As a scrum master I will have to educate PO on how to explain vision and direction of the product at the start of Sprint planning. The team needs to know how the sequence of the current backlog provides maximum value, and also need to voice their thoughts to the process.
Having Said that, If the PO is only exercising intuitions and not Analysis to order a backlog, as an SM we I will have to educate PO on analysis based sequencing, stressing the fact that it will take cognitive bias out of equation.

[Singh Rajbir] Backlog Prioritization is first step

Project Manager knows a project like a story / set of short stories.

Similar to a movie, before a breakup scene in a love story there must be a friendship scene preceding to it.

Prioritisation helps organising dependent stories in a later sequence to that of independent stories. Or stories of higher order of benefit or urgency are taken first in sequence