Home Chapter3: Internet Excursions

# Internet Excursions

### Choosing Sides

Stop by your typical playground and sooner or later you will witness an earnest and often comic playground ritual: a bunch of players trying to divide themselves into two supposedly "evenly matched" teams for the purpose of having a game. This ritual, commonly known as "choosing sides," is at heart just another fair division problem (the objects being divided are the players and the "players" in the fair division game are the captains doing the choosing). A significant example of "choosing sides" known as the expansion draft occurs in professional sports when new teams join an already existing league: The new teams are formed by the owners (or their representatives) drafting players from a designated free agent pool of players—choosing sides, if you will.

With just two teams, the most common approach for "choosing sides," and the one used in most expansion drafts, is the single alternating scheme: X chooses, then Y, then X again, and so on. It is clear that under this method, you want to be X. A better approach is the double alternating scheme: X chooses, then Y chooses twice, then X chooses twice, and so on (Y choosing once at the end). It's not quite as clear here whether you would want to be X or Y—it depends on the situation. Over the years, many other variations of these sequential approaches have been tried, in an effort to find the one that produces the fairest division of the talent pool.

Recently, Brian Dawson, a mathematician, proposed a new approach based on a simple variation of the divider-chooser method. This new approach generally gives a fairer result than any previously used drafting method, and is called Dawson's draft protocol.

This activity contains 4 questions.

## How would you modify the single and double alternating schemes for the case in which the players must be divided into k teams (k>2)?

 To create paragraphs in your essay response, type

at the beginning of the paragraph, and

at the end.

## Explain the purpose of Step 3 in Dawson's draft protocol.

 To create paragraphs in your essay response, type

at the beginning of the paragraph, and

at the end.

## Describe a scenario under which the "chooser" (Owner 2) would want to exchange one of his players with a player from the waiver pool.

 To create paragraphs in your essay response, type

at the beginning of the paragraph, and

at the end.

## Describe two different scenarios under which the "divider" (Owner 1) would want to exchange one of his players with a player from the waiver pool.

 To create paragraphs in your essay response, type

at the beginning of the paragraph, and

at the end.