[EM] Johnson, Sunak, Mordaunt Monty Hall (Three doors) problem

[Richard Lung]

Tory leader contest as the Monty Hall problem (three door problem).
 

The three door problem (associated with the compere Monty Hall) presents a contestant with three doors. One door hides a car and two doors each hide a goat.

The contestant chooses one door, left closed, and the compere opens another door, revealing a goat. The contestant knows the car is behind the door he has chosen, or the other door still closed. Does he stick with his initial choice, or choose instead the other unopened door?

The Tory leader contest for one of three candidates, Rishi Sunak, Boris Johnson, Penny Mordaunt. The future leadership abilities of the three candidates are unknowns, like the three blank doors.

Sticking with the former deposed leader, Boris Johnson, is equivalent to not changing ones choice of door, leaving the contestant with a one in three chance of winning the prize of best leader.

The compere opens another door, to reveal either Sunak or Modaunt – it doesn’t         matter which, because, like the blank doors, they are both unknown leaders. If the contestant changes choice of door, he will get either a Sunak or Mordaunt door. Even tho we don’t know which is the prize leader, there is a two thirds probability of winning that prize, compared to a one third probability of prize-winning, by sticking with a choice of the Johnson door.

This three doors rigmarole is perhaps not quite the same as saying, if you choose either Sunak or Mordaunt, instead of Johnson, you are likely to have a 2/3 to 1/3 probability of success.

That is because sticking with the same choice, Johnson, does not improve the one third probability of success. Whereas changing to one of the others, without knowing or asserting their relative merits, improves the probability, of successful choice of leader, to 2/3.

 Regards,

Richard Lung.

https://www.smashwords.com/profile/view/democracyscience



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