# Example Algorithms

Some Social Algorithms:

• One Divides, the Other Chooses
• Final Offer Arbitration
• the Gerrymander, a Mythical Beast
• Disputed-Area-Only Self-Determination

The first three of these are well-known social algorithms. The last one, Disputed-Area-Only Self-Determination may also be a well-known social algorithm although the author of this page could not remember hearing or reading about any such algorithm and was therefore forced to reinvent it.

## One Divides, the Other Chooses

To stop two little boys from fighting over the last piece of birthday cake, cut it into two equal pieces. The beleagered parent should not divide the piece of cake in two, or the boys will blame the parent for unfairness and continue to argue over which is the biggest piece and who should get it. Instead, one boy should cut the cake and the other choose his piece. The second boy (chosen e.g. by flipping a coin) is explicitly entitled to choose the bigger piece if there is one, so the first boy is strongly motivated to cut fairly.

## Final Offer Arbitration

A surprisingly subtle and effective arbitration algorithm to resolve disputes such as those in salary negotiations. After discussion of options, each side is constrained to produce a final offer and the arbitrator can only choose one of these final offers.  Each side is therefore strongly motivated to script as offer which are not only realistic but actually fair. Finding an arbitrator who is acceptable to both sides in the dispute is a non-trivial problem, but has proven possible in practice. Assuming a fair-minded arbitrator, each side is strongly motivated to propose a solution which the arbitrator will choose as “the fairest of them all”, so each side competes for what they want by searching for solutions which have few outrageous demands and many equitable trade-offs.

## The GerryMander

To ensure the election of candidates from the desired political parties, electoral boundaries can be carefully chosen to follow the contours dividing regions of differing political opinions. For example, by slicing away the largely white middle-class suburbs of large (black, working-class) American cities such as Baltimore and finding the often narrow corridors which can join such fragments into strangely shaped regions of the appropriate size for electoral districts, it is possible to arrange for black inner-city voters to be represented by black politicians from these districts.

Once common in American politics, the salamander-shaped electoral district has been ruled unconstitutional and is now supposedly extinct in that country — it is now only a mythical beast. But perhaps like the Sasquatch or Loch Ness Monster, rumours of its extinction may be somewhat exaggerated. Some strangely shaped constituencies still exist and it remains difficult to prove that district boundaries have been chosen without any attempt to influence the outcomes of elections. There are also strong arguments in favour of some gerrymandering to improve the chances of candidates from minority groups. A moments thought should convinced the appropriately educated reader that the division of a geographical region into electoral districts that are “fair” (or that do some gerrymandering) is a combinatorial optimisation problem that cannot be solved by committees or courts of law.

## Disputed-Area-Only Self-Determination

(There must be a better name for this algorithm!)

Self-determination in which resident voters of a geographical region could choose which of two neighbouring nations they would be a part of was enshrined in the charters of both the United Nations and the earlier League of Nations. It did not prove very effective and was rarely used. One reason it failed in practice was the difficulty of defining the region which would take part in this plebiscite or referendum. But there is a simple algorithm for solving this problem Each of the two neighbouring countries can be allowed to claim any or all of the region whose fate is to be decided, with the understanding that only the residentsn of areas claimed by both nations will get to vote on their national affiliation.

Like the other social algorithms described above, this disputed-area-only form of self-determination includes a mechanism for making each participant act fairly whether they want to or not. If a country claims more territory than it has resident voters to support, it decreases its chances of winning at the polls. If India claims all of Kashmir and so does Pakistan, whichever country has the most partisans living in Kashmir would win, and therefore the other country would do everything it can to prevent this ever coming to a vote. But in self-determination using Disputed-Area-Only (DAO) voting each country would be strongly motivated to claim only a part of Kashmir — a part settled mostly by people of their nationality. If they claim too much they thereby enfranchise many voters of their opponent’s nationality.

This DAO algorithm is not actually intended for resolving the status of a large area like Kashmir in a single appeal to the electorate. It should be applied piecewise, settling disputes for smaller portions of the territory, which may then remain settled or may participate in future iterations of the process.

(This is just a crude sketch, which unfortunately makes a simple but effective algorithm sound complicated and probably ineffective. These failings will be remedied on a future page dedicated to this topic).

### Notes

• this page exists partly to provide examples of social technology other than social network optimization
• the four examples on this page will each get a page of their own when time and energy permit
• the author of this page invented the fourth (Disputed-Area-Only Self-Determination) algorithm but acknowledges that the underlying idea is an old one and what seemed like invention was almost certainly reinvention