Negative trust

If you calculate trust by simple multiplication of percentages, trust quickly reaches near 0 as you get away from the central node.

For example:
 * Alan trusts Bob 80%
 * Bob trusts Charlie 65%, so Alan trusts Charlie 80% x 65% = 52%
 * Charlie trusts Donald 50%, so Alan trusts Donald 52% x 40% = 20%
 * Donald trusts Elaine 75%, so Alan trusts Elaine 20% x 75% = 15%

You can see from this simplified example that after a few links, you're approaching 0% trust.

Zero Trust
If you assume 100% is complete trust, what is 0%? Is it absolutely no trust? What about negative trust? Is it possible to mistrust somebody? That is, trust somebody less than a perfect stranger (who we assume is neutral trust).

If you say no, that it's not possible to negatively trust (distrust) someone, then 0% trust becomes neutral trust. In this scenario, the simple multiplication models works.

However, if you say yes, it's possible to give somebody a negative trust rating, then the simple multiplication model does not hold up.

This is a question to which I don't currently have a satisfactory answer. Callum 10:08, 24 September 2007 (PDT)

Conclusion
Update: I've considered the situation and decided negative trust or distrust is definitely necessary. I came up with the following example which answered it for me.

Scenario: Email servers trust each other based on the number of spams they send. One good email, +1, one bad email -1. Server A has received 10'000 messages from server X of which 2'000 are spam. Server A trusts server X +3'000. Server A has also received 10'000 messages from Server Y of which 8'000 are spam. Server A trusts server Y -3'000. Thus trust must be expressed on a scale that allows both negative and positive numbers.

Multiplication
If you consider positive and negative trust to be either side of 0 and expressed as percentages (-100% to +100%) then positive trust values can be calculated using simple multiplication. Trust descends towards zero (neutral trust) as you get further away from the originating node.

However, this doesn't work so well for negative numbers. They cannot be multiplied in the same way. I'm working on some ideas for how negative trust values might be calculated. I'll update here if I come up with anything that I think can work. Callum 12:57, 24 September 2007 (PDT)

If trust is on the scale [-1, 1] you can easily multiply values. I.e. Alice distrusts Bob with -0.5, Bob distrust Clarence with -0.5, multiplying gives 0.25, which could make sense, since a fiend of a fiend could be your friend.


 * That's an interesting point. An enemy of your enemy is your friend. I think that if A distrusts B -0.5 and B distrusts C -0.5 then A distrusts C -0.25. That's what instinctively makes sense in my head, but I'll give it some more thought and see if it holds up.Callum 15:06, 24 September 2007 (PDT)