What I understand about Witness

In a recent post I tell about the Witness page where every user can vote thirty witnesses from a list of one hundred of witnesses.

In the meantime I have tried to understand what does it means.

Here what I understand.

In a distributed system, without central authority, a criterion to establish what is true and what is false is needed.
In crypto-currencies world what is true and what is false means to establish which transanctions are legitimate and which are not (fraudolent).
For performance reasons distributed systems in crypto-currencies world does not validate a single transaction but a block of them.
The first and more popular criterion to validate a block of transactions is called Proof Of Work.
Proof of work is a consensus algorithm where who takes part in the consensus mechanism, the miners, has to calculate a particular number, having some specific features, called hash, according to the content of the current block and the hash of the previous one.
Hash computation is a complex task that require specialized hardware (GPU, ASIC) necessary to run cryptographic algorithm necessary to compute the hash.
The difficulty of the task and the fact that the computation of the hash of the current block is dependent from the computation of the previous block, ensure that no one in the world, under reasonably conditions, can falsify transactions.
Every time a miner find a correct hash, he is paid for the work.
Proof of work is an interesting system because maximize the democracy in the system: everyone can take part in the consensus system hoping to find the next hash.
In other words, Proof of work is like direct democracy.
The main drawback of proof of work is the waste of energy, unsustainable on the large scale.
An alternative consensus algorithm is called Proof of Stake
In brief, in Proof of Stake not every one can take part in consensus mechanism, but only an elite composed by users who demonstrate to have a significant amount of coin ensuring credibility and transparency.
Proof of stake guarantees energy efficiency but is not so democratic.
In other words, Proof of Stake is like an holigarchy.
Delegated Proof of Stake algorithm is similar to Proof of Stake algorithm. The main crucial difference is that those who participate to the consensus (the oligarchs), are anyway elected from the community.
In other words we can say Delegated Proof of Stake is like representative democracy and Witnesses, the oligarchs, are the politicians.