The problem of splitting the cake equally between two children
For my birthday, I got a book called "Scientists Joke." (compilers B. S. Gorobets, Y. A. Zolotov, S. N. Fedin)The one I've almost read. There are a lot of interesting stories in it, but one of the things I liked was the story of Beria, who appointed coal ministers. Below I will write it in its entirety, but now I want to talk about the simplistic formulation of the problem of honest allocation of resources, as I learned it almost immediately. 10 years ago from the courseMaking Better Group Decisions: Voting, Judgement Aggregation and Fair DivisionEric Pacuit of the University of Maryland: Suppose there is a cake and two hungry children. They want to share the cake equally without a third party. If the cake is homogeneous (For example, chocolate cake with evenly distributed vanilla glaze)It is not difficult to find a fair division - the cake can be cut relatively smoothly. But how do we find a "fair" split of a cake if it's heterogeneous? (for example, a glaze consisting of 1/3 chocolate, on 1/3 vanilla 1/3 strawberry)Every child wants different parts. > cake?>
Approximately this problem was helped by Beria two ministers, between whom the coal industry of the USSR was divided. (Quote from the book "Scientists Joking")
Appointment of Ministers of Coal Industry> (castling)
He's Beria.> He was a master of unexpected and unconventional solutions. <...> The Politburo decided to divide the People’s Commissariat for the coal industry, headed by V. V. Vakhrushev, into two for the western and eastern regions of the country. It was assumed that they would be headed respectively by V. V. Vakhrushev and D. G. Onik. We've ordered Beria to separate. One can imagine how much trouble such a procedure would cause under the usual bureaucratic approach. Beria called Vakhrushev and Onika and invited them to separate amicably. And at the end of the term called both and first asked Vakhrushev, a contender for the leadership of the Western areas of the industry, if there were any complaints. He replied that there were no complaints, and everything was divided correctly. Then Beria turned to Onika: "How are you?" Onika stubbornly said: I have complaints. All the best shots Vakhrushev took. And all the best sanatoriums and holiday homes too.” Seeing such a case, Beria reasoned: "Since Vakhrushev believes that everything is divided correctly, and Onika objects, we will do this: Vakhrushev will be the People's Commissar of the eastern regions, and Onika will be the Western ones." And the meeting ended there.
In general, if we refer to "The Challenge of Fair Cutting the PieBeria used an algorithm called division without envy. (envy-free). In this algorithm, each partner thinks that his piece as a minima is just as valuable as everyone else. Such a division can be made through a deli-and-choice procedure: one partner cuts the pie into two sectors he considers equal, and the other partner chooses the sector he considers best. There may be a better procedure for the pie, but it is harder for the coal industry to come up with one. I think that’s why Beria settled on this simple algorithm, but it’s funny that he didn’t warn the candidates in advance about how he would decide on their full-blown separation.
P.S. I recommend both the course and the book - they definitely broaden your horizons and are interesting to learn and help you be a better leader:)
P.P.S. I especially remember the course. errowIt is also called the “impossibility of democracy” theorem as “collective choice” or “the inevitability of a dictator.” The meaning of this theorem is that
In the Ordinalist approach, there is no method of combining individual preferences for three or more alternatives that satisfies certain quite fair conditions and always produces a logically consistent result. The ordinalist approach is based on the fact that the preferences of the individual regarding the proposed alternatives cannot be measured quantitatively, but only qualitatively, that is, one alternative is worse or better than another.
#PopularScience #Math #Management #Leadership