How do us economists think private ownership most affects property maintenance

Private ownership entails the existence of an owner/propietor, who has important economic incentives for the preservation of the value of his property and even for enhacing its future value. This occurs to a greater extent when private ownership takes place in countries with strong institutions that are able to enforce property rights if necessary.

On the other hand, when collective property forms are used instead, economists tend to forecast that it will be affected by the process known as the Tragedy of the Commons. It describes how when there is a shared resource, individual users who have access to it and use it in accordance to their own  interest, end up behaving in a manner that is harmful for the common property, even tough this is contrary to their personal interests too, as then the common good will not be in the same initial conditions anymore. For example, overexploitation due to unlimited grazing on a collectively-owned field.

the hereditary right of a monarch to rule from the mandate of heaven

representative government