Boaty McBoatface. That was the name chosen by the British public when asked to name a new scientific research vessel in April 2016. And of course, it was. It’s funny! You see, when you ask a lot of people for input on a topic that is not that important to them you’ll get a great deal of silly inputs. — Aran Rees, The stupidity of crowds
Let's imagine that your significant other is pregnant. The two of you decide to crowdsource the baby's name. Except, you want to filter out all the people who don't actually care what your baby is named. So you decide to replace voting with spending.
Your friends and family come up with a list of over 400 potential names. Here are the rules of the "game"...
1. Each participant can spend as much money as they want on their preferred names.
2. Participants can see each other's allocations.
3. Participants can change their allocations as many times as they want.
4. There's no time limit.
When no more "pareto improvements" can be made, whichever name has the most money will be selected. Assume that all the money will go into a college fund.
Is there an optimal strategy? Is there a "legal" way to "cheat"?