Lets say we have 4 friends who split a pizza each day. Person 1 gets 40%, person 2 gets 15%, person 3 get 20% and person 4 gets 25%. One day, Person 1 decides not to show up. Now the 3 friends must split Person 1's slice (40%) among themselves but they need to be given the weighted amount. I understand that .4/3 = ~13% but each person has a weighted share in the pizza for arbitrary reasons such as the percentage of money they add to the pool. What kind of problem is this? And how can this be solved?
My apologies if this is a repeat question but I am not sure what to search(google).
Thank you
It seems natural to me to think of shares. Person 1 has 40 shares, person 2 has 15 and so on. Now person 1 has abandoned his claim, so there are only 60 shares instead of 100. Person 2 then gets $\frac {15}{60}=25\%=\frac 14$. Person 3 gets $\frac {20}{60}=\frac 13$. Person 4 gets $\frac {25}{60}=\frac 5{12}$