Reasons to move a t-stat: Hot or cold external influences, such as but not limited to; light bulbs, heating elements, cold drafts, warm bodies, sunshine or anything else that will either warm to cool the t-stat faster than the surrounding room(s) will warm/cool.
Reasons to NOT move a t-stat: to balance the system. If one room is colder than the room with the t-stat, turn up the t-stat and let that room over heat while the colder room gets comfortable. Same result without the hassle and/or expense of relocating the t-stat.
If YOU want change, YOU have to first change.
If you are waiting for the 'other guy' to change first, just remember, you're the 'other guy's' other guy. To continue to expect real change when you keep acting the same way as always, is folly. Won't happen. Real change will only happen when a majority of the people change the way they vote!