Drawing straws

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Drawing straws is a selection method that is used by a group to choose one member of the group to perform a task after none has volunteered for it. The same practice can be used also to choose one of several volunteers, should an agreement not be reached.

Process[edit]

The group leader takes a number of straws (or similarly long cylindrical objects) and ensures that one of them is physically shorter than the others. The leader then grabs all of the straws in his fist, such that all of them appear to be of the same length.

The group leader offers the clenched fist to the group. Each member of the group draws a straw from the fist of the group leader. At the end of the offering, the group member who has drawn the shortest straw is the one who must perform the task.

This practice is epitomized in the cliché "drawing the short straw"—to mean being randomly, unluckily, or unfairly selected to perform a task, at the risk of suffering a penalty.

Probability[edit]

Drawing straws is a fair game, every participant has a \tfrac{1}{N} chance to draw a short straw and \tfrac{N-1}{N} chance NOT to draw it, where {N} is the initial number of straws before the drawing starts.

For example, the chances of the second person to draw the short straw are the product of the chances of the short straw NOT to be pulled out by the first person: \tfrac{N-1}{N}, and the chances of the second person to pull it out of the smaller (by one) bunch of straws: \tfrac{1}{N-1}. The multiplication gives: \tfrac{N-1}{N}\times\tfrac{1}{N-1} = \tfrac{1}{N}.

For the fourth person the chances to draw the short straw are a product of chances of the first three people consecutively NOT pulling the straw out and the fourth person to draw it afterwards (the size of the bunch gets progressively smaller by one for every next person): \tfrac{N-1}{N}\times\tfrac{N-2}{N-1}\times\tfrac{N-3}{N-2}\times\tfrac{1}{N-3} = \tfrac{1}{N}.

The fact that it's more likely to draw the short straw from a smaller bunch is perfectly compensated by the chance of somebody else pulling the straw out before you.

Politics[edit]

United Kingdom[edit]

In the United Kingdom, if a local or national election has resulted in a tie in which candidates receive exactly the same number of votes after three recounts, the winner can be decided either by drawing straws/lots, coin flipping,[1] or drawing the high card in a pack of cards.[citation needed]

See also[edit]

References[edit]

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