Implement REST\CSOM API method for setting list read and write security
Implement SPList.ReadSecurity and SPList.WriteSecurity for client model, like in the server object model.

We are happy to provide this update as part of the SPO CSOM updates released late August 2016. See more details from following blog post – dev.office.com/blogs/new-sharepoint-csom-version-released-for-Office-365-august-2016-updated.
Thanks for providing your valuable input on the needed APIs and product capabilities.
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PaulE commented
Excellent, the property has been added to CSOM. Anything for REST?
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Paul Ewert commented
I currently have a project whose success is dependent on this functionality. Without it, we will either have to use unique item permissions (YUCK!), or an intermediary list with a workflow (dirty) to move items from a source list (where users have edit permissions) to a target list (where users have more restrictive permissions)--although, this doesn't allow users the same flexibility as the ReadSecurity and WriteSecurity properties.
Cross-reference https://www.yammer.com/itpronetwork/#/Threads/show?threadId=739425256 for a screen shot of the Advanced List Settings > Item-Level Permissions section we need to reproduce in REST.