Polivate (verb) : Portmanteau combining "Polish" and "Motivate". The act of enhancing the effectiveness of a structure in another player's city either by random chance by pressing AID, or by visiting their city and selecting a specific structure to be either motivated or polished.
This should be your general guidelines when visiting a fellow Guild Member's city - unless you are looking for a specific age of Great Building blueprint:
1) Hall of Fame: Because of their tremendous benefit to the Guild, everyone should ensure every one of these structures are always motivated.
2) Event Buildings: Structures only won during special FoE Events. Their benefits are almost always greater than any other structure which that person may have in the same class, even if is of a similar or even slightly newer age(s). Examples include the Shrine of Knowledge, Log Cabin, and Confectionary.
3) Diamond Structures: Structures only able to be purchased with diamonds. Examples include the Theater and the Aqueduct.
4) Newest Buildings: For structures of the same class (Production-Supply / Residential-Coin / Culture-Happiness), the most advanced aged structures provide the player the most benefit.
5) Decorations: These items are low-benefit Culture items, primarily for filler, decorative value, or requested in certain tasks. Their common denominator is that they don't require roads. Polish them if nothing else remains, or if it is the only thing you can polish while looking for a specific-age Great Building blueprint. If you have to polish decorations, use the criteria above - event (Tree of Love), diamond (Aqueduct), and then the newest standard decorations Tree.