Ideas of possible technical details for the trust system

(The below description is a mere draft; it presents different possible ideas among which some choice will have to be made).
In a first step, is the question of how users can enter the data of trust declarations. Here is a description of a method based on the contacts list.

Declarations of trust between users

For the following, each user can decide for each of his pseudos if it will be a "protected" pseudo or not. The meaning and use of this is described below.
Each user has a list of contacts, that is, pseudos of people he corresponds with. (So a "contact" means a pseudo of another user). One can access an information page about a contact by clicking on it in the contacts lists, or when it is not yet listed, by clicking on it as the pseudo author of a message one reads (and this way one can add it to the contacts list).
This info page shows what oneself decided about this contact, and some information that the computer tells about it, as described below.

One can declare to the computer, then possibly modify later but archives will be kept for a while, the following information:

A relation of trust given, with two variables : x,y with values in the below set of trust values, where x is a pseudo and y is a contact (i.e. someone else's pseudo that this user knows), which says: "I, under the name of x, declare this trust to y".

To each contact, a user may optionally attribute different kinds of trust : possible attributes, more or less independent of each other (but complaint of a kind is not compatible with trust of another kind):

General ideas about trust and distrust

There are different possible definitions to be considered because conflicts mean there are contradictions in the logical system:

Then, the web servers will compute the transitive relation generated by the relation of valid trust declaration, for giving each user the possibility to see (when displaying someone's info) if he indirectly trusts someone or not. This question need not update every minute, but every day is OK. For this, it may be useful for the servers to regularly (every day ?) make a map of all users by equivalence class, where 2 users are in the same class if one indirectly trusts the other and conversely.

But the opposite information needs to be shared too:

This raises the problem of how can a self-contradictory logical system provide answers anyway.

One problem will be to anyway compute something about indirect trust towards a given pseudo (author of some information, or possible partner for any transaction) while the contradiction is not resolved yet.

Another problem is to resolve contradictions by means of complaints system : when 2 users who both received indirect trust, contradict each other about a third person, then the people involved in the chains of trust to them must be involved in the discussion and choose which side they support. Two people supporting different sides cannot trust each other anymore, so that any trust declaration between them is cancelled.

So, a trust declaration is worthless if it is not done in a responsible manner. To be responsible, the person giving trust has to be informed about possible conflicts in which the person may be involved, in order to take part in the debates (trials) and eventually remove his trust declaration. Also, we shall automatize the fact of disagreeing with the people who choose another side, while giving it a more anonymous form (with a concept of conflict of opinion with someone about a problem not directly involving him but only someone else), and making complaint automatically symmetric.

However, a user may not accept anyone "trusting him" to get informed about conflicts he may be directly involved in, as this would constitute a breech of privacy, while he can accept to take the responsibility of his opinions about somebody else's troubles. First, the spread of information about one's own conflicts can be a breech of privacy in itself (especially in the case of a small conflict, not a serious one, that might eventually be just a test, and can be solved easily between a few people) ; only serious conflicts where many people agree with the complaint, should be made public. Second, the mechanism of involvement brings a risk to the privacy of the information of which pseudos belong to the same user: if you are owner of two pseudos A and A', then a spy could discover this fact by declaring trust to A while (his friend) makes a foolish (testing) complaint against A'. The immediate, automatic involvement of those directly trusting A as the first invited participants in the trial, would be a way of revealing that A and A' are the same user. For this reason, we need to develop the following

How to manage the multiplicity of pseudos per user in the computation of indirect trust, to respect privacy

The idea is to let a user taking part in a conflict, choose which of the people trusting him will he invite to join the debate, in hope to get his support, with the risk to not get his support but to lose this trust instead.

I first imagined this choice to be made in advance, while the invitation during the conflict would be done automatically as determined by this prior choice :

Each user Y can see the list of trust declarations by anybody else X (displayed in Y's board in the form of some pseudo x of X) to any one of his own pseudos y. For each such declaration, user Y can choose to Receive or not Receive this declaration. If he chooses to receive it, then it is first received by the pseudo y to which X addressed this declaration, but then Y can choose to apply the reception of this trust declaration by X to his other pseudos as he chooses (y', y''...) as well.

Then, indirect trust is defined from a user A to a pseudo y, by the existence of a chain of trust :
A → B →...→ W → X → y
for any users A, B, .., W, X disregarding which pseudos of each user are involved, and whether these trust declarations are marked as received or not; but only the last trust link X → y needs to carry reception of this trust declaration from X to y, by the owner Y of pseudo y.

Anyway, except for the last link of the chain, pseudos of the same user can be confused and trust needs no confirmation of acceptance because :

For each user inside the chain, say B in the chain A → B → C →, it will not matter that he received trust from an unknown A to one of his pseudos b while he declared his trust to C next under another pseudo b', because if he intervenes in the conflict (participates in the discussion) he will do it under neither pseudo b or b', but under a third pseudo b'' ; only A might know that b and b'' are of the same user, while only C might know that b' and b'' are of the same user; they should not share this information (even if they share it together they still should not publish it), so that the information that b and b' are of the same user, remains private.

