Minimal Trust Assumptions in trade require a discovery phase whereby the risk is unbridled and volatile. This phase establishes the TTP or disproves its existence. The design of a listening security design ready to leap into the water of risk needs to be formulated. A listening protocol to establish the parameters required for a TTP. New and undiscovered trades happen outside of the formal channels and work towards normalization only after a very expensive period of discovery.

In the case of the Islands only trading with their nearest neighbor -- the expense of discovery -- could also serve as an explanation. So the cost of discovery is the first cost and once the parties and goods have been established the formation of a Trusted Third Party can begin. The designs should be of the listening variety so that the black hole of TTP can be plugged due to its earned trust via the cost of discovery. So the cost to establish a TTP is a function of the profit potential in the goods traded, the danger or risk associated with the parties, and the length of time for discovery.

The equation hides within it the TTPs black hole scenario. How long did it take to establish this TTP? If the time value is too long then the trust is never firmly secured and arbitrary transactions become the norm. Who are the counter parties I must discover for a transaction? The trading in bones with cannibals presents too high a risk and the trading of grains of sand within an archipelago of sandy island worthless.

The value of the transacted goods increases the tolerance for discovery. The ensuing TTP from a network of trade must be part of the discovery phase but play the role of listener and monitor. The black hole in the security emerges because two parties of a transaction do not see the third party as an active participant but rather the assister to both parties of the trade. The more accurate the recording of the transactions and knowledge of the participants the more trusted the third party.

This epicenter of information has no monitor no governance and merely emerges due to the disputes and risk of the discovery phase. A good example of a mechanism deployed for a TTP is war. The parties of a war have decided to physically assault each other until the other surrenders or is killed. This step is a failure of the discovery phase to generate a tolerant TTP and the most arbitrary of TTPs is elected by default. Courts of law are similar TTPs when the trade discovery phase fails.

I suggest that in order to establish a security protocol that assures the participants of transactions of its trusted intent and ability to execute properly a successful discovery phase must occur. The designer of the security for the TTP and its inherent weakness for security must be derived from the parties of transaction that find the need and see the weakness. This phase is a secondary discovery and must provide the forum for the establishing of verifiable terms for the RRP to operate in. This birth of the third party is a conscientious effort to bring order to the potential of an arbitrary TTP method like war or courts of law becoming established.

Since trade is a private activity and can only be hindered by governmental friction or violence the matter of discovery over time must be documented in a private fashion and that information by the participants will become the basis of the discovery in a civilized manner. A body of written or verbal history is the core requirement for a successful discovery and birth of a TTP and the eventual quality of the TTPs activity and the need to plug a black hole. A civilized, democratic, and educated population can always plug the hole since they are actively crafting the TTP as a satisfactory alternative to chaos.

"A civilized, democratic, and educated population can always plug the hole since they are actively crafting the TTP as a satisfactory alternative to chaos."
LOL

Government produces all order.

Under anarchy there is no government.

Therefore anarchy is chaos.

Q.E.D.

(due to D. D. Friedman)

A future failed TTP its not listening
http://www.first.org/cvss/

Jim Nesfeild reminds me that, when a security designer does have to rely on TTPs, the optimal configuration of such TTPs can't simply be built in, but they later emerge in unexpected and particular ways. Yet another reason security protocol designers should not build in broad scopes of trust into their designs. If they do, chances are good (as with random mutations in evolution) that the assumed institution will fail. To the extent one must assume some trustworthy behavior, it's a good idea to re-use specific existing TTPs (or at least existing patterns whereby virtual TTPs are constructed, such as the separation of duties and the principle of least authority) and a bad idea to try to make up a new kind of TTP from scratch. The worst thing of all is to simply postulate some unspecfiedly broad "trusted third party." This is basically an admission that you have no idea whether or not your protocol is secure.

Ian, much thanks for your encouraging comments. I think your description is good, keeping in mind what I have described is an abstraction that doesn't reflect many of the potentially important details of the kula (a major hazard in any social or historical science, alas). I think the "no trade" island is a good stand-in for an island that is simply much smaller in population or doesn't have very many complementary trade goods.

As for why collectibles rotate in the first place, remember that the function of collectibles and money in the first place is to lower transaction costs, especially costs from the non-coincidence of needs. The informal argument for specific cycles starts with the observation that higher-velocity collectibles are more efficiently amortized, because they save transaction costs on more transactions. When collectibles get "stuck" with somebody who has no opportunity to spend them further, this reduces this efficiency. Therefore in a high-transaction cost world characterized more by bilateral monopolies than efficient commodity markets (what I describe below as a "sparse flow network"), specific cycles will form that keep the collectibles moving. I also argue that large cycles will tend to be more efficient than shorter cycles.

Here's a stab at setting up a formal argument (drawing from graph theory and in particular network flow theory):
(0) Definitions:
"transaction cost velocity" of a particular collectible = "TC velocity" = sum(transaction costs saved in each transaction by using the collectible)/time) in a (potentially cyclic) transaction flow network.

"transaction flow network" = a cyclic directed graph along the arcs of which collectibles flow, with each arc weighted by the transaction cost savings from using collectibles for that transaction.

(1) The efficiency of collectibles are maximized when the TC velocity is maximized (when the collectible circulation is "TC-fast.") Nevertheless, due to other high transaction costs that collectibles could not address, hunter-gatherer and neolithic collectibles were far TC-slower than modern money.

(2) Observe that TC-velocity is impeded when collectibles are received by a particular party and not transacted further.

[this is an inuitive step but almost surely can be proven:]
(3) In a sparse flow network, TC-velocity is maximized when flows occur in cycles.

[another intution to verify empirically]
(4) Given a node B with two neighbors A and C, where the complentarity of goods between A and C is different from that between B and C and the trades with A and with C occur at different times of the year, the average velocity is higher for 3-cycles and 2-cycles.

[an argument by induction leading to this conclusion:]
(5) The larger the cyclic, the faster (on average) the TC-velocity. To prove this, I'd have to prove (4) and prove that given truth of (4), in a random graph cycles of size N+1 have a higher average TC-velocity than cycles of size N.

This way of looking at things may be of some practical value to financial cryptography. The lowering of transaction costs on EBay (taking credit cards is too expensive for very small businesses, e.g. when you just want to sell a handful of items on EBay) explains the success of PayPal, though in other ways the formal model may be very different than for collectibles (e.g. the costs being amortized are very different, and the network flow is simply spoke-and-hub.). If on the other hand one is marketing an actual alternative currency, and the cost to the issuer of redeeming that currency is significant, then the currency is much more efficient if it is used in specific cycles rather than having to be redeemed frequently. This makes initial marketing of the alternative currency very difficult unless specific transaction cycles that benefit from the currency are identified. Specific monetary cycles are an exception to the otherwise nasty problem that the value of a network generally tends to be the square of the number of nodes.

Thinking about marketing alternative currencies is how I thought of this theory in the first place, but it turns out also to be very good description of pre-efficient-market proto-money (what I call "collectibles") worked. (Recall that Carl Menger described the money as emerging in an already efficient commodity market, which gives good insight on the function of money but is ahistorical. Collectibles, which one may or may not choose to call "money," were very useful and much used long before there were any low transaction cost markets).

In step (4) above "and" should be "than":

(4) Given a node B with two neighbors A and C, where the complentarity of goods between A and C is different from that between B and C and the trades with A and with C occur at different times of the year, the average velocity is higher for 3-cycles than 2-cycles.