Here is how we do it in Africa. I think it works well everywhere else. 3 rules!
1. If someone is a trophy hunter, and someone else is a cull hunter. It doesn't matter, you shoot the first animal to come out. The cull hunter isn't allowed to upgrade, and the trophy hunter is not allowed to downgrade.
2. If I have an elk tag and you have a deer tag. The first animal found belongs to the person that has the tag.
3. If nothing above applies we draw straws. Every person switches off for half a day. If someone turns an animal down, the next guy can shoot it. I am mornings, you are evenings. More than 2 guys break the day into thirds, rotate the day the next day.
We used to do the whoever sees it gets it thing, I don't think this is fair or equitable, especially involving kids or people who have not hunted a lot.
Hunters should hunt alone. If they have a problem in a group setting with someone else.