(Note: Can Y be the same as another user in the chain, for example Y=W ? Does it even matter whether other users in the chain from Y to y, such as X, are real or if they are virtual, created by Y ? I think it makes no significant difference : it only has the effect of delaying the time when someone trusting Y is involved, and will know that he is invited due to his trust to W(=Y), and may or may not guess that W is direct part of the conflict (W=Y)... only a little bit later, compared to the case if Y accepted to receive this trust to y right from the start)

But there is another solution

That is to let someone taking part in a trial (= online debate about a conflict), to take his own initiative of who he will invite to join, among the people who trust him.
I had first ignored this possibility, but considered invitations (of participation in the trial) to be automatically sent at regular time intervals to any people who trust those who took part in that trial on each side, as long as such further people exist on both sides (otherwise there is a winner, who remains trusted while the loser lost his chains of trust), because without such automation, this process would have the risk to last forever without solution, one side being a group of hackers preserving the chain of mistaken trust to them, by not challenging it by invitation of members of that chain but inviting instead an endless list of fictional users (accounts of people who don't exist but are automatically generated by malicious software) to "support" them.

Finally, I consider another solution against this risk, by the following method:

The real identities of supporters of each side are known by their host but not published; only the number is published.
More precisely, each host publishes its the number of supporters on each side among its own users.
You may ask : what if a host is malicious and publishes a number of supporters on a side that does not fit the real number of his users actually supporting that side ?
Reply : if a number of supporters of a side published by a given host gets big and a suspicion is raised about its reality, we can verify this number by the method of online voting that all users of that host will be requested to take part in.

Complexification by different types of trust - the case of memberships

There will be standard trust, but other kinds of trusts will be handled in parallel according to the same (or different) logic. So, different kinds of trust are classified by logical structure (format of declarations with list of options, kind of computation on the graph, kind of interaction between these data and debating spaces) and label (meaningful for humans but just a label for computers).

One possible kind (logical structure) of trust, is memberships (or is there a better word ?). Any user can create a (label of) membership. Examples of memberships can be "having the True Faith", "being a genuine scientist" (= not a crank), or many other purposes where people need to identify the genuine members of their group. It is another graph of trust which is computed the same way, with
A membership can be public or private. If it is public, it gives non-members the possibility to view this trust towards people from the viewpoint of some existing member (who accepted this).

How to give values when trust declaration are mixed with complaints

A first approach would be to consider the following definitions:

But things may be more complicated. For example, what can happen if we have the chains of trust

A→ B → C

D → E

but E distrusts B, and C distrusts D ? If we accept the indirect trust from A to C as valid then this eliminates D from A's trust, and thus makes the indirect trust from A to E as invalid; however we have no more reason to reach this conclusion than to accept indirect trust to E as valid and thus reject trust to B as invalid. So we need more subtle definitions.
But, how likely is this kind of graph of trust, to happen in a large population ? If C is in fact honest then there should be high chances to have other chains of trust from A to C to confirm his honesty. However, if E is mad (or, for example, a fake user created by D), he could have created conflicts with everybody in order to affect other chains of trust from A to C as well, extending the same kind of configuration to parallel branches in the graph of trust.

Sides and complaints

A complaint opens a  disputes between opposed sides in a online forum. Members of the chains of trust that lead to either sides, can join and choose their side in the dispute, until one side "wins", as the losers lost the trust they had received from others before..

In details: A complaint requires to start from:
- either an existing private forum where the person was involved, which will be transformed into the debate space
- or anything where someone made an action, that will be the object of the complaint; then the debate will be created with reference to it.

First step is warning.

It has an explaining text or message, that is the start of debate, that the accused person will see (linked to) on his board (like any signal of a new message, but marked with this warning). This has no public effect on trust, but is there to give a chance for any misunderstanding to be resolved between the concerned people before any other people will be involved.
The warning can be cancelled by the person who did it if the problem is resolved, or, after some delay (one day or week ?), it will be possible to switch to the next step, making the complaint public.

Second step is open conflict

This has publicly visible effect on the trust information to the person.
Both people in conflict will become respective centers of a pair of opposed sides. At first, each side has one member: the complainer and the accused person.
These first two people, who have a dispute, will each be the head of one's own "side".
More people, that is, those who had made a trust declaration to anyone involved in the dispute, may also join the dispute (if invited by the one involved) and choose their "side".

Pairs of opposed sides modify the trust computation, in the following way.
For each pair of opposed sides, each user can choose to be either neutral (by default everyone is neutral) or supporter of (only) one of both.
Suppose there is only one pair of opposed sides (if there are several, the below definitions would have an exponential complexity of computation with respect to the number of such pairs, but there may be a more computable approach as well).

The one graph of normal trust will be replaced by 2 graphs of trust to be computed independently: one G that is the graph of trust relatively to one side, that excludes the supporters of the other side, the other G' excluding the supporters of the first side, that is the graph of trust relatively to the second side.

