One of the remaining parts to study about uCoin protocol is WoT algorithms.

With a few talks on the chat, it appears that WoT algorithm implies several consequences: minimum community size to exist, maximum size, and community growth speed. Probably non-exhaustive list.

So here is the subject: which algo to choose for which currency?

Given the following data:

We are dealing a space-time referential:

Space = members

Time = t

We have authentified members(t), members(t+1), …

We have authentified links(t), links(t+1), … between them

Here are few hints for algo rules:

maximum step (the maximum distance between two members)

quantity of links (in space and time)

quality of links (not 2 times the same link, age of the link, …)

Example: 30 members community

Each member must be recognized by at least 2/3 of the members

Example: 1.000 members community

Each member must have at least 20 links, with 2 years max old

Example: 10.000 members community

Each member must have at least 20 links, with 5 years max old

A link cannot between 2 members cannot be updated or repeated

must have n links available with 5 available members (space)

The Wot(t) is registered, since to be available, a new link must avoid the duration limit member repetition (spacetime integration control).

No sign with a 2 (or 3) graph steps is available (new sign must be done by people too far from the previous signs) = Limit of trust. (Humanity is connected with something near to 4 - 5 steps, not more, study Graphs Theory).

I understand here that a same link between 2 members must not be repeated to increase its duration. With a possible repetition after each link’s validity + a waiting period, however.

Yes, this is the point. And so, to obtain a new valid sign, must be a member different of the past 5 years signs for the member, and so in fact a member with step > 1, if we define step 0 = the member, step 1 = the members who signed him in the past 5 years.

Consequence : if we need a spatial number of valid signs, so at “t”, something like 7 valid signs for “living proof” at “t”, and 5 years or temporal validation, it means you always need, passed the 5 first years within the community, 7 x 5 = 35 valid signs.

And much more, with these data now, we know he will necessary need other 35 new signs for the next 5 years, so the community will need at least 35 + 35 = 70 members to exist within 2x5 = 10 years.

So being ts the time signing temporal control, Ns the Number of People to validate the living proof at “t”, we have

Ns.ts signs after ts within the community

2.Ns.ts people needed minimum within the community

Are you sure about second 35 signatures? I mean, with a 5 years temporal validation, it means the signatures made 5 years ago may be used for the 6th year: so we only have a 1 year validation rolling, which represents 7 signatures.

So in the end, with 7 spatial signatures + 5 years validation, we need 7x5 + 7x1 = 42 members to exist within 6 years, leading to (1 + Ts).Ns minimum people number within the community.

What’s the point? It is to see that a step (a link between to individuals) have kind of strength property: a link between you and your wife is not the same than a link between you and someone you met once in a conference. The first is stronger than the second, since you are closer to your wife in your every day life.

So, we can call weak a link done with someone you are not close to, and strong a link with someone you are ver close to. What the article says is: weak links make bigger communities, since you can make higher distance links.

To conclude, with a 3 steps constraint we could easily reach 10k members communtities, but 100k are not that hard to reach too.

Just a thought, please correct me if I’m wrong: if a minimum number of signatures is needed for a member, a maximum number may also be needed. Without this maximum the potential benefit for sybil attackers could be too high: whatever the minimum number N of signatures needed, N people can take the risk to collude in order to create an (potentially) infinite number of fake identities.
But this maximum number must be chosen wisely: with a number too close to N, it restrains the network from growing by the addition of new legitimate users; with a too big number, it becomes tempting for attackers.

This leads to another aspect: what about dynamic rules ? Rules are subject to change within time for a growing community. Could these rules be themselves part of the blockchain ?

As a quick answer: why not, we have to think a bit more about which rules to choose for the WoT.

But to be a bit more balanced, here is a little paragraph about max. distance rule which may already help us.

The max. distance rule

Any member must be at maximum n steps from any other. That is, if we have a -> b -> c -> d, then d may join the WoT since it is recognized by a. But a e individual could not join if we only have a d -> e, since e would be distance 4 from a.

It seems n = 3 is a good tradeoff to have communtities of ~100k members. Over 3 might be difficult to still have trust, but this is another debate.

Requires distance 2 members

Anyway, making fake identities with such a rule implies the fake identity to be signed by members with distance 2 from other members, since signing someone adds a step for others. So, such cheating people have to be step 2, or at least find others step 2 which will accept to sign the fake identity.

Is combo with signature delay

But then you also have the other rule avoiding signature repetition in a given period. This would imply cheaters to find other people to participate to the cheating.