This is a post I first wrote in the Italian Blog. But I think it might be of interest also to the English speaking readers.
The decision making system where everybody who is present can vote is called direct democracy. And it is universally considered a democratic system.
The decision making system in which each person can delegate its vote to someone else, but this one can delegate someone else (and the mandate received), is called proxy voting. And the kind of democracy that comes out of it is called “liquid democracy”. This also is considered a democratic system.
The system that me and Daniele Gewurz were suggesting, in which the mandate of a vote is worth for is between the direct democracy system and the liquid democracy system.
If we want to express this in equations (and we definitely would not miss that, right!) if x is the number of people that mandate someone, in a direct democracy we would have v(x)=1 (for every x); in a liquid democracy we would have v(x) = x+1; and in the non linear weighted system we would have for .
In other words the non linear democratic system is clearly in between among the two systems, both accepted as “democratic”.
To be pedantic, we could object that this is not enough to keep it Democratic. If, for example, the new system did not act in a symmetric way. In other words did not act symmetrically by not treating all the participants in the same way, but we would let some people mandate others and some not, then we could say that the system is non democratic. But this is not the case. Sure, the vote of the people who are absent is weighted less than the vote of the people who are present. But since Direct Democracy (where this vote in not counted at all) is accepted as a Democratic System, the fact of counting it less cannot change the Democraticity of the system.
This concludes the defence on this point. I would like to make some other considerations.
Democracies are not suche because they permit to people to vote on things. Democracies are such because they prevent a series of possible development that could make their system un-democratic in time. Often to do this they lightly sacrifice what people are allowed to do, to make the system more stable. From this point of view systems are not democratic or undemocratic, but are more or less democratic, and more or less stable. Depending how faithfully do they represent the will of the people, and if they have characteristics such that make sure that they will keep on representing such will in future.
The morst interesting thing is that if we look at the constitution of various States there are many extra articles that have been inserted to avoid problems that were present in the past. So in Italy “apologia di Fascismo” is illegal; in Turkey the government does not control the army, but the army is controlled by the Constitution, to prevent a religious party to get in power and set up a Teocracy. It is as if Democracies would fall ill, and would generate antibodies.
Well, the liquid democracy system has shown itself to be weak against a possible “illness”: the control of the system from a small group of people. With the mandate of others uninterested. And the use of non linear weight in evaluating the mandate reppresents the antibody. Is this the only possible solution? No, nearly certainly no. It is a solution (actually a class of solutions, since the weight depends on K and M which needs to be defined) that it seem to me that it solves in a simple and elegant way the problem. It permits to everybody to vote; it evaluates the vote of the people that are present more than the people that are absent, but does not exclude the absentee; it avoids that someone might gather too much weight. Obviously you are welcome to present other solutions, but please do not ignore the problem because it is serious.
Let us make another example more recent. No one claims that Silvio Berlusconi did not have in some moment a very vast support. But the Italian Law prevents a person from being elected if he controls too much media (journals and televisions). This makes him “unelectable”. Obviously the people who vote for Berlusconi consider those laws “un-democratic”. But those laws are there to let Democracy function. And in fact they are generally present also in other democracies.
So, since the non linear delegation system is between the direct democracy system and the liquid democracy system, both democratic. Since it does not make distinctions among people that vote. Since it is, in any case, ok to have in a democratic system little corrections that keep the system stable. And in this case the correction prevents the system from becoming controlled by a small group of people. Seen all this I would say that the non linear democratic system is not just democratic, but democratic and more stable than liquid feedback.