Mathematical No-risk Trade Resolution Tool

This is a tool to help resolve the "mathematical" or no-risk trade lists used on boardgamegeek.

See: How no-risk trades work, How this tool works

How No-risk Trade Lists Work

For an initial period, people can add "offers" to the list.
Once offers are closed, all users submit a ranked list of other user's offers they would be willing to trade for their offer.
These Rankings will be in order or preference, but should only include other offers they'd be willing to trade. If you do not want the other offer in trade, do not list it.
If you do not care to trade for any offer on the list, inform the moderator.
The moderator will use this tool to submit those rankings (see below)
The offer which appears on the most lists will get first selection (ties broken by ranking of the offer)
The evaluation will continue in order of the most frequently ranked offers.
This tool will provide a complete list of all the resolution rounds and the final trades.

How to use this resolution tool

In the text box below, list each person and their preferences on one line. List each persons username (removing any spaces) followed by a space separated list of the usernames of the offerers they are interested in, in order. For example, if Matthew is interested in the offer of Scott or Derk, Derk is interested in the offer of Brett or Alan, Scott is interested in the offer of Derk only, Brett is interested in the offer of Alan, Matthew or Rick, Rick is interested in the offer of Alan, and Alan is interested in the offer of Matthew, Scott, Rick, Brett or Derk, in order, you'd enter:

Matthew Scott Derk
Derk Brett Alan
Scott Derk
Brett Alan Matthew Rick
Rick Scott
Alan Matthew Scott Rick Brett Derk

This would result in Derk sending to Scott who sends to Matthew who sends to Alan who sends to Brett who sends to Derk. Everyone is happy, except maybe Rick, but he didn't gain or lose anything. Sometimes, due to exact ties (exact same number of rankings with the same relative rankings) there may be ambiguity, in which case one outcome is selected randomly. In this case, I recommend running it a few times (hitting reload after submitting is sufficient) and choosing the outcome that yields the most trades, but this is rare.

The current default (and most popular) algorithm is the "Maximize Trades" algorithm. A lot of people have been curious how it works, so I have a poorly written description of how it works.