So far I have found four methods proposed for generating new blocks:
1. Proof of work -- The most common method that has worked well so far, but some problems seem to be apearing. One is the high cost of maintaining the network compared to other methods. The other is the centralization of hashing power(If GHash and BTCGuild cooperated, they could perform a 51% attack right now)
2. Proof of stake -- https://en.bitcoin.it/wiki/Proof_of_Stake -- This method has been developed to eliminate the high cost of mining. It may be able to make a network with lower transaction fees than a proof of work network. The main objection to this is that it is possible for the big holders of coins to monopolize the mining, creating a situation where the rich get richer and the poor get poorer.
3. Proof of burn -- https://en.bitcoin.it/wiki/Proof_of_burn -- This is a method where a miner has to send coins to an invalid address in order to purchase a virtual mining rig. The argument here is that the burnt coins are not a real expense from a global perspective (whereas electricity is a real expense for the global economy) because the price of coins will increase to compensate for the deflation. I have my doubts about destroying coins being healthy for the currency, but could imagine a scenario where the "burnt" coins are instead used as part of the reward for future mining. I don't believe that anything like this has been implemented in a real coin.
4. Proof of bet -- https://bitcointalksearch.org/topic/proof-of-bet-an-alternative-to-everything-else-131230 -- This is a method where the miner must pay to try to mine a block. The chance that the block is accepted is proportional to the amount that the miner paid. If the block is accepted the miner recieves the block reward. If the block is not accepted the miner loses the coins paid. This seems to be in the idea stage of development, with much work requred to make it a real thing.
If anyone knows of any other methods or has an idea please share it.
It seems to me that it would be a good idea for the bitcoin network to have another minting process implemented as a backup in case something goes wrong with the current method. I don't know if there would be a way to implement something slowly and painlessly, or if a hard fork would be the only way to do it. It is clear that other methods of transaction verification have not been developed sufficiently to be usable at this point, but it is also clear that bitcoin mining has been becoming more centralized and therefore less trustworthy. It may be nessesary at some point in the future to change the mining process.
