Useful work is not actually a good foundation for securing a decentralized cryptocurrency. The value of PoW in cryptocurrency is that I know for a fact that you have to burn $X million dollars if you want to double-spend my cryptocurrency. That has to be burned in electricity, and that burn can't be used for anything else. It's expensive for you to attack me. If suddenly we've got useful works, such that you can appl…
first if we ignore the part "not everyone is going to have equal access to people who are willing to pay for solutions of useful work"
I think this can never happen.
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People should think PoW as lottery.
Every X minutes there is a prize draw giving you Y coins.
But ticket price converges to market value of:
ticket price = (Y coins)/(total tickets sold)
So if you add a value to 'not winning ticket' by introducing 'useful work', you are changing ticket price to:
ticket price = (Y coins)/(total tickets sold)-'work value'
so you are just giving coins more value, means making 'new ticket' more expensive.
new ticket = old ticket + work value
In the end you will still 'waste' the same amount at equilibrium.