Now to the question, that a user A may ask in the network, whether he indirectly trusts B, 2 possible answers might be considered depending on which side is right:
Then the question is to choose between them, or may we be interested to know both answers. Of course, supporters of each side can look at the graph of trust relatively to their own side.


Previous drafts of ideas, maybe to be discarded

If there are N pairs of opposed sides, it would not be rational to compute another graph for each of the 2^N ways to take sides. A possible idea is for each pair of opposed sides, to have 2 graphs of trust as if nobody took any other side, and also a synthesis into one graph or relation, for computation by another server busy with another pair of opposed sides. But to make computation approach approximately the taking into account of an opposition when computing other opposition, we will consider as invalid any trust declaration between supporters of opposed sides.

The invitations to the forum, of the trusters (which means, a pseudo y such that C(y,x) = Trust ) (or a subset of this set, decided how ??) of supporters of the involved sides will happen progressively (at which rhythm ?) depending on whether participants consider that they need to extend the conflict, or whether they are many enough and just need time to debate.

The conflict can run into the following states, to be chosen by heads of sides: to be weak (without effect on trust, but just for debating and clarifying problems), then medium (with this effect on trust), then strong (with public note on profiles visible by anyone in none of G and G'.
But we can also consider the possibly for a user to support a side weakly or strongly, in the same spirit (this complexifies the trust calculations as sides will have strong supporters and weak supporters).

(Eventually, if the dispute becomes big, each side may need to structure itself by a memberships for writing a document, for example a wiki, of arguments for the defence of this side).

(Here is a previously considered algorithm, possibly worthless)
Compute the preorder relation T1 generated by trust declarations between users.
For each user x, compute the set of pseudos z indirectly distrusted by x, that is, Z(x,z) if there exists a pseudo y with T1(x,y) and y made a strong complaint against z.
Then consider the indirect trust defined by the chains of trust from x that avoid users indirectly distrusted by x in this way, that is a new relation T2(x,y) as "Clear indirect trust by x to y".
So, when x sees the pseudo y, the status of y is displayed, be it T1(x,y), T2(x,y) and the text of the complaint against y if Z(x,y).

Complexification by network of independent servers

A problem is for a server to handle tens of thousand users without saturating the server resources (cpu and memory). It would be possible to have the result in a rather compact form made of the list of equivalence classes of users (or pseudos) so that two users A and B are equivalent if there is a chain of trust from A to B and from B to A.are chains of trust both weach is trustworthy from the point of view of the other.

Another problem is to extend the graph to millions of users by combining the trust declarations from different servers.

In short:
The trust system will work as a combination of the data of the local graph of trust between users of the same host (working inside the "black box" of the host, therefore with no need of electronic signature) and the web of trust between different hosts (with electronic signatures).

In details:
The site publishes (with signature) the subset of the ordered set defined by quotienting the set of users by the equivalence relation of the preorder generated by the trusting relation.
Hopefully this ordered set is made of only one element, so that there is nothing publicly revealed of the internal structure of the site.

Each server will first make the map for trust relations among its own users. So, for the subgraph of trust between its users it computes equivalence classes and publishes it for other servers, without saying how many people in each class, but only as the list of abstract ids of classes which contain users who received a trust by a user of another server (the classes who receive no trust by outside are known but stay invisible in the published map).
So it publishes a list of abstract ids with the info of the relation of indirect trust (by internal chains of trust) between classes, and of trust from its own classes to the classes of other servers. Then, when a user A wants to know the trust to a user B, A's server requests B's server about which class B belongs to, or if B is not in a published class, which classes trust B. Then uses the union of graphs of all inter-site trusts and local trust.

Declaration of any trust or anything else between members of different sites are published as "a member of this class here trust a member of that class of that other site".

Maybe not useful: computing the shortest path between 2 points ?

If N is the number of users, we can define for each user two tables with slightly more than sqrt(N) entries made of
1) the people he indirectly trust,
2) the people that indirectly trust him,
by chains of trust no longer than a certain number. Each table gives the parent and the length of the chain from the considered user. Then, to find some shortest trust chain between 2 users we just need to see (if one is not already in the other's list), what names appear in the two tables. But most of the time, what will be needed is not all the trust chain but the first and last elements of this chain. So, we can put in the table of user x, for each user y that has a trust chain of length no longer than () with x, what are the end elements near x and y, for the chain of minimal length. Unfortunately, it may not be unique.

A possible further development about credit

The following quantities can be computed about a user y for the account of a user x:

One is the affordability, that is, how much y could afford to pay to x at a given time as defined in the theory of credit, when not including the trust reserved credit as a credit. Note that this affordability relation is transitive, in the sense that the affordability of x towards z is always higher than or equal to the minimum between the one of x towards y and the one of y towards z.
One is the reliability, which is the same as affordability except that it includes the trust reserved credit among credits (so, it is higher than affordability). This quantity is also equal to how much x can obtain to be paid back for damages done to him by y once y will be complained against if x did not make mistakes in his own trust declarations.

For concrete details about how trials can be processed, see among the comments about Google Wave