More on RLS and DMPR

In soccer World Cup Final match there can't be a tie. If there is a tie, a 30 minute overtime period follows and if there is still a tie, penalty shootout. In American Football final, there are multiple 15 minute overtime periods. Penalty shootout is a FAIR way to get a winner. If a team is good at penalties, the coach may try to keep the tie in overtime, instead of trying to score.

An AGREEMENT will probalby get a BETTER ARRANGEMENT of GROUPS in COALITIONS, compared to DMPR or RLS process. But if there is NO AGREEMENT, DMPR or RLS is FAIR way to GET an ARRANGEMENT of GROUPS in COALITIONS. Like in soccer, if one or more leaders feel that there are better chances to get a more favorable outcome in DMPR or RLS, they may prefer it instead of the best possible arrangement derived from the negotiations.

Obviously, DMPR (Decision Makers' Pick in Rounds)  and RLS (Raniking List Selection)  can be used only for the AVAILABLE groups. It was mentioned in previous article when it was suggested that a Coalition of non participants I-E1-A3 can be formed. But it was not stated clearly. A simpler and more straightforward version of RLS is to consider only ranking, not the grants given to leaders.

This will get the exaclty same result in the DMPR process, if leaders follow the order of their ranking in picking. We will examine this because it is a case of both RLS and DMPR. If leaders do not follow the order of ranking, as it was explained in "Very challenging game", the outcome will be different. We will use the table with India being among the leaders, first without a veto and then with one veto.

In the first round, M3 is placed with C, E1 with I, A2 with A1 and R1 with E2. In the second round, R4 is in C's and A1's list. One way to decide is to follow the order of assigning. The other way is to choose randomly, each time a Group is in more than one Coalitions. The order of assigning could be C-I-A1-E2 since C and I have only two Groups. Another way is to select the order randomly, as in drawing numbers from a hat.

In the example, we will assume that the order C-I-A1-E2 is followed. So R4 should be replaced in A1's list with another Group. Third is R1 which has been already assigned to E2 in the first round. Fourth is E1 which has been assigned to I in the first round. Fifth is A3 which is available. So A1 gets A3 in the second round. Second in E2's list is E1 which has been assigned to I in the first round.

Third is M1 which is available. E2 gets M1 in the second round. So far the four Coalitions are C-M3-R4, I-E1-R2, A1-A2-A3, E2-R1-M1. In the first two rounds, China's and India's Coalitions are complete. In the next three rounds, only A1 and E2 will participate, since they need three more Groups in their Coalition. Sixth in A1's list is M2 which is available. Next in E2's list is M2 which was assigned to A1. M3 follows which is with C.

Number six and seven in E2's list are R4 and A2. R4 has been assigned to C and A2 to A1. Next available is eight choice S2. So in the third round, the two remaining Coalitions will be A1-A2-A3-M2 and E2-R1-M1-S2. Seventh in A1's list is M1 which has been assigned to E2. Eight is S4 which is available. In E2's list, A3 which is ninth place is assigned to A1. Last is R3 which is available.

In the fourth round, the two Coalitions will be A1-A2-A3-M2-S4 and E2-R1-M1-S2-R3. In the last fifth round A1 can't get R3 and S2 because they have been assigned E2. There are only two Groups left, S1 and S3. In the example, the lists of the leaders have only ten Groups. All Groups are fourteen. We show the rest of the list below, only for A1 and E2, since C's and I's Coalitions are complete. The final Coalitions would be C-M3-R4, I-E1-R2, A1-A2-A3-M2-S4-S1, E2-R1-M1-S2-R3-S3.

We will examine the same two tables with one veto. In the first round M3, E1, A2, R1 are assigned to C, I, A1, E2 respectively. Suppose that E1 does not want to participate in India's Coalition. E1 is NON PARTICIPANT in DECISION MAKING and has NO VETO. Western Europeans will be assigned to India's Coalition, even if they do not want. These are the negative consequences of insisting with manic obsession on a highly defective plan from the Dark Ages that has failed tremendously.

In the second round R4, R2, R4, E1 are assigned to C, I, A1, E2. For the sake of arguement, suppose that R4 is a participant in decision making and vetoes its placement in China's Coalition. We are not suggesting that something like that may happen. It is only used as an example. The same is true for the other vetoes that we will use as an example. We do not need to repeat it every time. These are only examples.

A veto will be as if the Group had already been assigned in another Coalition. It will make it unavailable. Next in China's list is R1 which has been assigned to E2 in the first round. Fourth is M2 which is available. Suppose that there are no more vetoes in second round. R4 will be assigned to A1, The four Coalitions will be C-M3-M2, I -E1-R2, A1-A2-R4, E2-R1-M1.

With out the veto, the four Coaltiions were C-M3-R4, I-E1-R2, A1-A2-A3, E2-R1-M1. Two of them changed and the other two are the same. China's and India's Coalitions are complete. In the next three rounds, only A1 and E2 will participate. In the third round, the next available Group for A1 is A3. S2 is for E2. After the third round the two remaining Coalitions will be A1-A2-R4-A3 and E2-R1-M1-S2.

In fourth round, next available for A1 is S4. Suppose that S4 vetoes that placement. The only alternative is to be in E2's Coalition. As it can be seen in E2's list, S4 is in the last place. Nevertheless, it is unavoidable to get it, as it will be understood in the coming rounds. S4's veto makes it unavailable for A1. Next available is R3. For E2, next available is S1.

Let's say that S1 vetoes as well. E2 will go down the list and get S3. After the end of the fourth round, the two Coalitions will be A1-A2-R4-A3-R3 and E2-R1-M1-S2-S3. In the final fifth round, A1 will get S1 that vetoed participation in E2's Coalition. E2 will get S4 that vetoed participation in A1's Coalition. The two final Coalitions will be A1-A2-R4-A3-R3-S1 and E2-R1-M1-S2-S3-S4. The assignments in rounds are shown in the table below.

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