PoMoW - Proof of MEANS of Work?

[TCraver]

PoW's hunger for electricity is one of the reasons people try to come up with alternatives - including this one:

Instead of miners solving computationally difficult "puzzles" for every block, what if they only had to demonstrate they have the MEANS to do so?

For example, there might be a 5-10 minute contest once a week, during which all miners demonstrate how much processing capacity they have.
Those with the most capacity would be granted the right to publish a larger share of the blocks over the following week, against much lighter competition and with much lighter processing power per block.

I find it appealing is that it would take cryptocurrency to a new level of absurdity as far as the outside world is concerned:  Not only would miners do lots of (otherwise) pointless calculations to earn money, with this they would own a bunch of expensive hardware that sits idle all week, but which they need to win chances to publish blocks during the brief contest period each week.

I have some ideas about how this might be done, but nothing like 'white paper' level.
I'm just tossing it out as an interesting idea that others might want to mull over.

[monsterer2]

If someone has the ability to fix your car, do you pay them just for having that ability, or do you pay them to actually fix your car?

[HeRetiK]

Instead of miners solving computationally difficult "puzzles" for every block, what if they only had to demonstrate they have the MEANS to do so?

Those "puzzles" are the cryptographic functions that keep the blockchain from being rewritten and thus securing transaction finality. It's more than just computation for the sake of computation.

For example, there might be a 5-10 minute contest once a week, during which all miners demonstrate how much processing capacity they have.
Those with the most capacity would be granted the right to publish a larger share of the blocks over the following week, against much lighter competition and with much lighter processing power per block.

Who grants the right to publish blocks?

How to ensure that all miners involved only publish their predetermined share of blocks, ie. how to limit their respective hashrate and thus prevent someone without the right to publish blocks to simply rewrite the blockchain?

How to keep block times steady?

How to prevent miners with the permission to publish blocks from blocking other people's transactions or forcing double spend attacks of their own?

How to determine how long a week is without relying on an external centralized oracle?

How to determine how long 5-10 minutes are without relying on an external centralized oracle?


Edit:

Apart from the above, what then prevents these miners from simply pointing their hashrate at a different cryptocurrency when no contest is taking place?

What prevents these miners from simply spending resources on hardware rather than electricity, now that they have less electricity to pay for?

[TCraver]

I got the idea, but there many problems such as :
1. How to choose/select which miners will generate a new block based on their "proven" computation power in decentralized way?

Maybe something like this:
- Puzzles are standard hash-puzzles, but easier and a lot more of them, say 2^32, by adding different nonces AND the miner's address to the data of the last block added to the chain just before the contest.  (The address is there to prevent copied solutions.)
- Each miner publishes all solutions (nonce-hash pairs) and the address that was added to the contest blocks, allowing verification of solutions.

For the week's blocks:
- A 'selection' algorithm (TBD)  'fairly' distributes block slots for the next week based on each miner's demonstrated processing power. The actual assignments are 'randomized' based on some shared data that can't be predicted prior to the contest end - perhaps an XOR of all unique puzzle hash solutions from the contest.  Miners could randomly select which puzzles to solve, to prevent anyone predicting that XOR value.  (This is needed to avoid miners arranging to eliminate competition for their blocks.)
- All miners would run the 'selection' algorithm, and reject block solutions from anyone not approved to mine a particular block.  Also reject all blocks from a miner that generates multiple block candidates.
- Each miner initially publishes half their candidate block solution and half their block hash. 
- Another shared algorithm picks one of the candidate blocks when all partial blocks are submitted (or all within a time window).  Maybe take all the hash solutions for all candidate blocks, XOR them together, and compare to each miner's solution hash to see which has the most bits in common with the combination.  (Needs a tie-breaker... )
- All miners publish their remainder block and hash portions.  Only the winner's is used, but a fall-back algorithm would select one of the others if the winner doesn't respond with a valid block.
 

2. How to make sure the miners have actual ASIC all of the time, not only rent ASIC when on competition?

Not sure it matters, except in the context of your final remark (addressed below).  If someone rents it out, they are giving up their own opportunity to take part in the contest.

3. What happen if the chosen/selected miners don't do their job?

They don't get paid?  But more generally, one would aim to have several miners for each block - see above.

Also, i think your idea only benefits miners since they can mine altcoin while the "competition" don't happen and they still "waste" lots of electricity while mining the altcoin.

This is a good point.  OTOH, those other altcoins could implement the same method. 
If they don't, THEY are wasting the power, and blame is removed from those that implement PoMoW.