Proof Of Importance? based on what?
POI is based on serveral things: How much NEM you have, how much NEM you are transferring to others, how much NEM other are transferring to you. The exact formula is not set in stone so far. That's we are a little vage how it works in details.
I would really like to see a third aspect which is how long the NEM client/node has been running put in the mix too. This could help to encourage more people with smaller amounts of NEM to also turn their client on and leave it on in the background. Hopefully someday the network will be supported by lots and lots of regular people.
Node Coin
https://bitcointalk.org/index.php?topic=590421.0 has gone with client time (one point per second) and spending score (one point per coin spent) and then which ever Node has the highest score is more likely to harvest. I think this is good, but they are missing the "coins received" and traditional Proof of Stake found in NEM.
Crypti has also added proof of merchant, which means that special merchants that register can get a discount on transaction fees. By doing this, they can also be rated and won't be anonymous. A trait that we actually want when buying something from another. Basically as buyers we want to be anonymous and have our privacy protected, but at the same time we want the exact opposite for merchants. We want merchants out in the open and their history and reputation easily known. Basically, we want to know who we are sending our money too and what kind of person they are. This power in reputation has been a huge part of the success of Amazon and Ebay and really should also be incorporated into crypto too.
I would call this PoS^4
Proof of Stake - Money held in account
Proof of Spend - Money going in and out
Proof of Service - How long a node has been supporting the network
Proof of Status - Registering with the network and allowing a reputation status
You wouldn't want to choose harvesters based on just running a node, as that is too easy to attack (you don't want to make it easy for people to be able to control when they harvest). However, we are currently trying to find a way to reward nodes who are active and also have a reputation for sending valid data (as determined by eigentrust++). The problem is, how do you keep track of the active nodes that are online at any given time?