Access Point Roaming
Switching to the strongest signal will automatically happen if the Wifi SSID (the name of the wifi you see in Wifi Settings) of both Wifi signals are the same. (So in your case, both the AP should be named either Bob or Mary, and be on different Wifi channels so that they don't weaken each others signal).
If the SSID are different then it won't work. One possible reason for the lack of this feature is that Wifi consumes a lot of power, and if your device has to always keep scanning for all Wifi signals to determine their strength, the battery will drain faster.
(Jailbroken devices can have this feature - StrongerFi – Automatically switch to the strongest WiFi signal - though I wouldn't really advise opting for this route.)
Apple support article &quot;How iOS decides which wireless network to auto-join&quot; explains how iOS automatically determines the Wifi to connect to, based on your past wifi activity.