Then I have the option to engage the attorney to appeal the tax and only pay if they succeed to reduce the assessment based on a percentage of the reduction.

Any deal with upside potential (expense reduction, renovations to drive revenue, undermanaged property, etc) the in-place cap rate may hold very little relevance to the deal.Per your follow-on question about generating higher returns: you are 100% right.  

Actually, given the opportunity to generate rental income and the potential for risk reduction via diversification, modest multifamily residences could be a prudent investment.Kindly feel free to ask any specific questions or seek advice before starting your next real estate venture.

Conversely, a Write-Down is a a documented and verifiable reduction in the book value of assets whose fair market value has fallen below its book value.

If they are already asking for a reduction, what is next? 

If they are your gardener most expect a reduction or compensation.

Account Closedhttps://www.newscientist.com/article/2193136-universal-income-study-finds-money-for-nothing-wont-make-us-work-less/https://www.technologyreview.com/s/611418/basic-income-could-work-if-you-do-it-canada-style/"“All of the evidence from the project demonstrated the pilot was helping people get back into the workforce, eat healthier and participate in community activities,” Tom Cooper, director of the Hamilton Roundtable for Poverty Reduction, which helped enroll citizens in the UBI plan, told Motherboard"

BP is the only place where you will find real estate investors wishing for a reduction in their property values.

Sometimes you can get those bills reduced significantly with a bit of negotiation and other times they´ll offer a $50 reduction on a bill of $2550. 

Id buy it in a heartbeat, assuming there's a price reduction premium for it.