Did you ever consider attributing publicly damaging negative reviews a somewhat higher weight, within any kind of equation that connects user feedback/requests with product roadmap decisions?

Ideally, your product roadmap reflects long-term strategy, narrative, and investment. If you are confident in your roadmap, you shouldn't need a rule that automatically places more weight on negative reviews than positive or neutral reviews. Feedback is very important - but it's equally important to avoid knee-jerk reactions and keep Product, Dev, and Marketing teams focused on the plan. 

Generally, I try to balance negative reviews with understanding that (a) we're not necessarily marketing to everyone and (b) product is a journey - some will follow and others will not. 

Negative reviews that come from particularly prominent people, or reviews that have the potential to go viral should be addressed directly, if possible. This response doesn't necessarily have to be public - but there could be value in a conversation that unpacks strong feelings or corrects a misunderstanding. In context of roadmap decisions, I would consider these types of prominent reviews individually (versus on an aggregate basis), just to make sure I understand the real issue at hand and whether it's something for us to solve.

This is a really interesting question. Leadership typically look at a number of factors when determining what goes in the roadmap. For example, at Zendesk we look at industry trends, innovative use cases, new market expansion, our competitors, partners, and of course customer feedback.

For customer feedback we run a robust “Voice of the Customer ” program that looks at feature requests across all our customers and then ranks them based on a number of factors including revenue opportunity, churn risk, number of votes, and alignment with long-term strategy. I don’t think damaging negative reviews have ever been a factor we've considered. 

There are two types of customer: one that posts a negative review and decides never to be your customer again (this happens sometimes) or one that is more thoughtful about how they go about sharing the same feedback. I would say that the latter is going to be a better long-term customer and one worth investing in.

Our team always looks at negative feedback and incorporates it in product roadmap decisions... BUT there is one rule that myself and my teams always use in these feedback sessions. 1 is not a constant, meaning that if it is just one negative feedback we don't use it, as this doesn't mean scale, this could just be an issue with this customer and no one else is feeling it. So we look at critital mass of feedback or reviews around the same topic. As a Product Marketer you need to take the good with the bad and you can find great learnings and growth in negative feedback. My favorite custmers are the ones that are most upset with us, they give me raw and honest feedback that I can take to improve the customer ecxperience for others coming down to our products down the road. So I would make sure the complaints/negative reviews are in groups or segmented by complaint so you can make sure that you are moving things on the roadmap that can scale and have impact. One word of advice, have really hard conversations in the mirror! You can't be good at everything and it is ok if you aren't, if you can't improve there is no growth.

For the definition of reviews, I will consider analyst product evaluations also as reviews. It is also important to know that not all public reviews have the same weight. 

From my own experience, well articulated, attributed - negative feedback can have the right impact on product roadmap decisions. It allows the PM-PMM team to even reach out for further investigations and understand the key gaps for the customer. It also gives the team a chance to respond to the feedback by providing acceptable work arounds or provide product roadmap guidence.