# Business MathContingent payment-actuaries, math whiz, insurance expert, others-all welcome

#### howru

##### New member
How to fairly divide the contingent payout of \$25,000 (sum insured/face value) as part of total insurance payout \$35,913.33 (balance was from dividends and bonuses)?
1. A paid 8 yearly premium @\$348.25/year (total=\$2,786) inclusive for a relative C(the life insured person).
2. A's yearly dividends (insured company used premium to buy shares etc) were used to buy additional amounts of participating insurance called Paid up additions (PUA/bonuses). The cash value of any PUA will not be less than the dividend used to purchase the dividend additions.
3. On year 9 (financial reasons) A asked B to help with premium payment and stopped the premium but A left all yearly dividends and yearly PUA in the fund to accumulate more future dividends and PUA from year 9 to year 22.
4. B (year 9 to year 22) helped A pay the same premium \$348.25/year (total = \$4,875.5). Any yearly dividends (received by B) were used to buy additional PUA(bonuses) similar to item 1 above.
5. There was no contract or agreement made at year 9 as how to divide amount in future between them.
6. At end of year 22, the insurance made a settlement payment because C (the life insured) passed away.
7. The total settlement payment was \$35,913.33 includes Face Value = \$25,000 (the insured amount); PUA/bonuses = \$10,455.55; Interim dividend = \$14.92; interest = \\$442.86 (accrued from date of application to date of payment.
Need your opinion/help. Thank you.

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#### howru

##### New member
Don't be shy. Your input/opinion would be appreciated. As a start, let me quote an interesting article in Science News “Mathematician answers Supreme Court Plea” by Julie Rehmever in June 2 issue that described how mathematicians were asked to answer Supreme Court Plea on the matter of fairness.

So what’s fair?
An entire field of mathematics is devoted to answering just this kind of question. For example, take the classic “I cut, you choose” method of dividing cake: If I cut a cake into two pieces I’d be equally happy with, and you pick which of the two you like better, then neither of us will prefer the other person’s piece to the one we have. The division will be fair in that sense even if our priorities are different. For example, I might really want the rose made of frosting, while you might care only about the size of your piece.
Landau and his collaborators, students Ilona Yershov and Oneil Reid of the City College of New York, realized that the mathematics of fair division could be used to solve the redistricting problem. They used a variation on another cake-cutting method: A third party wields the knife, moving left to right across the cake until one of us calls out, “Stop!” when it seems that both sides are equally good. Then the person who called out gets the left piece and the other gets the right one.
The researchers proposed that a variation of this method be used to divide the state into two regions such that neither political party preferred the other’s region. From there, each party would divide up its own region however it liked.
At first blush, this plan doesn’t seem to solve the problem at all. After all, if one party has only 40 percent of the vote, why should it get a full half of the control of the process of dividing the state into districts?
But the mathematicians showed that equally shared control will lead to about the right outcome even if the parties get very different proportions of the votes. If Democrats get only 40 percent of the vote, they can divide up their half of the state to get at most 80 percent of the seats in that region. If the Republicans get all the seats in their half, that means the Democrats would get about 40 percent of the total seats, which corresponds to their percentage of the total vote anyway.
“The idea is to set up the rules of the game so that cheating isn’t really possible,” Landau says.
Landau points out that any restrictions ordinarily applied to the entire state would continue to be applied to the two half-states. So, for example, districts would continue to be required to have approximately equal populations, and the Voting Rights Act would continue to require that for both half-states, the majority of the population in some districts be ethnic minorities.
This fair division method offers the alluring possibility that each party may feel it got the better deal. The reason goes back to the cake: If I care most about the rose made of frosting and you care most about the size of your piece, we each may think our piece superior to the other’s. Similarly, Landau points out, one political party might particularly want to be able to win the district with a stadium in it, while the other party cared more about a district with an important donor.
The team presented its findings in January at the Joint Mathematics Meetings in Washington, D.C., and the research will appear in an upcoming issue of Social Choice and Welfare.
Political scientist David Epstein of Columbia University praised the approach as innovative, but said it’s unlikely to be politically feasible. “The idea that any subset of people is going to have 100 percent dictatorial control of any portion of any state is totally incompatible with the democratic process,” he says. Still, he believes the idea could be useful in other settings, such as perhaps for sharing power within a corporation.
Landau points out that in the current scheme, the ruling party has nearly dictatorial control already, and his scheme assures that that control can’t be used unfairly. “The problem is that the underpinnings of its fairness aren’t quite transparent,” he says. “It requires a paper to explain it.”